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(D) To factorize the quadratic polynomial $p(x) = x^{2} + 5x - 24$,we need to find two numbers whose product is $-24$ and whose sum is $5$.These two n

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$(x + 8)(x - 3)$

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(D) To factorize the quadratic polynomial $p(x) = x^{2} + 5x - 24$,we need to find two numbers whose product is $-24$ and whose sum is $5$.These two numbers are $8$ and $-3$,because $8 	imes (-3) = -24$ and $8 + (-3) = 5$.Now,split the middle term $5x$ as $8x - 3x$:$p(x) = x^{2} + 8x - 3x - 24$Group the terms:$p(x) = (x^{2} + 8x) - (3x + 24)$Factor out the common terms:$p(x) = x(x + 8) - 3(x + 8)$Finally,factor out the common binomial $(x + 8)$:$p(x) = (x + 8)(x - 3)$

Factorize the following polynomial: $p(x) = x^{2} + 5x - 24$

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