If $- 4 x^{2} - 7 x + 5$ is multiplied by one of the monomial the product is $32 x^{3} + 56 x^{2} - 40 x$ , then the monomial is

8 x

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- 8 x

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4 x

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- 4 x

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Solution

The correct option is B $- 8 x$
$32 x^{3} + 56 x^{2} - 40 x = 8 x (4 x^{2} + 7 x - 5)$
$- 8 x (4 x^{2} + 7 x - 5)$
$∴ \frac{- 8 x (4 x^{2} + 7 x - 5)}{- (4 x^{2} + 7 x - 5)} = 8 x$
$∴ - 8 x$ is the monomial when multiplied by $4 x^{2} + 7 x - 5$ gives the polynomial $32 x^{3} + 56 x^{2} - 40 x$

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Similar questions

What is the result if a monomial is multiplied by a monomial?

8 x^{4}, 4 x^{3}

10 x^{2} ?

$\frac{F i r s t m o n o m i a l \to}{S e c o n d m o n o m i a l ↓}$	$2 x$	$- 5 y$	$3 x^{2}$	$- 4 x y$	$7 x^{2} y$	$- 9 x^{2} y^{2}$
$2 x$	$4 x^{2}$	.....	.....	.....	.....	.....
$- 5 y$	.....	.....	$- 15 x^{2} y$	.....	.....	.....
$3 x^{2}$	.....	.....	.....	.....	.....	.....
$- 4 x y$	.....	.....	.....	.....	.....	.....
$7 x^{2} y$	.....	.....	.....	.....	.....	.....
$- 9 x^{2} y^{2}$	.....	.....	.....	.....	.....	.....

First monomial $\to$ Second Monomial $↓$	$2 x$	$- 3 y$	$4 x^{2}$	$- 5 x y$	$7 x^{2} y$	$- 6 x^{2} y^{2}$
$2 x$	$4 x^{2}$	....	....
$- 3 y$
$4 x^{2}$
$- 5 x y$				$25 x^{2} y^{2}$
$7 x^{2} y$
$- 6 x^{2} y^{2}$		$18 x^{2} y^{2}$

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