5.4A- Factoring & Solving Polynomials

• Completely factored= Can’t factor any ( ) more. Each factor has integer coefficients.

• Factors= (ax + #)(ax + #) – Each power of x is HALF the degree– Multiply (FOIL, distribute) to check factors

• Solutions= zeros= roots= x-intercepts– Set each factor = 0 and solve– Solutions = opposite of # ÷a– Total solutions = degree– Factor of # has solution of ZERO , n times

Types of factoring

• 1.) Divide out largest common monomial• 2.) Difference of square• 3.) Perfect square trinomials• 4.) Factorable trinomial(Guess & check with X)

• 5.) Cubes• 6.) Grouping

Dividing out largest common monomial

• Divide ALL terms – Largest # possible– Smallest power of shared variables

• Monomial(remaining polynomial)• Remaining polynomial MAY need to be

factored more.

Examples: Factor & solve

• 1.

• 2. + 20x

• 3.

Factoring with Squares

• 1.) Difference of 2 squares– 2 terms with SUBTRACTION– BOTH terms have nice (may need to ÷ first)– Factors: ( + )( -

• 2.) Perfect Square trinomials– Middle = 2()()– First AND last have nice – Factors: ( )( )– BOTH signs are SAME and match MIDDLE term – BOTH factors are the SAME ( repeated solution)

Examples: Factor & Solve

• 4.

• 5. - 36

• 6.

• 7. + 8x + 16

• 8.

• 9.

Factorable Trinomial (Guess & Check)• + bx + c b= “O + I” of the “FOIL”

(a #) (a #) : Factor More if possibleSolutions: OPPOSITE of # ÷ a if factor power = 1Solutions: set each ( ) = 0 & solve if factor power>1

ac

b

Mult. = acADD = b

+ + - -

+ - + -+ +

- - Big +

- Sm Big - + Sm

Examples: Factor & Solve

• 10.

• 11. + 3x – 28

• 12.

• 13. + (Divide first!)