Verified answer

by synthetic division:

-5] 1 10 -23 -348 -540

0 -5 -25 240 540

1 5 -48 -108 0

so these are the new coeffecients starting with x³ + 5x² - 48x - 108

The answer is C

If you weren't already given the answers, you could first factor then simplify of the factors.

Since you are given the answers already, I will tell you to use the distributive property on it and if it equals the first equation then it is correct.

A) (x+5)(x^3+5x^2+48x-108)

(x^4+5x^3+5x^3+ 25x^2+48x^2+240x - 108x - 540)

x^4+10x^3+ 73x^2+132x- 40 does not equal (x^4 + 10x^3 - 23x^2 -348x -540)

Do that for all the answers until you get it. That's how you do it in tests such as the CAHSEE or the ACT Math Sections.

When we divide x^4 + 10x³ -23x² -348x - 540) by x + 5, we get: x³ + 5x² - 48x -108. Hence C is the correct answer.

Further factorisation of (x³ + 5x² - 48x -108) gives:

(x + 9) (x - 6) (x + 2)

AJM

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