Question

Which of the following expressions is equivalent to 3x2 + 6x – 24?

A. 3(x + 2)(x – 4)
B. 3(x – 2)(x + 4)
C. (x + 6)(x – 12)
D. (x – 6)(x + 12)

Answer 1

It's B. 3(x-2)(x+4)

first simplify the 3 from 3,6,-24
that leaves you to have an equation of x^2+2x-8 which you would then use the quadratic formula to get (x-2)(x+4).
don't forget to add the 3 from when you simplified, so it leaves you to have answer of 3(x-2)(x+4)!

DM me if you need me to show the work on paper :D!

Answer 2

3x² + 6x - 24

Simplify 3.

3(x² + 6x - 8)

Think of x² +2x−8. Factor the expression by grouping. First, we need to rewrite the expression as x² + ax + bx - 8. To find a and b, set up a system to be solved.

• a + b = 2
• ab = 1( −8 ) = −8

Since ab is negative, a and b have opposite signs. Since a+b is positive, the positive number has a greater absolute value than the negative. Show all pairs of integers whose product is −8.

• −1,8
• −2,4

Calculate the sum of each pair.

• −1 + 8 = 7
• −2 + 4 = 2

The solution is the pair that gives sum 2

• a=−2
• b=4

Rewrite x² + 2x − 8 as (x² − 2x ) + (4x − 8).

• (x² − 2x ) + (4x − 8)

Simplify x in the first group and 4 in the second.

• x ( x − 2) + 4( x − 2 )

Simplify the common term x−2 with the distributive property.

• ( x − 2 )( x + 4 )

The entire factored expression is rewritten.

3 ( x − 2 )( x + 4 ) ===> Answer

We conclude that the correct option is "B".

{ Pisces04 }