The expression x^{4}+7 x^{2}+16 can be factor | vedclass

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(C) To factor the expression $x^{4}+7 x^{2}+16$,we can complete the square.First,rewrite the expression by adding and subtracting $x^{2}$:$x^{4}+7 x^{

Vedclass · Accepted Answer

$(x^{2}+x+4)(x^{2}-x+4)$

Vedclass · Answer

(C) To factor the expression $x^{4}+7 x^{2}+16$,we can complete the square.First,rewrite the expression by adding and subtracting $x^{2}$:$x^{4}+7 x^{2}+16 = (x^{4}+8 x^{2}+16) - x^{2}$Recognize that $(x^{4}+8 x^{2}+16)$ is a perfect square trinomial:$(x^{4}+8 x^{2}+16) = (x^{2}+4)^{2}$Now,substitute this back into the expression:$(x^{2}+4)^{2} - x^{2}$Use the difference of squares formula,$a^{2}-b^{2} = (a+b)(a-b)$,where $a = (x^{2}+4)$ and $b = x$:$(x^{2}+4+x)(x^{2}+4-x)$Rearranging the terms,we get:$(x^{2}+x+4)(x^{2}-x+4)$

The expression $x^{4}+7 x^{2}+16$ can be factored as:

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