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Test: Factoring - SAT MCQ


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10 Questions MCQ Test Mathematics for SAT - Test: Factoring

Test: Factoring for SAT 2024 is part of Mathematics for SAT preparation. The Test: Factoring questions and answers have been prepared according to the SAT exam syllabus.The Test: Factoring MCQs are made for SAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Factoring below.
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Test: Factoring - Question 1

What is the factored form of the quadratic expression x2 + 6x + 8?

Detailed Solution for Test: Factoring - Question 1

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).

Test: Factoring - Question 2

Which of the following expressions is a factor of 6x2 - 21x?

Detailed Solution for Test: Factoring - Question 2

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

Test: Factoring - Question 3

What is the value of 'a' if the expression x2 + ax + 36 is divisible by (x + 6)?

Detailed Solution for Test: Factoring - Question 3

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.

Test: Factoring - Question 4

Which of the following is NOT a factor of 12x3 - 16x2 + 4x?

Detailed Solution for Test: Factoring - Question 4

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.

Test: Factoring - Question 5

What is the factored form of the quadratic expression x2 - 5x - 14?

Detailed Solution for Test: Factoring - Question 5

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).

Test: Factoring - Question 6

What is the factored form of the quadratic expression x2 - 7x + 12?

Detailed Solution for Test: Factoring - Question 6

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).

Test: Factoring - Question 7

What is the factored form of the quadratic expression x2 + 5x + 6?

Detailed Solution for Test: Factoring - Question 7

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).

Test: Factoring - Question 8

What is the factored form of the quadratic expression 2x2 - 5x - 3?

Detailed Solution for Test: Factoring - Question 8

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).

Test: Factoring - Question 9

What is the factored form of the expression 18x2 - 27x?

Detailed Solution for Test: Factoring - Question 9

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

Test: Factoring - Question 10

What is the factored form of the quadratic expression x2 - 4?

Detailed Solution for Test: Factoring - Question 10

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

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