Question

multiply the polynomials.
(2x² + 5x + 5)(4x − 3)

a. 8x³ + 14x² − 5x + 15
b. 8x³ + 14x² − 15x − 15
c. 8x³ + 14x² + 5x − 15
d. 8x³ + 14x² + 5x + 15

Explanation:

Step1: Distribute \(2x^2\)

Multiply \(2x^2\) by each term in \((4x - 3)\):
\(2x^2 \cdot 4x = 8x^3\), \(2x^2 \cdot (-3) = -6x^2\)

Step2: Distribute \(5x\)

Multiply \(5x\) by each term in \((4x - 3)\):
\(5x \cdot 4x = 20x^2\), \(5x \cdot (-3) = -15x\)

Step3: Distribute \(5\)

Multiply \(5\) by each term in \((4x - 3)\):
\(5 \cdot 4x = 20x\), \(5 \cdot (-3) = -15\)

Step4: Combine like terms

Combine \(x^2\) terms: \(-6x^2 + 20x^2 = 14x^2\)
Combine \(x\) terms: \(-15x + 20x = 5x\)
Now, combine all terms: \(8x^3 + 14x^2 + 5x - 15\)

Answer:

C. \(8x^3 + 14x^2 + 5x - 15\)