Find the product.

1.(x + 4)(x + 7)

2.(x + 14)(x + 2)= x2 + 16x + 28

= 5(2x + 5)

Factor.

3. 10x + 25

4. 28x2 + 35x

5. x3 + 2x2 + 4x + 8

= 7x(4x + 5)

= (x2 + 4) (x + 2)

= x2 + 11x + 28

Sign Rule:Sign Rule:When the last term is POSITIVE…When the last term is POSITIVE…

The signs inside the parenthesis will The signs inside the parenthesis will be the SAME as the be the SAME as the middle middle number’s signnumber’s sign

Figuring out the Figuring out the NumbersNumbers

Check to see…Check to see… What factors to give you the last What factors to give you the last

number AND adds to give you the number AND adds to give you the middle number?middle number?

x2 +7x + 6

For polynomials, how is factoring related to multiplying?

( )( )x x +

1+ 6

x2 +7x + 6

x2 + 9x + 14

For polynomials, how is factoring related to multiplying?

( )( )x x +

2+ 7

x2 + 9x + 14

x2 – 6x + 8

For polynomials, how is factoring related to multiplying?

( )( )x x – 2– 4

x2 – 6x + 8

x2 – 10x + 16

For polynomials, how is factoring related to multiplying?

( )( )x x – 2– 8

x2 – 10x + 16

Sometimes Sometimes you can you can

factor out a factor out a GCF 1GCF 1stst!!

2x2 – 16x + 24

For polynomials, how is factoring related to multiplying?

2( )( )x x – 2

– 6

2(x2 – 8x +12)

3y2 + 36y + 60

For polynomials, how is factoring related to multiplying?

4x2 +24x + 32

3(y +10)(y +2)

4(x + 2)(x + 4)

Sign Rule:Sign Rule:When the last term is NEGATIVE…When the last term is NEGATIVE…

The parenthesis will have The parenthesis will have DIFFERENT SIGNS.DIFFERENT SIGNS.

The The largerlarger factor will have the factor will have the SAME sign as the middle numberSAME sign as the middle number

x2 + 8x – 20

For polynomials, how is factoring related to multiplying?

( )( )x x – 2+

10

x2 – 4x – 21

For polynomials, how is factoring related to multiplying?

( )( )x x – 7+ 3

x2 – 9x – 36

For polynomials, how is factoring related to multiplying?

( )( )x x –

12+ 3