Find the G.C.D. of the polynomials 36 x^{2}-4 | vedclass

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Question

(C) Let $p(x) = 36 x^{2}-49$.Using the identity $a^{2}-b^{2} = (a-b)(a+b)$,we get:$p(x) = (6 x)^{2}-(7)^{2} = (6 x+7)(6 x-7)$.Let $q(x) = 6 x^{2}-25 x

Vedclass · Accepted Answer

$6 x-7$

Vedclass · Answer

(C) Let $p(x) = 36 x^{2}-49$.Using the identity $a^{2}-b^{2} = (a-b)(a+b)$,we get:$p(x) = (6 x)^{2}-(7)^{2} = (6 x+7)(6 x-7)$.Let $q(x) = 6 x^{2}-25 x+21$.To factorize this quadratic,we split the middle term:$q(x) = 6 x^{2}-18 x-7 x+21$$q(x) = 6 x(x-3)-7(x-3)$$q(x) = (6 x-7)(x-3)$.The $G.C.D.$ (Greatest Common Divisor) is the common factor present in both polynomials.Therefore,$G.C.D. = (6 x-7)$.

Find the $G.C.D.$ of the polynomials $36 x^{2}-49$ and $6 x^{2}-25 x+21$.

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