Factorise 16 x^{2}-16 x-21. | vedclass

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Question

(A) To factorise the quadratic expression $16 x^{2}-16 x-21$,we look for two numbers whose product is $16 	imes (-21) = -336$ and whose sum is $-16$.

Vedclass · Accepted Answer

$(4 x+3)(4 x-7)$

Vedclass · Answer

(A) To factorise the quadratic expression $16 x^{2}-16 x-21$,we look for two numbers whose product is $16 	imes (-21) = -336$ and whose sum is $-16$.These two numbers are $-28$ and $12$,because $(-28) 	imes 12 = -336$ and $(-28) + 12 = -16$.Now,split the middle term $-16 x$ as $-28 x + 12 x$:$16 x^{2} - 28 x + 12 x - 21$Group the terms:$(16 x^{2} - 28 x) + (12 x - 21)$Factor out the common terms from each group:$4 x(4 x - 7) + 3(4 x - 7)$Finally,factor out the common binomial $(4 x - 7)$:$(4 x - 7)(4 x + 3)$.

Factorise $16 x^{2}-16 x-21$.

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