FACTORING TRINOMIALS OF THE FORM X2+BX+C

Section 6.2

Factoring Trinomials of the Form x2 + bx + c

Section 6.2

Factor trinomials of the form x2 + bx + cFactor out the greatest common factor and

then factor a trinomial of the form x2 + bx + c

Factoring Trinomials of the Form x2 + bx + c

Section 6.2

Multiply the binomials1.

2.

Trinomials of the form x2 + bx + c result from the product of two binomials of the form (x + m)(x + n).

( 2)( 5)x x

( 3)( 4)x x

2

2

5 2 10

7 10

x x x

x x

2

2

4 3 12

12

x x x

x x

Factoring Trinomials of the Form x2 + bx + c

Section 6.2

Multiply the binomials1.

2.

Notice, the first term in the trinomial comes from the product of the first terms in each binomial.

( 2)( 5)x x

( 3)( 4)x x

2

2 5 2 10

7 10

x x

x

x

x

2

2 4 3 12

12x

x x x

x

Factoring Trinomials of the Form x2 + bx + c

Section 6.2

Multiply the binomials1.

2.

Notice, the first term in the trinomial comes from the product of the first terms in each binomial.

Notice, the last term in the trinomial comes from the product of the last terms in each binomial.

( )(2 5)x x

( )(3 4)x x

2

2 5 2 1

7 1

0

0

x x

x

x

x

2

2 4 3 12

12x

x x x

x

Factoring Trinomials of the Form x2 + bx + c

Section 6.2

Multiply the binomials1.

2.

Notice, the first term in the trinomial comes from the product of the first terms in each binomial.

Notice, the last term in the trinomial comes from the product of the last terms in each binomial.

Notice, the middle term in the trinomial comes from the sum of the last terms in the binomial.

( )(2 5)x x

( )(3 4)x x

2

2 5 2 1

7 1

0

0

x x

x

x

x

2

2 4 3 12

12x

x x x

x

Factoring Trinomials of the Form x2 + bx + c

Proof Multiply (x + m)(x + n)

Section 6.2

x m x n 2x nx mx mn

2x n m x mn

The last term, the constant, is the product of the constants in

the binomials.

The middle term, the coefficient of x, is the sum of

the constants in the binomials.

Factoring Trinomials of the Form x2 + bx + c

Section 6.2

Factor1.

Trinomials of the form x2 + bx + c result from the product of two binomials of the form (x + m)(x + n) where m+n=b and mn=c.

To factor a trinomial:1. List all factor pairs of c

Start here since the amount of factors for a number is finite.

2. Find the pair whose sum or difference is b

3. Check the factorization by multiplying it back out

If c is positive, m and n will have the same sign and will add to b

If c is negative, m and n will have different signs and will subtract to b

2 9 20x x 4 5x x

What sums to 9?

1 8

2 7

3 6

...

1 10

41 50

...

AAACK!Infinite

possibilities!

What multiplies

to 20?

1 20

2 10

4 5

1 20

2 10

4 5

Limited number of options!

Which of

these sum to

9?

Factoring Trinomials of the Form x2 + bx + c

Section 6.2

Factor1.

2.

3.

4.

Trinomials of the form x2 + bx + c result from the product of two binomials of the form (x + m)(x + n) where m+n=b and mn=c.

To factor a trinomial:1. List all factor pairs of c

Start here since the amount of factors for a number is finite.

2. Find the pair whose sum or difference is b

3. Check the factorization by multiplying it back out

If c is positive, m and n will have the same sign and will add to b

If c is negative, m and n will have different signs and will subtract to b

2 9 20x x

2 13 22x x

2 3 40x x

2 5 36x x

4 5x x

2 11x x

4 9x x

8 5x x

Factoring Trinomials of the Form x2 + bx + cSpecial Cases

Factor1.

2.

A polynomial that cannot be factored is called prime.

Section 6.2

2 6 15y y

2 213 30a ab b 10 3a b a b

prime

Factoring Out the Greatest Common Factor

Section 6.2

Factor1.

Always begin by factoring out the GCF if it exists.

2.

3 23 4x x x

5 4 35 25 30x x x

1 4x x x

35 6 1x x x