Factoring a Trinomial where a>1

Factoring a Trinomial where a>1

Remember that factoring is rewriting a polynomial as the product of it's factors!

Rules for Factoring Trinomials with a > 1

ax² + bx + c

• ALWAYS check for a GCF first.

• Multiply a and c.

• Find the pair of numbers that multiply to give you ac and add up to b.

• Break b into the two factors that you found.

• Factor by Grouping.

• Make sure there is nothing else you can factor.

• Check your work!

ax² + bx + c

Example: 3a² + 4a + 1 (a=3, b=4, c=1)

1. Multiply ac - so 3(1) = 3

2. We need two numbers that multiply to give us 3 that add up to 4. What are they??

3. They are 3 and 1. (3)(1) = 3 and 3 + 1 = 4

4. Replace 4a with 3a + 1a.

5. 3a² + 3a + a + 1

6. Now factor by grouping!

7. 3a(a + 1) + 1(a + 1) = (a + 1)(3a + 1)

8. FOIL to check your work!

ax² + bx + c

Example: 4y² + 7y - 2 (a=4, b=7, c=-2)

1. Multiply ac - so 4(-2) = -8

2. We need two numbers that multiply to give us -8 that add up to 7. What are they??

3. They are 8 and -1. (8)(-1) = -8 and 8 + -1 = 7

4. Replace 7y with 8y - 1y.

5. 4y² + 8y - 1y - 2

6. Now factor by grouping!

7. 4y(y + 2) - 1(y + 2) = (y + 2)(4y - 1)

8. FOIL to check your work!

ax² + bx + c

Example: 6x² + 5x - 6 (a=6, b=5, c=-6)

1. Multiply ac - so 6(-6) = -36

2. We need two numbers that multiply to give us -36 that add up to 5. What are they??

3. They are 9 and -4. (9)(-4) = -36 and 9 + -4 = 5

4. Replace 5x with 9x - 4x.

5. 6x² + 9x - 4x - 6

6. Now factor by grouping!

7. 3x(2x + 3) - 2(2x + 3) = (2x + 3)(3x - 2)

8. FOIL to check your work!

Multiple Choice

Factor: 2x² + 11x + 12

• (x + 4)(2x + 3)

• (x + 4)(x + 6)

• (x + 6)(2x + 4)

• (x + 3)(2x + 3)

Multiple Choice

Factor: 2x² - 7x - 15

• (x + 1)(2x - 15)

• (x - 3)(3x + 5)

• (x - 5)(2x + 3)

• (x - 5)(x + 3)

Multiple Choice

Factor: 5x² - 14x + 8

• (2x - 4)(x - 2)

• (x - 8)(2x + 1)

• (x - 4)(5x + 2)

• (x - 2)(5x - 4)

Multiple Choice

Factor: 3v² - 4v - 7

• (v + 3)(3v - 7)

• (3v - 7)(v + 1)

• (v - 7)(2v + 1)

• (v - 7)(3v - 1)

Open Ended

Factor: 2n² + 13n + 15