4.4: FactoringTrinomials with a Leading

Coefficient of 1

November 9th

Trinomials with a leading coefficient of 1.

EX 2:

x2 + 5x + 6

How:Make a table of factors of the

last number.

Pick the factors that add up to the middle number.

Solution:

FACTORING

(x + 2)(x + 3) 6 1 6 2 3

After you’ve factored, what does it look like?

A FOIL problem!

So FOIL it and make sure you get the original problem.

FACTORING

Trinomials with a leading coefficient of 1.

EX 3:

x2 + 5x + 6

How:Make a table of factors of the

last number.

Pick the factors that add up to the middle number. Check.

Solution:

FACTORING

(x + 2)(x + 3) 6 1 6 2 3

Trinomials with a leading coefficient of 1.

EX 4:

x2 + 7x + 12

How:Make a table of factors of the

last number.

Pick the factors that add up to the middle number. Check.

Solution:

FACTORING

(x + 3)(x + 4) 12

1 12

2 6

3 4

Trinomials with a leading coefficient of 1.

EX 5: as an Equation:

y = x2 + 7x + 6

How:Make a table of factors of the

last number.

Pick the factors that add up to the middle number. Check.

Solution:

FACTORING

y = (x + 6)(x + 1) 6

1 6

2 3

Trinomials with a leading coefficient of 1.

EX 6:

x2 - 5x + 4 = y

How to do it:Make a table of factors of the

last number.

Pick the factors that add up to the middle number.

Solution:

FACTORING

notice the signs

Trinomials with a leading coefficient of 1.

EX 6:

x2 - 5x + 4 = y

How to do it:Make a table of factors of the

last number. 4

1 4

2 2

Pick the factors that add up to the middle number. None of these work! TRY negatives.

Solution:

FACTORING

notice the signs

Trinomials with a leading coefficient of 1.

EX 6:

x2 - 5x + 4 = y

How to do it….Make a table of factors of the

last number. 4

-1 -4

-2 -2

Pick the factors that add up to the middle number. None of these work! TRY negatives. Check with foil.

Solution:

FACTORING

(x – 1)(x – 4) = y

notice the signs

EX7: x2 + 6x + 5 = (x + 5)(x + 1)

EX 8:x2 + 10x + 16 =(x + 2)(x + 8)

EX 9:a2 – 5a + 6 = (a – 2)(a – 3)

Trinomials with a leading coefficient of 1.

EX 10: notice the signs

f(x) = x2 + 2x – 15

How to do it….Make a table of factors of the

last number.

Pick the numbers that add up to be the middle number. Check with foil or graph in y= screen.

Solution:

f(x) = (x + 5)(x – 3) -15 1 -15 3 -5 -1 15 -3 5

EX 11:

y2 + 3y - 10 =

(y + 5)(y – 2)

9.5 FACTORING

Take out the GCF & Factor the Remaining Trinomial

EX 12:

5x2 – 25x + 20

How:

Find what is in common in each term and put in front. See what is left.

Check answer by foiling first, then distributing or in y= screen.

Solution:

5( )x2 – 5x + 4

5(x – 4)(x – 1)

Homework

worksheet