+0

# polynomials

0
40
2

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.

Jun 19, 2021

#1
+505
+2

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

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

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

Jun 19, 2021
#2
+287
+2

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

Jun 19, 2021