What is the product of all the possible values of x if

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 am; Thanked: 1 times; Followed by:5 members

What is the product of all the possible values of x if

by M7MBA » Wed May 16, 2018 1:34 am

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What is the product of all the possible values of x if $$x^2\left(x+2\right)+7x\left(x+2\right)+6\left(x+2\right)=0$$

A. -29
B. -12
C. 12
D. 29
E. 168

The OA is B.

Is there a simple way to solve this PS question? I would like someone give me a good approach here. Please. Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Wed May 16, 2018 1:34 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Wed May 16, 2018 2:01 am

M7MBA wrote:What is the product of all the possible values of x if $$x^2\left(x+2\right)+7x\left(x+2\right)+6\left(x+2\right)=0$$

A. -29
B. -12
C. 12
D. 29
E. 168

xÂ²(x+2) + 7x(x+2) + 6(x+2) = 0.

Factor out x+2:
(x+2)(xÂ² + 7x + 6) = 0

Factor the quadratic in red:
(x+2)(x+6)(x+1) = 0

Option for x:
x=-2, x=-6, x==-1.
Thus, the product of all the solutions = (-2)(-6)(-1) = -12.

The correct answer is B.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Thu May 17, 2018 5:19 pm

M7MBA wrote:What is the product of all the possible values of x if $$x^2\left(x+2\right)+7x\left(x+2\right)+6\left(x+2\right)=0$$

A. -29
B. -12
C. 12
D. 29
E. 168

We first factor the common (x + 2) from the left side. We have:

(x + 2)(x^2 + 7x + 6) = 0

Now, we can factor the quadratic x^2 + 7x + 6:

(x + 2)(x + 6)(x + 1) = 0

The three possible values for x are x = -2 or -6 or -1, for a product of -12.

Answer: B

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