8.1 Multiply a Trinomial by a Binomial

(2x + 3)(x² + 4x + 1)

• 2x³ + 10x² + 14x + 4 

• 2x³ + 11x² + 14x + 3 

• -2x³ - 11x² + 14x + 5 

• x³ - 11x² + 14x + 3 

Answer explanation

To expand (2x + 3)(x^2 + 4x + 1), use the distributive property: 2x*x^2 + 2x*4x + 2x*1 + 3*x^2 + 3*4x + 3*1. This results in 2x^3 + 8x^2 + 2x + 3x^2 + 12x + 3, which simplifies to 2x^3 + 11x^2 + 14x + 3.

Tags

CCSS.HSA.APR.A.1

Multiply

(x + 1)(6x² - 2x + 4)

• 6x³ + 4x² + 2x

• 6x³ + 8x² + 2x + 4

• 6x³ + 8x² + x + 4

• 6x³ + 4x² + 2x + 4

Answer explanation

To multiply (x + 1)(6x² - 2x + 4), use the distributive property: x(6x² - 2x + 4) + 1(6x² - 2x + 4). This results in 6x³ + 4x² + 2x + 4, matching the correct choice.

Tags

CCSS.HSA.APR.A.1

Multiply

(y - 3)(4y² + y - 5)

• 4y³ - 11y² - 8y - 15

• 4y³ - 11y² - 8y + 15

• 4y³ - 12y² - 8y + 15

• 4y³ - 11y² + 8y + 15

Answer explanation

To multiply (y - 3)(4y^2 + y - 5), use the distributive property. This results in 4y^3 - 12y^2 - 8y + 15. The correct answer is 4y^3 - 12y^2 - 8y + 15.

Tags

CCSS.HSA.APR.A.1

(5x+2)(x²-3x+6). (write this out on paper please)

• 5x³ - 17x² +24x +12

• 5x³ + 17x² - 24x +12

• 5x³ - 13x² + 24x +12

• 5x³ +13x² - 24x - 12

Answer explanation

To expand (5x+2)(x^2-3x+6), use the distributive property. Multiply each term in the first polynomial by each term in the second. This results in 5x^3 - 15x^2 + 30x + 2x^2 - 6x + 12, which simplifies to 5x^3 - 13x^2 + 24x + 12.

Tags

CCSS.HSA.APR.A.1

Find the product:

(3x - 5) ( 4x² - 2x - 3)

• 12x³ - 26x² - 25x + 15

• 12x³ - 20x² - 5x + 15

• 12x³ - 20x² - 6x + 15

• 12x³ - 26x² + x + 15

Answer explanation

To find the product, use the distributive property: (3x)(4x^2) + (3x)(-2x) + (3x)(-3) + (-5)(4x^2) + (-5)(-2x) + (-5)(-3). This simplifies to 12x^3 - 26x^2 + x + 15, matching the correct answer.

Tags

CCSS.HSA.APR.A.1

Find the product:

(x - 2) (3x² + 2x - 4)

• 3x² -4x +8

• 3x³ +4x² -8x -8

• 3x³ -4x²-8x +8

• 3x³ -x² +8x +8

Answer explanation

To find the product, apply the distributive property: (x - 2)(3x^2 + 2x - 4) = 3x^3 + 2x^2 - 4x - 6x^2 + 8. Combine like terms to get 3x^3 - 4x^2 - 8x + 8, which matches the correct answer.

Tags

CCSS.HSA.APR.A.1

Find the product:

(5x + 2) (x² - 3x +6)

• 5x³ - 17x² +24x +12

• 5x³ + 17x² - 24x +12

• 5x³ - 13x² + 24x +12

• 5x³ +13x² - 24x - 12

Answer explanation

To find the product, use the distributive property: (5x)(x^2) + (5x)(-3x) + (5x)(6) + (2)(x^2) + (2)(-3x) + (2)(6). This simplifies to 5x^3 - 15x^2 + 2x^2 + 24x + 12, resulting in 5x^3 - 13x^2 + 24x + 12.

Tags

CCSS.HSA.APR.A.1

Find the product:

(x + 1)(x² - 2x + 1)

• x³-x²-x+1

• x³-2x+2

• x³+x²+x+1

• x³-3x²-3x+1

Answer explanation

To find the product, use the distributive property: (x + 1)(x^2 - 2x + 1) = x(x^2 - 2x + 1) + 1(x^2 - 2x + 1). This simplifies to x^3 - 2x^2 + x + x^2 - 2x + 1 = x^3 - x^2 - x + 1, which matches the correct answer.

Tags

CCSS.HSA.APR.A.1

Answer explanation

To find the product, apply the distributive property: (2r-4)(7r^2-6r-6) = 2r(7r^2-6r-6) - 4(7r^2-6r-6). This results in 14r^3 - 12r^2 - 12r - 28, which simplifies to 14r^3 - 40r^2 + 12r + 24, matching the correct answer.

Tags

CCSS.HSA.APR.A.1

Answer explanation

To find the product, apply the distributive property: (2n-4)(n^2+6n-4) = 2n(n^2+6n-4) - 4(n^2+6n-4). This simplifies to 2n^3 + 12n^2 - 8n - 4n^2 - 24n + 16, which combines to 2n^3 + 8n^2 - 32n + 16, matching the correct answer.

Tags

CCSS.HSA.APR.A.1