+0

# Polynomials

0
156
1

If the product (3x^2 - 5x + 4)(7 - x) can be written in the form ax^3 + bx^2 + cx + d, where a,b,c,d are real numbers, then find 8a + 4b + 2c + d.

Jan 11, 2022

Let $$f(x) = ax^3 + bx^2 + cx + d = (3x^2 - 5x + 4)(7 - x)$$. Note that $$8a + 4b + 2c + d = f(2)$$, so hence we can just plug $$x = 2$$ into $$(3x^2 - 5x + 4)(7 - x)$$ for an answer of $(3 \cdot 2^2 - 5 \cdot 2 + 4)(7 - 2) = (12 - 10 + 4)(7 - 2) = (6)(5) = \boxed{30}.$