Factoring
Factor out the greatest common monomial: 6x²y + 9xy²
3xy(2x+3y)
x² + 5x + 6
(x+3)(x+2)
Factor a perfect square trinomial: 9x² + 24x + 16
(3x+4)(3x+4)
(x – 3)(x + 2) = 0
x1=-2
x2=3
A right triangle has legs of length 3 and 4. Find the hypotenuse.
5
Factor the polynomial by grouping: x² + 3x + 2x + 6
x2+5x+6
2x² + 7x + 3
(x+3)(2x+1)
Factor a difference of squares: x² – 49
(x-7)(x+7)
x² + 4x = 0
x1=-4
x2=0
The hypotenuse of a right triangle is 13 and one leg is 5. Find the other leg.
12
Factor the multivariate polynomial by grouping: xy + 2y + x + 2
(x+2)(y+1)
Use the ac-method: 6x² + 5x – 6
(2x+3)(3x-2)
Factor a difference of squares in two variables: a² – b²
(a-b)(a+b)
x² + 5x + 6 = 0
x1=-3
x2=-2
A right triangle has a hypotenuse of length 10 and one leg is x. The other leg is x+2x + 2x+2. Find x.
x=6
Factor out a constant before factoring: 5x² + 15x + 10
5(x+2)(x+1)
3x² + 11x + 6
(x+3)(3x+2)
Factor a sum of cubes: x³ + 8
(x+2)(x2-2x+4)
2x² + 3x – 2 = 0
x1=-2
x2=1/2
One leg of a right triangle is 6, and the other leg is 8. Find the hypotenuse.
10
Factor the quadratic in two variables: x² + 6xy + 9y²
(x+3y)(x+3y)
4x² – 12x + 9
(2x-3)2
Factor involving GCF & difference of squares: 4x² – 16
4(x-2)(x+2)
Simplify and solve: (x + 1)² = 9
x1=-4
x2=2
A right triangle has a hypotenuse of 15 and one leg of 9. Find the other leg.
12