Factoring Polynomials
Factoring expressions using common factors, trinomials, and special patterns
Factoring Polynomials
Factoring expressions using common factors, trinomials, and special patterns
Math - Grade 9-12
- 1
Factor the expression 6x + 12.
Look for the greatest common factor first.
The expression factors as 6(x + 2). The greatest common factor of 6x and 12 is 6. - 2
Factor the expression 5x^2 - 15x.
Both terms have a number factor and a variable factor in common.
The expression factors as 5x(x - 3). The greatest common factor of both terms is 5x. - 3
Factor the trinomial x^2 + 7x + 12.
The trinomial factors as (x + 3)(x + 4). The numbers 3 and 4 multiply to 12 and add to 7. - 4
Factor the trinomial x^2 - 9x + 20.
Find two numbers that multiply to 20 and add to -9.
The trinomial factors as (x - 5)(x - 4). The numbers 5 and 4 multiply to 20 and add to 9, and both signs are negative. - 5
Factor the expression x^2 - 25.
The expression factors as (x - 5)(x + 5). This is a difference of squares. - 6
Factor the expression 3x^2 + 12x + 12.
Factor out the greatest common factor before factoring the trinomial.
The expression factors as 3(x + 2)(x + 2), which can also be written as 3(x + 2)^2. First factor out the greatest common factor 3. - 7
Factor the trinomial x^2 + 2x - 15.
The trinomial factors as (x + 5)(x - 3). The numbers 5 and -3 multiply to -15 and add to 2. - 8
Factor the expression 4x^2 - 16.
There is a greatest common factor, and the remaining expression is a difference of squares.
The expression factors as 4(x - 2)(x + 2). First factor out 4, then factor the difference of squares. - 9
Factor the trinomial 2x^2 + 7x + 3.
The trinomial factors as (2x + 1)(x + 3). Expanding this product gives 2x^2 + 7x + 3. - 10
Factor the trinomial 6x^2 + 11x + 3.
Try pairs of factors of 6x^2 and 3 that produce a middle term of 11x.
The trinomial factors as (3x + 1)(2x + 3). The product of the binomials simplifies to 6x^2 + 11x + 3. - 11
Factor the expression x^2 - 10x + 25.
The expression factors as (x - 5)^2. This is a perfect square trinomial. - 12
Factor the expression 9x^2 - 24x + 16.
Check whether the first and last terms are perfect squares.
The expression factors as (3x - 4)^2. This is a perfect square trinomial because 9x^2 and 16 are perfect squares and the middle term matches -2(3x)(4). - 13
Factor the polynomial 2x^3 + 8x^2 - 18x.
The polynomial factors as 2x(x + 1)(x - 9). First factor out the greatest common factor 2x to get 2x(x^2 + 4x - 9). Then factor the trinomial inside as (x + 1)(x - 9). - 14
Factor the polynomial x^3 - 4x^2 - 12x.
Start by factoring out the greatest common factor x.
The polynomial factors as x(x - 6)(x + 2). First factor out x to get x(x^2 - 4x - 12), then factor the trinomial. - 15
Factor the expression 8x^3 - 27.
Use the difference of cubes pattern a^3 - b^3 = (a - b)(a^2 + ab + b^2).
The expression factors as (2x - 3)(4x^2 + 6x + 9). This is a difference of cubes because 8x^3 = (2x)^3 and 27 = 3^3.