2021-02-19

Factor the GCF from the polynomial.
${x}^{2}\left(x-1\right)+{y}^{2}\left(x-1\right)$

joshyoung05M

Step 1
The given polynomial is,
${x}^{2}×\left(x-1\right)+{y}^{2}×\left(x-1\right)$
The GCF of a polynomial is the greatest common factor of the polynomial.
The polynomial can be rewritten as,
${x}^{2}×\left(x-1\right)+{y}^{2}×\left(x-1\right)=\left(x-1\right)×\left({x}^{2}+{y}^{2}\right)$
Thus, the term (x-1) is common for the polynomial.
Step 2
Thus, the factorised expression is,
$\left(x-1\right)×\left({x}^{2}+{y}^{2}\right)$
Thus, the GCF of the polynomial (x-1).

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