Factoring Test Review

Answer explanation

To factor the quadratic n^2 + 5n + 6, we look for two numbers that multiply to 6 (the constant term) and add to 5 (the coefficient of n). The numbers 2 and 3 satisfy this, leading to the factors (n+2)(n+3).

Answer explanation

To factor 2x^2 + 7x + 3, we look for two numbers that multiply to 6 (2*3) and add to 7. The numbers 6 and 1 work. Thus, we can write it as (2x + 1)(x + 3), which is the correct choice.

Which of the following is a difference of squares?

Answer explanation

The expression x^2 - 9 is a difference of squares, as it can be factored into (x - 3)(x + 3). The other options do not fit this form.

Tags

CCSS.HSA.APR.C.4

Answer explanation

To factor 3k^2 + 8k + 4, we look for two numbers that multiply to (3*4=12) and add to 8. The numbers 6 and 2 work. Thus, we can rewrite the middle term: 3k^2 + 6k + 2k + 4, which factors to (3k+2)(k+2).

Answer explanation

The expression x^2 - 16 is a difference of squares, which factors as (x - 4)(x + 4). This is because 4^2 = 16, making it a perfect square. The other options do not correctly factor the expression.

Tags

CCSS.HSA.APR.C.4

Answer explanation

To find the GCF of 6x^3 and 9x^2, factor each term: 6 = 2 * 3, 9 = 3 * 3. The GCF of the coefficients is 3. For the variable part, the lowest power of x is x^2. Thus, GCF = 3x^2.

Answer explanation

To factor by grouping, combine like terms: z^2 + (3z + 2z) + 6 = z^2 + 5z + 6. Then, factor: (z + 2)(z + 3) is the correct factorization.

Answer explanation

To factor the expression 12x^2y + 8xy, first find the GCF, which is 4xy. Factoring this out gives 4xy(3x + 2). Thus, the correct answer is 4xy(3x + 2).

Answer explanation

To factor by grouping, combine like terms: 2x^2 + 9x + 10. Group as (2x^2 + 4x) + (5x + 10). Factor each group: 2x(x + 2) + 5(x + 2). Factor out (x + 2): (x + 2)(2x + 5). Thus, the correct answer is (x + 2)(2x + 5).

Answer explanation

To factor the quadratic w^2 - 2w - 15, we look for two numbers that multiply to -15 and add to -2. The numbers -5 and 3 fit this, leading to the factors (w-5)(w+3). Thus, the correct choice is (w-5)(w+3).