Factor
\left(x^{2}-5x+7\right)\left(x^{2}+px+q\right)
Evaluate
\left(x^{2}-5x+7\right)\left(x^{2}+px+q\right)
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x^{2}\left(x^{2}-5x+7\right)+px\left(x^{2}-5x+7\right)+q\left(x^{2}-5x+7\right)
Do the grouping x^{4}-5x^{3}+7x^{2}+px^{3}-5px^{2}+7px+qx^{2}-5qx+7q=\left(x^{4}-5x^{3}+7x^{2}\right)+\left(px^{3}-5px^{2}+7px\right)+\left(qx^{2}-5qx+7q\right), and factor out x^{2},px,q in each of the groups respectively.
\left(x^{2}-5x+7\right)\left(x^{2}+px+q\right)
Factor out common term x^{2}-5x+7 by using distributive property. Polynomial x^{2}-5x+7 is not factored since it does not have any rational roots.
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