The product of two polynomials is x^{2}+8x+15 | vedclass

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(B) Let the two polynomials be $P(x)$ and $Q(x)$.Given that $P(x) \cdot Q(x) = x^{2}+8x+15$.We are given one polynomial $P(x) = x+3$.To find the other

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$x+5$

Vedclass · Answer

(B) Let the two polynomials be $P(x)$ and $Q(x)$.Given that $P(x) \cdot Q(x) = x^{2}+8x+15$.We are given one polynomial $P(x) = x+3$.To find the other polynomial $Q(x)$,we divide the product by the given polynomial:$Q(x) = \frac{x^{2}+8x+15}{x+3}$.We can factorize the quadratic polynomial $x^{2}+8x+15$ by splitting the middle term:$x^{2}+5x+3x+15 = x(x+5)+3(x+5) = (x+3)(x+5)$.Substituting this back into the division:$Q(x) = \frac{(x+3)(x+5)}{x+3} = x+5$.Therefore,the other polynomial is $x+5$.

The product of two polynomials is $x^{2}+8x+15$. If one of the polynomials is $(x+3)$,then the other polynomial is $\ldots \ldots$

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