The product of two polynomials is x^{2}-x-72 | vedclass

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(D) Let the two polynomials be $P(x)$ and $Q(x)$.Given that $P(x) 	imes Q(x) = x^{2}-x-72$.One polynomial is $P(x) = x+8$.To find the other polynomia

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$x-9$

Vedclass · Answer

(D) Let the two polynomials be $P(x)$ and $Q(x)$.Given that $P(x) 	imes Q(x) = x^{2}-x-72$.One polynomial is $P(x) = x+8$.To find the other polynomial $Q(x)$,we divide the product by the given polynomial:$Q(x) = \frac{x^{2}-x-72}{x+8}$.We can factorize the quadratic expression $x^{2}-x-72$ by splitting the middle term:$x^{2}-9x+8x-72 = x(x-9)+8(x-9) = (x+8)(x-9)$.Therefore,$Q(x) = \frac{(x+8)(x-9)}{x+8} = x-9$.Thus,the other polynomial is $x-9$.

The product of two polynomials is $x^{2}-x-72$ and if one of the polynomials is $(x+8)$,then the other polynomial is $\ldots \ldots \ldots \ldots . .$

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