Test: Factoring - SAT MCQ

In order to factor the given expression, look for two numbers that multiply to 8 and add to 6.
These numbers are 2 and 4.
So, we can rewrite the expression as (x + 2)(x + 4).

Factor out the greatest common factor (GCF) from the expression, which is 3x.
The factored form of the expression is 3x(2x - 7).

If the expression is divisible by (x + 6), then x = -6 is a root of the quadratic expression.
Substitute x = -6 into the expression: (-6)² + a x (-6) + 36 = 0.
Solve for a: 36 - 6a + 36 = 0, which simplifies to 6a = 72.
Thus, a = 12.

Factor out the GCF of the expression, which is 4x.
The factored form of the expression is 4x(3x² - 4x + 1).
x - 5 is not a factor of the expression.

Look for two numbers that multiply to -14 and add to -5.
These numbers are 2 and -7.
So, we can rewrite the expression as (x + 2)(x - 7).

Look for two numbers that multiply to 12 and add to -7.
These numbers are -3 and -4.
So, we can rewrite the expression as (x - 3)(x - 4).

Look for two numbers that multiply to 6 and add to 5.
These numbers are 2 and 3.
So, we can rewrite the expression as (x + 2)(x + 3).

We can use the factoring method called "ac method." Multiply 'a' (2) and 'c' (-3) to get -6.
Look for two numbers that multiply to -6 and add to -5.
These numbers are -6 and 1.
Rewrite the middle term (-5x) as -6x + x.
Then factor by grouping: 2x² - 6x + x - 3 = 2x(x - 3) + (x - 3).
Factor out the common factor (x - 3) to get (x - 3)(2x + 1).

Factor out the GCF from the expression, which is 9x.
The factored form of the expression is 9x(2x - 3).

The given expression is a difference of squares.
The factored form of the expression is (x + 2)(x - 2).