algebra 2a - unit 1: factoring and solving quadratics lesson 1-4

what is the factored form of the expression 9x^2 + 42x + 49?

(3x + 7)^2

what is the factored form of the expression 36x^2 − 49y^2?

(6x + 7y)(6x - 7y)

what is the factored form of the expression x^2 − 7x − 18?

(x + 2)(x - 9)

what is the factored form of the expression x^2 − 2x − 15?

(x + 3)(x - 5)

what is the factored form of the expression x^2 − 8x − 48?

(x + 4)(x - 12)

what is the factored form of the expression x^2 − 2x − 63?

(x + 7(x - 9)

what is the factored form of the expression x^2 − 22x + 121?

(x - 11)^2

solve the equation x^2 + 21x + 110 = 0 by factoring. what are the solutions to the equation?

-10, -11

what are the solutions to the equation (x − 4)(x + 2) = 0? select all that apply.

-2, 4

what are the solutions to 3(x + 2)(x − 9) = 0? select all that apply.

-2, 9

given the complex numbers s and t below, what is s − t? s = 9 + 5i t = 12 - 6i

-3 + 11i

which expression represents the number √-81 - √32 rewritten in a + bi form?

-4√2 + 9i

which expression represents the number √-16 - √25 rewritten in a + bi form?

-5 + 4i

which expression represents the number -3i^4 + 2i^3 + 2i^2 + √-9 rewritten in a + bi form?

-5 + i

solve the equation −2x^2− 2x + 40 = 0 by factoring. what are the solutions to the equation?

-5, 4

what are the solutions of the equation x^2 = 25/36?

-5/6, 5/6

use the quadratic formula, to solve the quadratic equation 4x^2 + 28x + 49 = 0. which answer provides the correct solution(s) to the equation?

-7/2

which expression represents the number i^4 + √-81 + i^2 + √-36 rewritten in a + bi form?

0 + 15i

the standard form of a complex number is a + bi. what is the standard form for the expression √-64?

0 + 8i

which expression represents the number 3 - (-7 + 4i) + i(4i^2) rewritten in a + bi form?

10 - 8i

which expression represents the number 12.3 rewritten in a + bi form?

12.3 + 0i

which expression is equivalent to (2 - 3i)(5 + i)?

13 - 13i

what are the solutions of the equation (x - 9)^2 = 25? select all that apply.

14, 4

which expression is equivalent to (7 + 4i) + (8 + i)?

15 + 5i

which expression represents the number -2i(5 - i) + (17 - 8i) rewritten in a + bi form?

15 - 18i

given the complex numbers v and w below, what is v + w? v = 7 + 2i w = 8 - 9i

15 - 7i

solve the quadratic equation x^2 − 14x + 24 = 0 by completing the square. what are the solutions to the equation? select all that apply.

2, 12

what is the factored form of the expression 2m^3 − 26m^2 + 80m?

2m(m - 5)(m - 8)

solve the quadratic equation −4x^2 + 6x + 16 = 0 by completing the square. which expression represents the correct solutions to the equation?

3 ± √73 / 4

what is the factored form of the expression 3x^2 + 6x − 24?

3(x + 4)(x - 2)

what are the zeros of the function f(x) = x^2 − 10x + 21? select all that apply.

3, 7

which expression or value is equivalent to (-3 + 5i)(-3 - 5i)?

34

solve the quadratic equation −x^2 + 8x − 4 = 0 by completing the square. which expression represents the correct solutions to the equation?

4 ± 2√3

use the quadratic formula, to solve the following equation. 3x^2 - 7x + 4 = 0. what are the solutions to the equation? select all that apply.

4/3, 1

which expression represents the number -√9 + 14i - i√-4 (4 + 7i) rewritten in a + bi form?

5 + 28i

what are the solutions to the equation x^2 = 49/100? select all that apply.

7/10, -7/10

which expression is equivalent to 2i(7 - 4i)?

8 + 14i

what are the solutions of the equation x^2 + 15 = 79? select all that apply.

8, -8

solve the equation 25b^2 − 64 = 0 by factoring. what are the solutions to the equation?

8/5, -8/5

which expression represents the number 9 + √−49 rewritten in a + bi form?

9 + 7i

the standard form of a complex number is a + bi. what is the standard form for the number 94?

94 + 0i

which equations are true? select all that apply.

9x^2 - 1 = (3x - 1)(3x + 1) x^2 - 169 = (x - 13)(x + 13) 16x^2 - 64y^2 = (4x - 8y)(4x + 8y)

which simplifications of the powers of i are correct? select all that apply.

= -1 = -1

all imaginary numbers can be written as complex numbers in the form a + bi. for the number 5i, what is the value of a and b?

a = 0 and b = 5

examine the complex number 3 + 2i. a: what is the real part of the complex number? b: what is the imaginary part of the complex number?

a: the real part is 3 b: the imaginary part is 2

examine the complex number 8 - 4i. a: what is the real part of the complex number? b: what is the imaginary part of the complex number?

a: the real part is 8 b: the imaginary part is -4

lesson 3

complex numbers

match each power of i with its equivalent value.

i^8 : 1 i^13 : i i^2 : -1 i^7 : -i

adrian solved the equation x^2 + 9 = 16 using the following steps. which statement identifies a mistake adrian made, if any?

in line 2, he should have subtracted 9 from both sides of the equation because it is not part of the expression that is squared.

ellen solved the equation x^2 − 5 = 59 using the following steps. which statement identifies a mistake ellen made, if any?

in line 4, she forgot to take the negative square root, because squaring both 8 and −8 equals 64.

enrique used the following steps to solve an equation. what mistakes, if any, did enrique make?

in step 3, enrique used the difference of squares pattern incorrectly when factoring.

gemma completed the following steps to find the zeros of the function f(x) = 3x^2 − 6x − 45. what mistakes, if any, did gemma make?

in step 4, when solving for x + 3 = 0, gemma should have subtracted 3 from both sides of the equation to get x = −3.

nando solved the quadratic equation 4x^2 − 24x − 16 = 0 by completing the square as shown. which statements identify nando's mistakes? select all that apply.

in step 7, his final answer should have been x = 3 ± √13. in step 2, he divided 4x^2 - 24x by 4, but he should have also divided 16 by 4. in step 6, he added 3 to the left side of the equation, but he subtracted 3 from the right side

aurora used the quadratic formula, to solve the equation y = -2x^2 + 6x - 11 as follows. did aurora make a mistake? if so, where?

no, she did not make a mistake.

lesson 4

operations with complex numbers

lesson 2

other methods for solving quadratics

lesson 1

solving quadratics by factoring

what are the steps to simplify (4 + 6i)(4 − 6i)? match each step with the correct expression or number.

step 1 : 4(4 - 6i) + 6i(4 - 6i) step 2: 16 - 24i + 24i - 36i^2 step 3: 16 - 36(-1) step 4: 52

what are the steps to simplify (5 + 3i) - (2 + 7i)? match each step with the correct expression.

step 1: 5 + 3i - 2 - 7i step 2: 5 - 2 + 3i - 7i step 3: 3 - 4i

use the quadratic equation, to solve the equation x^2 + 12x - 7 = 0. match each step to the correct method for solving the equation.

step 1: x = -12±√12^2 -4(1)(-7) / 2(1) step 2: x = -12±√144+28 / 2 step 3: x = -12±√172 / 2 step 4: x = -12±2√43 / 2 step 5: x = -6 ± √43

use the quadratic formula, to solve the equation -2x^2 - 6x + 3 = 0. match each step to the correct method for solving the equation.

step 1: x = 6±√(-6)^2 -4(-2)(3)/2(-2) step 2: x = 6±√36+24/-4 step 3: x = 6±√60/-4 step 4: x = 6 ±2√15/-4 step 5: x = -3±√15/2

what is the correct order for completing the square to solve x^2 - 2x - 4 = 0? match each step with the correct equation.

step 1: x^2 - 2x = 4 step 2: x^2 - 2x + 1 = 4 + 1 step 3: (x - 1)^2 = 5 step 4: x - 1 = ±√5 step 5: x = 1 ± √5

what are the solutions, if any, of the equation x^2 + 38 = 16?

this equation has no real solutions.

use the quadratic formula, to solve the quadratic equation 2x^2 + 4x - 1 = 0. what are the solutions to the equation?

x = -2 - √6 / 2 and -2 + √6 / 2

what are the solutions to the equation x^2 + 4x + 17 = 0.

x = -2 ± i√13

what are the solutions to the equation -2x^2 - 8x - 22 = 0? use the completing the square method to find the values of x?

x = -2 ± i√7

use the quadratic formula, to find the solutions to x^2 + 8x + 25 = 0. what are the solutions?

x = -4 ± 3i

consider the equation x^2 + 4x + 9 = 0 in standard form. which equation shows the coefficients a, b, and c correctly substituted into the quadratic formula?

x = -4 ±√(4)^2 -4(1)(9) / 2(1)

solve the equation 40 = 2x^2 + 2x by factoring. what are the solutions?

x = -5 and x = 4

what are the solutions of the equation (x - 13)^2 = 400?

x = -7 and x = 33

use the quadratic formula, to find the solution(s) to 2x^2 - 4x + 27 = 0.

x = 1 ± 5i√2 / 2

use the quadratic formula, to find the solutions to 3x^2 - 4x + 7 = 0. what are the solutions?

x = 2 ± i√17 / 3

use the quadratic formula, to solve the following equation. 9x^2 - 12x + 4 = 0. which option provides the solution(s) to the equation?

x = 2/3

what are the solutions to the quadratic equation x^2 + 625 = 0?

x = 25i x = -25i

what are the solutions to the equation x^2 + 4 = 0?

x = 2i and x = -2i

consider the equation 3x^2 − 2x + 7 = 0 in standard form. which equation shows the coefficients a, b, and c correctly substituted into the quadratic formula?

x = 2±√(-2)^2 - 4(3)(7) / 2(3)

use the quadratic formula, to find the solutions 5x^2 - 6x + 5 = 0

x = 3 ± 4i / 5

what are the solutions to the equation (x - 32)^2 = 56?

x = 32 ± 2√14

solve the quadratice equation x^2 + 8x - 30 = 0 by completing the square. what are the solutions to the quadratic equation, if any?

x = 4 ± √46

solve the quadratic equation x^2 - 4x - 12 = 0 by completing the square. what are the solutions to the quadratic equation? select all that apply.

x = 6 x = -2

what are the solutions to the quadratic equation 9x^2 + 64 = 0?

x = 8/3i x = -8/3i

use the quadratic formula, to solve the following equation. 5x^2 - 9x - 10 = 0. what are the solutions to the equation? select all that apply.

x = 9 + √281 / 10 x = 9 - √281 / 10

what are the solutions, if any, to the equation x^2 - 25 = -7?

x = ±3√2

what are the solutions, if any, of the equation (x + 49)^2 = 24?

x = −49 ± 2√6

use the discriminant to determine which equation has complex solutions.

x^2 + 2x + 5 = 0

use the discriminant, b^2 - 4ac, to determine which equation has complex solutions.

x^2 + 3x + 12 = 0

briana used the quadratic formula, to solve the equation 0 = 3x^2 - 2x + 9, as follows. did briana make a mistake? if so, where did the mistake occur, and what was it?

yes, in step 1, she should have had written 2(3) in the denominator.

roman completed the square to solve the equation 0 = -x^2 + 6x - 15 as follows. did roman make a mistake? if so, where?

yes, in step 6, he should have added 3 to both sides of the equation.

urie completed the square to solve the equation 0 = 3x^2 - 9x + 27 as follows. did urie make a mistake? if so, where?

yes, step 3, he should have added 9/4 to both sides of the equation

what are the zeros of the function f(x) = x^2 − 36?

zeros occur when x = 6 and x = -6

checkpoint: match the numbers that have the same value.

√-36 : 6i √-5 : i√5 √-8 : 2i√2

match the numbers that have the same value.

√-49 : 7i √-3 : i√3 √-50 : 5i√2