polynomials

Question

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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.

Guest Jun 19, 2021

amygdaleon305 · Answer 1 · 2021-06-19T04:59:06

\((3x^2-5x+4)(7-x) = -3x^3+26x^2-39x+28\)

a = -3, b = 26, c = -39 and d = 28

8a + 4b + 2c + d = 30

Bginner · Answer 2 · 2021-06-19T06:39:08

Alternatively
\[
8a+4b+2c+d
=a\cdot 2^2 + b\cdot 2^2 + c\cdot 2+d
= (3\cdot 2^2-5\cdot 2 +4)(7-2)
= 6\cdot 5
= 30.
\]