Solving Polynomial EquationsType Rules

Difference of two squares

Perfect Square Trinomials

General trinomials

Grouping ax+bx+ay+by = x(a+b)+y(a+b) = (x+y)(a+b)

Greatest Common Factor 4

Sum of Two Cubes

Difference of Two Cubes

Factoring

• If a polynomial is not factorable then it is PRIME.

• is prime

Factor Completely

1)

2)

1¿(2𝑐−5𝑑 )(4𝑐2+10𝑐𝑑+25𝑑2)

2)

Quadratic formEquations with degrees higher than 2 (or lower than 2) can sometimes be “reduced” or converted to quadratic equations .

we can substitute w = and rewrite the equation as: and then solve the new equation(w-3)(w-1)=0 so w=3, w=1 butw=so x=

Or

-3) -1)=0

Equations Reducible to Quadratic Form• Changing an equation that is not in quadratic form into

quadratic form is called reducing the equation to quadratic form.

• Steps1. Change any verbal equation into an algebraic equation.2. Determine what, if any, substitution can be made to

change the equation into a quadratic equation.3. Solve using any method of solving a quadratic equation4. Reverse the substitution to get the answer to the

original problem.5. CHECK – make sure the answer makes sense.

substitution

Substitute y= =0 (2y+3)(y-4)Substitute back

(2 +3)(-4)=02 +3=0 -4 2 3 4No real solution +2,-2

Practice• What would we substitute in the following

equations?• 1.• 2. 023

04536

24

xx

xx 2xy 3xy

Now solve problem 1. Remember to check the solutions!

Solution

• 1) x = {±1,±2}

More challenging!!

• What would we substitute:

0211 222

x

x

x

x

1±√2 ,12± √5

2

x

xy

12

Worksheets Factoring and Word Problems