Factoring Techniques (Traditional, GCF, Difference of Squares)

Answer explanation

To factor the trinomial x^2 + 5x + 6, we look for two numbers that multiply to 6 and add to 5. The numbers 2 and 3 satisfy this, so we can write it as (x + 2)(x + 3). Thus, the correct answer is (x + 2)(x + 3).

Answer explanation

To factor the expression 3x^2 + 9x, we first identify the greatest common factor, which is 3x. Factoring this out gives us 3x(x + 3), making it the correct choice.

Answer explanation

To factor the trinomial x^2 - 7x + 10, we look for two numbers that multiply to 10 and add to -7. The numbers -5 and -2 satisfy this, leading to the factors (x - 5)(x - 2). Thus, the correct choice is (x - 5)(x - 2).

Answer explanation

The expression x^2 - 16 is a difference of squares, which factors as (a - b)(a + b) where a = x and b = 4. Thus, it factors to (x - 4)(x + 4), making this the correct choice.

Tags

CCSS.HSA.APR.C.4

Answer explanation

To factor the trinomial x^2 + 4x + 4, we look for two identical factors that add to 4 and multiply to 4. The correct factorization is (x + 2)(x + 2), which can be written as (x + 2)^2.

Tags

CCSS.HSA.APR.C.4

Answer explanation

To factor the expression 5x^2 - 20x, first identify the greatest common factor, which is 5x. Factoring this out gives 5x(x - 4), making it the correct choice.

Answer explanation

The trinomial x^2 + 6x + 9 can be factored as (x + 3)(x + 3), which is the same as (x + 3)^2. This shows that the correct choice is (x + 3)^2.

Tags

CCSS.HSA.APR.C.4

Answer explanation

The expression 9x^2 - 25 is a difference of squares, which factors as (a - b)(a + b) where a = 3x and b = 5. Thus, it factors to (3x - 5)(3x + 5), making this the correct choice.

Tags

CCSS.HSA.APR.C.4

Answer explanation

To factor the trinomial x^2 - 9x + 14, we look for two numbers that multiply to 14 and add to -9. The numbers -7 and -2 fit this, leading to the factors (x - 7)(x - 2). Thus, the correct answer is (x - 7)(x - 2).

Answer explanation

To factor the expression 2x^2 + 8x, first identify the greatest common factor, which is 2x. Factoring this out gives 2x(x + 4), making it the correct choice. The other options do not correctly factor the expression.