Question

Which shows one way to determine the factors of x3 – 12x2 – 2x + 24 by grouping?


1. ) x(x2 – 12) + 2(x2 – 12)

2.) x(x2 – 12) – 2(x2 – 12)

3.) x2(x – 12) + 2(x – 12)

4.) x2(x – 12) – 2(x – 12)

Answer 1

Answer:

the answer is no.4

Step-by-step explanation:

x^3 - 12x^2 - 2x + 24

x^2(x-12)-2(x-12)

Answer 2

Option 4

$x^3 - 12x^2 -2x + 24 = x^2\left(x-12\right) -2\left(x-12\right)$

Solution:

Given equation is:

$x^3 - 12x^2 -2x + 24$

We have to find the factors by grouping

$x^3 - 12x^2 -2x + 24 \\\\Break\ the\ expression\ into\ group\\\\\left(x^3-12x^2\right)+\left(-2x+24\right) \\\\\mathrm{Factor\:out\:}x^2\mathrm{\:from\:}x^3-12x^2 \\\\x^2(x - 12) + (-2x + 24) \\\\\mathrm{Factor\:out\:}-2\mathrm{\:from\:}-2x+24\mathrm{:\quad } \\\\x^2(x - 12) - 2(x - 12)$

Thus option 4 is correct

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