Question

select the correct answer.
which quadratic expression represents the product of these factors?
(2x + 5)(7 - 4x)

a. -8x² + 6x - 35
b. -8x² + 34x - 35
c. -8x² - 34x + 35
d. -8x² - 6x + 35

Explanation:

Step1: Apply distributive property (FOIL)

Multiply each term in the first factor by each term in the second factor:
$$(2x + 5)(7 - 4x)=2x\times7+2x\times(-4x)+5\times7+5\times(-4x)$$

Step2: Simplify each term

Calculate each product:
$$2x\times7 = 14x$$
$$2x\times(-4x)=-8x^{2}$$
$$5\times7 = 35$$
$$5\times(-4x)=-20x$$
So the expression becomes:
$$-8x^{2}+14x + 35-20x$$

Step3: Combine like terms

Combine the \(x\)-terms:
$$14x-20x=-6x$$
So the quadratic expression is:
$$-8x^{2}-6x + 35$$

Answer:

D. \(-8x^{2}-6x + 35\)