Factoring Polynomials

To factor by grouping, we will take the greatest common factor of the first pair of terms and the greatest common factor of the second pair of terms.

x^{3} + 4 x^{2} - x - 4

FactorOutFactor out

x^{2}

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

FactorOutFactor out

- 1

x^{2} (x + 4) - 1 (x + 4)

FactorOutFactor out

(x + 4)

(x + 4) (x^{2} - 1)

WritePowWrite as a power

(x + 4) (x^{2} - 1^{2})

a^{2} - b^{2} = (a + b) (a - b)

(x + 4) (x + 1) (x - 1)

Note that in the process we have used the difference of two squares.

Factoring Polynomials 1.4 - Solution