Factoring Polynomials Worksheet

Question 1

Factor the expression 6x + 12.

Accepted Answer

The expression factors as 6(x + 2). The greatest common factor of 6x and 12 is 6.

Question 2

Factor the expression 5x^2 - 15x.

Accepted Answer

The expression factors as 5x(x - 3). The greatest common factor of both terms is 5x.

Question 3

Factor the trinomial x^2 + 7x + 12.

Accepted Answer

The trinomial factors as (x + 3)(x + 4). The numbers 3 and 4 multiply to 12 and add to 7.

Question 4

Factor the trinomial x^2 - 9x + 20.

Accepted Answer

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.

Question 5

Factor the expression x^2 - 25.

Accepted Answer

The expression factors as (x - 5)(x + 5). This is a difference of squares.

Question 6

Factor the expression 3x^2 + 12x + 12.

Accepted Answer

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.

Question 7

Factor the trinomial x^2 + 2x - 15.

Accepted Answer

The trinomial factors as (x + 5)(x - 3). The numbers 5 and -3 multiply to -15 and add to 2.

Question 8

Factor the expression 4x^2 - 16.

Accepted Answer

The expression factors as 4(x - 2)(x + 2). First factor out 4, then factor the difference of squares.

Question 9

Factor the trinomial 2x^2 + 7x + 3.

Accepted Answer

The trinomial factors as (2x + 1)(x + 3). Expanding this product gives 2x^2 + 7x + 3.

Question 10

Factor the trinomial 6x^2 + 11x + 3.

Accepted Answer

The trinomial factors as (3x + 1)(2x + 3). The product of the binomials simplifies to 6x^2 + 11x + 3.

Question 11

Factor the expression x^2 - 10x + 25.

Accepted Answer

The expression factors as (x - 5)^2. This is a perfect square trinomial.

Question 12

Factor the expression 9x^2 - 24x + 16.

Accepted Answer

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).

Question 13

Factor the polynomial 2x^3 + 8x^2 - 18x.

Accepted Answer

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).

Question 14

Factor the polynomial x^3 - 4x^2 - 12x.

Accepted Answer

The polynomial factors as x(x - 6)(x + 2). First factor out x to get x(x^2 - 4x - 12), then factor the trinomial.

Question 15

Factor the expression 8x^3 - 27.

Accepted Answer

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.

Factoring Polynomials

Factoring Polynomials

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