Factoring Polynomials

These videos show the different methods to factor polynomials.

Exercises

1.

\((x-8)(x-2)\)

2.

\((3x-4)(x+1)\)

3.

\((x-3)(x-\sqrt{5})(x+\sqrt{5})\)

4.

\(14x+4xy-8xy^2=2x\left(7+2y-4y^2\right)\)
\(30x^3y-45x^2y^2+135xy^3=15xy\left(2x^2-3xy+9y^2\right)\)
\(3x(3x+2)^{-\frac{1}{4}} -5(2x+3)^{\frac{3}{4}}=(2x+3)^{-\frac{1}{4}}(-7x-15)\)

5.

\(x^2+8x+15=(x+3)(x+5)\)
\(x^2-4x-12=(x+3)(x-7)\)
\(x^2-5x-6=(x-6)(x+1)\)
\(x^2-20x+100=(x-10)(x-10)=(x-10)^2\)

6.

\(2x^2+9x-18=(2x-3)(x+6)\)
\(6x^2+5x-4=(2x-1)(3x+4)\)

7.

\(x^3+7x^2+3x+21=(x+7)\left(x^2+3\right)\)
\(y^3-3y^2-25y+75=(y-3)(y+5)(y-5)\)

8.

\(x^2-16=(x-4)(x+4)\)
\(3x^2-75=3(x+5)(x-5)\)

9.

\(x^3+216=(x+6)\left(x^2-6x+36\right)\)
\(27y^3-8=(3y-2)\left(9y^2+6y+4\right)\)