Factors of x^{2}-23x+120 are......... | vedclass

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Question

(C) To factorize the quadratic polynomial $x^{2}-23x+120$,we need to find two numbers whose sum is $-23$ and whose product is $120$.Let the two number

Vedclass · Accepted Answer

$(x-15)(x-8)$

Vedclass · Answer

(C) To factorize the quadratic polynomial $x^{2}-23x+120$,we need to find two numbers whose sum is $-23$ and whose product is $120$.Let the two numbers be $a$ and $b$.We have $a+b = -23$ and $ab = 120$.By testing factors of $120$,we find that $-15$ and $-8$ satisfy these conditions because $(-15) + (-8) = -23$ and $(-15) 	imes (-8) = 120$.Now,rewrite the middle term $-23x$ as $-15x - 8x$:$x^{2}-15x-8x+120$Group the terms:$(x^{2}-15x) - (8x-120)$Factor out the common terms:$x(x-15) - 8(x-15)$$(x-15)(x-8)$Thus,the factors are $(x-15)(x-8)$.

Factors of $x^{2}-23x+120$ are.........

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