Multiplying and Dividing polynomials Practice

Determine the simplified form of the expression 5(3x + 2)

• 3x + 10
• 15x + 10
• 15x - 10
• 3x - 10

Expand 3a(5a² + 8a + 2) using the distributive property.

• 15a³ + 24a² + 6a

• 10a³ + 24a + 6

• 8a³ + 11a² + 6a

• 15a² + 24a + 6

Answer explanation

The correct expansion is obtained by multiplying each term inside the parentheses by 3a and then combining like terms. This results in 15a^3 + 24a^2 + 6a.

Divide the polynomial by the monomial.

• 15x⁹ - 8x³

• 3x⁶ - 8x³

• -5x¹²

• 3x⁶ - 40x³

Answer explanation

To divide the polynomial 15x^9 - 8x^3 by the monomial x^3, we divide each term by x^3. This results in 15x^6 - 8, which simplifies to 3x^6 - 8x^3.

• 5p² - 16p
• 5p + 4
• 5p - 4
• 5p + 4p

Divide the polynomial by the monomial.

• 2x⁸-8x²-28x
• 2x⁸-2x²-7x
• 8x⁷-8x-28x
• 2x⁷ -2x -7

(5x-1)(x+1)

• 5x² + 4x - 1

• 5x²+6x - 1

• 5x² - 4x -1

• 5x² + 4x + 1

Answer explanation

The correct answer is 5x^2 + 4x - 1. This is obtained by multiplying the terms in each bracket and then combining like terms to get the final expression.

Simplify the following expression using FOIL.
(x + 5)(x + 4)

• x² + x + 20
• x² + 20x + 9
• x² + 9x + 20
• x² - 9x + 54

Find the product.

(x - 2)²

• x² + 2x + 2x + 4

• x² + 2x + 2

• 7x² + x + 7

• x² - 4x + 4

Answer explanation

To find the product of (x - 2)^2, we use the formula (a - b)^2 = a^2 - 2ab + b^2. Therefore, (x - 2)^2 = x^2 - 2*x*2 + 2^2 = x^2 - 4x + 4.

(3x − 6)(7x + 7)

• 21x² − 63x + 42
• 21x² − 21x − 42
• 21x² − 42
• 21x² + 63x + 42

Find the product:
(x + 12)(x - 12)

• x² - 144

• x² + 144

• x² + 12x - 144

• x² - 12x + 144

Answer explanation

To find the product, apply the FOIL method: (x + 12)(x - 12) = x^2 - 12x + 12x - 144 = x^2 - 144. Therefore, the correct answer is x^2 - 144.