Algebra 2
Which statement is true about the polynomial 3j4k − 2jk3 + jk3 − 2j4k + jk3 after it has been fully simplified?
It has 1 term and a degree of 5.
Which is true about the completely simplified difference of the polynomials 6x6 − x3y4 − 5xy5 and 4x5y + 2x3y4 + 5xy5?
The difference has 4 terms and a degree of 7.
cube root
a number that, when multiplied by itself twice, results in the number that appears under a cube root symbol
strategy
a plan of action designed to achieve a specific goal
equivalent
having the same amount, value, area, volume, or force
perfect square
the product of two identical factors
verify
to apply what is known to confirm an expected result
What is a difference of squares that has a factor of x + 8?
x^2-64
Which expression is equivalent to 100 n2 − 1?
(10n)2 − (1)2
Which is the completely factored form of 4x2 + 28x + 49?
(2x + 7)(2x + 7)
6x2 + 11x - 10?
(2x+5)(3x-2)
Which product is equivalent to 25x2 - 16?
(5x − 4)(5x + 4)
Ricardo is factoring the polynomial, which has four terms. 5x3 + 20x2 + 2x + 8 5x2(x + 4) + 2(x + 4) Which is the completely factored form of his polynomial?
(5x2 + 2) (x + 4)
What is 125x9 + 64y12 written as a sum of cubes?
(5x3)3 + (4y4)3
What is the factorization of 49b2 − 81?
(7b - 9)(7b + 9)
Antonia is factoring the polynomial, which has four terms. 7x3 - 21x2 + 5x - 15 7x2(x - 3) + 5(x -3) Which is the completely factored form of her polynomial?
(7x2 + 5) (x - 3)
Which is the factorization of 8x2 + 13x - 6?
(8x - 3)(x + 2)
What is the factorization of 81a6 - 100?
(9a3 − 10)(9a3 + 10)
What is the factorization of 729x15 + 1000?
(9x5 + 10)(81x10 - 90x5 + 100)
trinomial
(noun) a polynomial consisting of exactly three terms
prime polynomial
(noun) an irreducible polynomial with integer coefficients that cannot be factored into polynomials of lower degree over the real number system.
coefficient
(noun) the number value in a monomial
factor
(verb) to break up a polynomial into a product of polynomials that can be multiplied to get the original polynomial
Which product will result in a sum or difference of cubes?
(x - 9)(x2 + 9x + 81)
What is the factored form of the polynomial? x2 - 16x + 48
(x − 4)(x − 12)
What is the factored form of x2 − 4x − 5?
(x − 5)(x + 1)
What is the factored form of the polynomial?
(z − 5)(z − 5)
The model represents the factorization of 2x2 + 5x + 3. What is the missing term in the factorization of 2x2 + 5x + 3? (2x + 3)(x +___
1
Which is a factor of 144 − 49x2?
12 - 7x
Which polynomial can be simplified to a difference of squares?
16a2 - 4a + 4a - 1
Which monomial is a perfect cube?
1x3
Simon is factoring the polynomial. x2 - 4x - 12 (x - 6)(x + ___)
2
Which polynomial is a difference of squares?
25x2 - 36
Which monomial is a perfect cube?
27x15
Which is the completely factored form of 4x3 + 10x2 - 6x?
2x(x + 3)(2x - 1)
What is the greatest common factor of the terms in the polynomial 8x4 - 4x3 - 18x2?
2x2
What is the cube root of 8x27?
2x9
Sari is factoring the polynomial 2x2 + 5x + 3. What is the missing number in her factorization? 2x2 + 5x + 3 = (2x +____)(x + 1)
3
Which is the completely factored form of 3x2 - 12x - 15?
3(x + 1)(x - 5)
The diagram represents 6x2 - 7x + 2 with a factor of 2x - 1. What is the other factor of 6x2 - 7x + 2?
3x - 2
Which binomial is a factor of 9x2 - 64?
3x - 8
Which product of prime polynomials is equivalent to 36x3 - 15x2 - 6x?
3x(3x - 2)(4x + 1)
What is the cube root of 27x18?
3x6
What is the greatest common factor of 8m, 36m3, and 12?
4
Completely factor the polynomial 8x2 - 24x + 20x - 60.
4(x - 3)(2x + 5)
What is the greatest common factor of the terms in the polynomial 4x4 - 32x3 - 60x2?
4x2
Which polynomial has factors of 4x - 7 and x + 4?
4x2 + 9x - 28
Which expression is a difference of squares with a factor of 2x + 5?
4x2 - 25
What is the greatest common factor of 4xy2 and 20x2y4?
4xy2
What is the polynomial 3y2 + (y + 7)2 - 15 after it has been fully simplified and written in standard form?
4y2 + 14y + 34
Which product of prime polynomials is equivalent to 30x3 - 5x2 - 60x?
5x(2x - 3)(3x + 4)
Juanita begins to factor an expression as shown. x2 + 3x - 18 = (x +__ )(x -__ )
6 and 3
Logan saves the same amount of money each month for college. His current total savings is 300m2 + 120m + 180 dollars. Which factorization could represent the number of months and amount of a monthly deposit in dollars?
60(5m2 +2m +3)
Which is the completely factored form of 18x4 - 42x3 + 24x2?
6x2(3x - 4)(x - 1)
Which equation is true?
9x2 - 25 = (3x - 5)(3x + 5)
A rectangle has an area of (x2 − 17x + 72) square units. Since the area of a rectangle is determined using the formula, A = lw, what could be the length and width of the rectangle?
length = (x − 8) units and width = (x − 9) units
Which is a difference of cubes?
x6 - 27
