Factoring polynomials
Lesson 15 of 20 in Union Aptitude Prep. The start plays free here.
- 3x² + 9x − 30
- = 3(x + 5)(x − 2)
- Factor out the GCF first
- Trinomials: multiply and add
- Difference of squares: (a − b)(a + b)
- Sum of squares: no binomial factors
- Number series trainer
- Algebra & functions with worked steps
- Reading comprehension sets
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How the lesson starts
Factoring means writing an expression as pieces multiplied together. Those pieces are called factors. You change the form, not the value.
An official apprenticeship sample asks you to multiply these factors. Factoring goes the other way: from the expanded expression back to the multiplied form.
You see 2x² + 10x + 12 in your booklet. All three terms share 2. That's the greatest common factor, or GCF: the largest factor they share.
Then, in the full lesson
- GCF first
- Two numbers
- Squares subtract
- Watch the sign
- 2 questions along the way
A question from this lesson
How do you factor x² + 7x + 12?
- (x − 3)(x − 4)
- (x + 2)(x + 6)
- (x + 3)(x + 4)
Show the answer
C. (x + 3)(x + 4). (x + 3)(x + 4) works because 3 × 4 = 12 and 3 + 4 = 7. The numbers 2 and 6 add to 8. Negative 3 and negative 4 add to −7.
The full class, $39 once.
Paid once, no subscription. Ask for a refund within 7 days of buying if you’ve done less than 25% of the class.
- Number series trainer
- Algebra & functions with worked steps
- Reading comprehension sets
Not affiliated with IBEW, NECA, ETA or any JATC. Original practice questions only.