algebra 1a - unit 4: polynomials and factoring quadratic expressions

match each expression with the correct result.

(6x + 2)(3x + 1) : 18x^2 + 12x + 2 (6x - 2)(3x + 1) : 18x^2 − 2 (6x - 2)(3x - 1) : 18x^2 − 12x + 2 (6x - 2)(-3x - 1) : −18x^2 + 2

what are the factors of 2a^3 + a^2 + 2a + 1?

(a^2 + 1)(2a + 1)

factor: b^2 - 64

(b - 8)(b + 8)

which product of factors is equivalent to x^2 + 4x + 4?

(x + 2)^2

which expression represents the expanded version of the expression below? 4x(3x + 7)

12x^2 + 28x

what are the factors of 4x^5 − 8x^4 + 12x^2 − 24x?

4x(x^3 + 3)(x − 2)

match each value or variable to its part in the expression 68h + 13.

68 : coefficient h : variable 13 : constant term

simplify the following expression. (x^2 − 4 + x) − (x − 5x^2 − 9)

6x^2 + 5

what expression shows the greatest common factor correctly factored from the expression 28m^2n − 14mn + 35n^2?

7n(4m^2 − 2m + 5n)

what is the standard form of the expression 5x − 7 − 2x^2 + 11 − 2x?

−2x^2 + 3x + 4

what is the product of −6y^3(y^4 + 3y^3 − y^2 − 5)?

−6y^7 − 18y^6 + 6y^5 + 30y^3

consider the equation x^2 + 11x + 10 = x^2 + mx + nx + 10, where m ⋅ n = 10 and m + n = 11. what are the values of m and n?

m = 10 and n = 1

stefan evaluated the sum of the polynomials 3x^4 − 6x^2 + 4x − 9 and 5x^4 + 3x^2 + 10x + 2 as shown. did stefan make a mistake?

no, all of his work is correct.

lesson 20

other methods for factoring quadratics

what are the factors of 2xy + y + 8x + 4?

(2x + 1)(y + 4)

what are the factors of the expression 9a^2 − 64b^2?

(3a − 8b)(3a + 8b)

factor: 16x^2 - 9

(4x - 3)(4x + 3)

what are the factors of the polynomial 25x^2 − 10x + 1?

(5x − 1)^2

what expression shows the greatest common factor correctly factored from the expression −12nm^2 + 6mn + 8m?

2m(−6nm + 3n + 4)

match each expression with the correct result.

2x(−x^2 + 6xy + 3y − 7) : −2x^3 + 12x^2y + 6xy − 14x xy^2(−5x^3 − 4x^2 + 2x − 3) : −5x^4y^2 − 4x^3y^2 + 2x^2y^2 − 3xy^2 −5xy(x^2 − 8y^2 + 9xy) : −5x^3y + 40xy^3 − 45x^2y^2

what are the factors of 36m^3 − 9m^2 + 12m − 3?

3(4m − 1)(3m^2 + 1)

what is the greatest common factor of 30a − 60b?

30

which option correctly simplifies the expression (3a − 4b)(a^2 + 5ab − b^2)?

3a^3 + 11a^2b − 23b^2a + 4b^3

which expressions are polynomials? select all that apply.

3x^2 − 5x − 4 11ab − 3.2a^2 + 15 2/3m^3 − m^2n + 1/2n^2

which equation is the standard form of −8x + 3x^2 = −19?

3x^2 − 8x + 19 = 0

select an expression equivalent to (29r^4 − 11r^3s + 5r^2s^2 + 19rs^3 + 4) − (20r^4 − 10r^3s + 13r^2s^2+ 14rs^3 − 33).

9r^4 − r^3s − 8r^2s^2 + 5rs^3 + 37

lesson 16

adding and subtracting polynomials

lana uses factoring by grouping to factor the polynomial. her work follows, but the last two lines of work are missing. which answers correctly fill in the blanks?

blank 1: 2xy(4x − 5y) + 3(4x − 5y) blank 2: (2xy + 3)(4x − 5y)

lesson 18

introduction to quadratic expressions

match each step with the correct expression to factor 20x^2 + 25x − 30 by using the decomposition method.

step 1 : 5(4x^2 + 5x − 6) step 2 : 5(4x^2 + 8x − 3x − 6) step 3 : 5(4x(x + 2) − 3(x + 2)) step 4 : 5(4x − 3)(x + 2)

simplify: (3x^3 + 5x^2 − 9x − 2) − (2x^3 + 3x^2 − x − 3)?

x^3 + 2x^2 − 8x + 1

did gilbert make a mistake?

yes, he did not distribute the −1 over the polynomial −4x^5 + 7x^4 + 9x − 5.

simplify: (4x + 3y)^2

16x^2 + 24xy + 9y^2

what are the coefficients in the polynomial 55a + 22b − 1.4? do not include the constant term. select all that apply.

22 55

simplify. (3x − 2y) + (5x − 4y)

8x - 6y

what are the factors of the quadratic expression 49x^2 + 56x + 16?

(7x + 4)^2

factor the polynomial x^2 + 18x + 81 as the product of two binomials.

(x+9)(x+9)

factor the polynomial x^2 − 81 as the product of two binomials.

(x+9)(x-9)

what expression correctly fills in the following blank? 3m(3mn^2 − 4n^2 − 5m) = [blank]

9m^2n^2 − 12mn^2 − 15m^2

which answer represents the polynomial x^2 + 1/4x^6 + 9 − 1/4x rewritten in descending order?

1/4x^6 + x^2 − 1/4x + 9

which expression is a perfect square trinomial?

100x^2 − 20x + 1

what is the difference of 24a + 32b − 7 and 13a − 8b + 5?

11a + 40b − 12

which equation is the standard form of −56x + 14x^2 = −51?

14x^2 − 56x + 51 = 0

what is the product of 3 and a^4 + 4a^3 + 7a + 9?

3a^4 + 12a^3 + 21a + 27

which expressions are polynomials? select all that apply.

3x + 9y x^2 + x - 4

match each expression with the correct result.

6(x^2 − 4xy + 2y^2) : 6x^2 - 24xy + 12y^2 −7(−x^4 + 8x^3 − 5x^2 − 4x + 6) : 7x^4 − 56x^3 + 35x^2 + 28x − 42 3/4(8xy^2 - 20x^2 + 12y - 40) : 6xy^2 − 15x^2 + 9y − 30

what is the standard form of the equation −27 = −10x − 7x^2?

7x^2 + 10x − 27 = 0

which expressions represents the simplified version of the following expression? (5x^3y^2 − 3xy + 2) + (2x^3y^2 − 3x^2y^2 + 4xy − 7)

7x^3y^2 − 3x^2y^2 + xy − 5

multiply. (9w + 1)(9w - 1)

81w^2 - 1

lesson 19

factoring quadratic expressions by grouping

rewrite the polynomial x^2 − 5x + 6 as x^2 + mx + nx + 6, where m ⋅ n = 6 and m + n = −5. what are the values of m and n?

m = −3 and n = −2

lesson 17

multiplying polynomials

which statement is true regarding elizabeth's work?

she didn't make any mistakes.

what are the terms of the polynomial 6x^2 + 4/7y^2 − 4x − 45?

​6x^2,​ 4/7y^2, −4x, and −45

match each expression with the correct result.

−2(3a^2 − 5ab + 9b^2 − a + 15) : −6a^2 + 10ab − 18b^2 + 2a − 30 −5(−a^2 + 2ab − 5b^2) : 5a^2 − 10ab + 25b^2 11(2a^2b − 3a^2 + ab − 4b^2) : 22a^2b − 33a^2 + 11ab − 44b^2

evaluate. (x - 4)(4x^2 -8x + 7)

4x^3 - 24x^2 + 39x - 28

which quadratic equations are in standard form? select all that apply.

12x^2 + 4x − 3 = 0 −x^2 − 3x + 20 = 0 0.5x^2 − 3.2x + 5.8 = 0

match each step with the correct expression to factor s^2 + 7s + 6 by using the decomposition method.

step 1 : s^2 + s + 6s + 6 step 2 : s(s + 1) + 6(s + 1) step 3 : (s + 6)(s + 1)

which polynomial is equivalent to (0.5xy + 2x^2 − 7y^2x + 4y^2 − 1.25x^2y) + (−0.75x^2 + 8y^2 − xy + 3x^2y − 9y^2x)?

1.75x^2y − 16y^2x + 1.25x^2 − 0.5xy + 12y^2

which option correctly simplifies the expression 4x(x^2 + 3)?

4x^3 + 12x

which expression correctly shows the factors for 20x^4 − 25x^3 + 60x^2 − 75x?

5x(x^2 + 3)(4x − 5)

what expression shows the greatest common factor correctly factored from the expression 12a^2 − 36ab + 18b^2?

6(2a^2 − 6ab + 3b^2)

match each trinomial with its correct factors.

x^2 - 8x - 20 : (x - 10)(x + 2) x^2 + 9x + 20 : (x + 4)(x + 5) x^2 + x - 20 : (x + 5)(x - 4) x^2 + 12x + 20 : (x + 10)(x + 2)