SAT Math formula sheet · all 24 · Advanced Math · #7 of 24

Factoring on the SAT: How It Is Tested

Equivalent expressions

Factoring diagram for the SAT: When comparing factored form to expanded form, notice that in FOIL first times first gives the first term in expanded fo
What it is really testingWhen comparing factored form to expanded form, notice that in FOIL first times first gives the first term in expanded form, and last times last gives the last term.

The question from the sheet

Medium
SAT Advanced Mathanswer 3
If the expression 3x2+7x−63x^{2} + 7x - 6 is rewritten in the form (3x−2)(x+k)(3x - 2)(x + k), where kk is a constant, what is the value of kk?
Student-produced response: 3

How the diagram applies

  1. The two numbers in the factors multiply to the LAST term: (−2)(k)=−6(-2)(k) = -6, so k=3k = 3.
  2. Check the middle with First and Last: 3x⋅3+(−2)⋅x=9x−2x=7x3x \cdot 3 + (-2) \cdot x = 9x - 2x = 7x. It matches.

Answer: 3

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Common Questions

It comes up as an SAT equivalent expressions question. When comparing factored form to expanded form, notice that in FOIL first times first gives the first term in expanded form, and last times last gives the last term.

The two numbers in the factors multiply to the LAST term: (-2)(k) = -6, so k = 3. Check the middle with First and Last: 3x × 3 + (-2) × x = 9x - 2x = 7x. It matches.

No. The SAT reference sheet is twelve geometry formulas and three notes, and Factoring is not one of them. It is one of the 24 things the test expects you to know without being given them. See what the reference sheet does cover at /blog/sat-math-reference-sheet.