Question

question 9 of 10
multiply the polynomials.
(4x² + 3x + 7)(8x − 5)
a. 32x³ + 4x² + 41x + 35
b. 32x³ − 44x² − 71x − 35
c. 32x³ − 4x² − 41x + 35
d. 32x³ + 4x² + 41x − 35

Explanation:

Step1: Apply distributive property (FOIL for polynomials)

Multiply each term in the first polynomial by each term in the second polynomial:
$$(4x^2)(8x) + (4x^2)(-5) + (3x)(8x) + (3x)(-5) + (7)(8x) + (7)(-5)$$

Step2: Simplify each product

• $(4x^2)(8x) = 32x^3$
• $(4x^2)(-5) = -20x^2$
• $(3x)(8x) = 24x^2$
• $(3x)(-5) = -15x$
• $(7)(8x) = 56x$
• $(7)(-5) = -35$

Step3: Combine like terms

• For $x^3$: $32x^3$
• For $x^2$: $-20x^2 + 24x^2 = 4x^2$
• For $x$: $-15x + 56x = 41x$
• Constant term: $-35$

So the result is $32x^3 + 4x^2 + 41x - 35$.

Answer:

D. \( 32x^3 + 4x^2 + 41x - 35 \)