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Factoring Trinomials

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Factoring Trinomials

Lesson 29

- Trinomial – 3 terms.
- When factoring a trinomial, we need to look at the second term and the third term to help find the factors.
- The factors of a trinomial will be two binomials.

y2 + 3y + 2

Middle Term: Sum of 3

Last Term: Product of 2

What two numbers add up to +3

( 2 and 1 )

Same two numbers that multiply to give you +2

Factors:

Options: 1 and 2

Therefore: y2 + 3y + 2

= (y + 1)(y + 2)

g2 – 4g + 3

Middle Term: Sum of -4

Last Term: Product of 3

What two numbers add up to -4

Same two numbers that multiply to give you 3

Factors:

Options: 1 and 3

or -1 and -3

Therefore: g2 – 4g + 3

= (g - 1)(g - 3)

x2 – 7x + 12

Middle Term: Sum of -7

Last Term: Product of 12

What two numbers add up to -7

Same two numbers that multiply to give you 12

Factors:

Options: 1 x 12 or -1 x -12

2 x 6 or -2 x -6

3 x 4 or -3 x -4

Which gives a sum of -7?

(-3) + (-4)

Therefore: x2 – 7x + 12

= (x - 4)(x - 3)

YOU TRY!

x2 + 6x + 8

Middle Term: Sum of 6

Last Term: Product of 8

What two numbers add up to + 6

Same two numbers that multiply to give you 8

Factors:

Options:

Which gives a sum of +6?

Therefore: x2 + 6x + 8

= (x )(x )

SOLUTIONS

x2 + 6x + 8

Middle Term: Sum of 6

Last Term: Product of 8

What two numbers add up to + 6

Same two numbers that multiply to give you 8

Factors:

Options: 1 x 8 or -1 x -8

2 x 4 or -2 x -4

Which gives a sum of +6?

(2 and 4)

Therefore: x2 + 6x + 8

= (x + 2)(x + 4)

YOU TRY!

x2 + 2x - 15

Middle Term: Sum of 2

Last Term: Product of -15

What two numbers add up to + 2

Same two numbers that multiply to give you -15

Factors:

Options:

Which gives a sum of +2?

Therefore: x2 + 2x - 15

= (x )(x )

SOLUTIONS

x2 + 2x - 15

Middle Term: Sum of 2

Last Term: Product of -15

What two numbers add up to + 2

Same two numbers that multiply to give you -15

Factors:

Options: 1 x 15 or -1 x -15

3 x 5 or -3 x -5

Which gives a sum of +2?

-3 and +5

(use chart to help with signs)

Therefore: x2 + 2x - 15

= (x -3)(x + 5)

YOU TRY!

y2 - 4y - 12

Middle Term: Sum of - 4

Last Term: Product of -12

What two numbers add up to - 4

Same two numbers that multiply to give you - 12

Factors:

Options:

Which gives a sum of - 4?

Therefore: y2 – 4y - 12

= (y )(y )

SOLUTIONS

y2 - 4y - 12

Middle Term: Sum of - 4

Last Term: Product of -12

What two numbers add up to - 4

Same two numbers that multiply to give you - 12

Factors:

Options: 1 x 12 or -1 x -12

2 x 6 or -2 x -6

3 x 4 or -3 x -4

Which gives a sum of - 4?

- 6 and + 2

Therefore: y2 – 4y - 12

= (y - 6)(y + 2)

YOU TRY!

y2 - 5y + 4

Middle Term: Sum of - 5

Last Term: Product of + 4

What two numbers add up to - 5

Same two numbers that multiply to give you + 4

Factors:

Options:

Which gives a sum of - 5?

Therefore: y2 – 5y + 4

= (y )(y )

SOLUTIONS

y2 - 5y + 4

Factors:

Middle Term: Sum of - 5

Last Term: Product of + 4

What two numbers add up to - 5

Same two numbers that multiply to give you + 4

Options: 1 x 4 or -1 x -4

2 x 2 or - 2 x -2

Which gives a sum of - 5?

-1 and - 4

Therefore: y2 – 5y + 4

= (y -1)(y - 4)

- Check solutions to Lesson 28(2) on my desk
- Lesson 29 worksheet
- Reminder that Solutions are are on my desk