If x is not equal to $-\frac{1}{2}$, then $\frac{6... | Free GMAT Practice Question | GMAT Panda

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If x is not equal to - \frac{1}{2}, then \frac{6 x ^{3} + 3 x ^{2} - 8 x - 4}{2 x + 1} =

Explanation	Calculations	Help
$We group the numerator into two pairs to set up factoring.$	$6 x^{3} + 3 x^{2} - 8 x - 4 = 3 x^{2} (2 x + 1) - 4 (2 x + 1)$
$We factor out the common binomial from each group.$	$3 x^{2} (2 x + 1) - 4 (2 x + 1) = (2 x + 1) (3 x^{2} - 4)$
$We remove the common factor since 2 x + 1 is nonzero under the given condition.$	$\frac{( 2 x + 1 ) ( 3 x ^{2} - 4 )}{( 2 x + 1 )} = 3 x^{2} - 4$	Theory & Tactics Method Card FDPR2-A Click to view full details

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3x^2 - 4

If x is not equal to - \frac{1}{2}, then \frac{6 x ^{3} + 3 x ^{2} - 8 x - 4}{2 x + 1} =

Explanation	Calculations	Help
$We group the numerator into two pairs to set up factoring.$	$6 x^{3} + 3 x^{2} - 8 x - 4 = 3 x^{2} (2 x + 1) - 4 (2 x + 1)$
$We factor out the common binomial from each group.$	$3 x^{2} (2 x + 1) - 4 (2 x + 1) = (2 x + 1) (3 x^{2} - 4)$
$We remove the common factor since 2 x + 1 is nonzero under the given condition.$	$\frac{( 2 x + 1 ) ( 3 x ^{2} - 4 )}{( 2 x + 1 )} = 3 x^{2} - 4$	Theory & Tactics Method Card FDPR2-A Click to view full details

Scroll horizontally to view all columns

3x^2 - 4