Solving and Factoring Polynomials

Methods to Solving and Factoring Polynomials

One way is the box method. The other is the F.O.I.L. mehtod.

First Oustide Inside Last

(x+a) (x+b)

(x+a) (x+b)

(x+a) (x+b)

(x+a) (x+b)

x

a

x

b

x squared

x times a

x times b

a times b

Box Method

For the box method you have to change (x+a) times (x+b) to x squared + ax + bx + ab. To get that you have to first make a box. Next you split the box into two by two, two by three, or so on. Now you put the x and a down in one colum and the other x and b in the row. Lastly you solve.

1.

2.

3.

x a

x b

4.

x b

x a

xx ax

bx ab

x squared + ax + bx + ab

F.O.I.L. Method

First you multiply the first two numbers in both ( ). Next you do the outside of both. Now the inside of both. Last the last two of both.

1.

2.

3.

4.

(x + a) (x + b) x times x is x squared

(x + a) (x + b) x times b is bx

(x + a) (x + b) x times a is ax

(x + a) (x + b) a times b is ab

So overall you will have x squared + bx + ax + ab

Examples

(m + 4) (m + 8)

1.

2.

3.

4.

(a + 16) (a + 2)

(t + 3) (t + 4)

(h + 10) (h + 5 + 2h)

a 16

a 2

h 10

h 5 2h

a^2 16a

2a 32

h^2 10h

5h 50

2h^2 20h

a^2 + 18a + 32

3h^2 + 35h + 50

m(m)= m^2 m(8)= 8m m(4)= 4m 4(8)= 32

m^2 + 12m + 32

t(t)= t^2 t(4)= 4t t(3)= 3t 3(4)= 12

t^2 + 7t + 12