Rewriting Polynomials by Factoring

To find the error the Ron-Jon made, we will factor the given polynomial by grouping on our own first. Notice that the first two terms share a common factor of

x^{2}

and the greatest common factor of the last two terms is

1 .

3 x^{3} + x^{2} + 3 x + 1

FactorOutFactor out

x^{2}

x^{2} (3 x + 1) + 3 x + 1

FactorOutFactor out

1

x^{2} (3 x + 1) + 1 (3 x + 1)

Midway through, we obtained a different partial result than Ron-Jon. He made a mistake when factoring the second group. Let's continue to correctly factor the polynomial.

x^{2} (3 x + 1) + 1 (3 x + 1)

FactorOutFactor out

(3 x + 1)

(3 x + 1) (x^{2} + 1)

Rewriting Polynomials by Factoring 1.2 - Solution