Factoring Polynomials

GCF

100

Solve this porblem using gcf 

y³+9y²

y²(y+9) 

200

-x²+x+20

-1(x-5)(x+4)

300

2y²-16y+32

2(y-4)²

400

4x³-25x²+6x

x(4x-1)(x-6)

500

ay-yx-x²+ax

(y+x)(a-x)

Grouping

100

12a³ − 9a² + 4a − 3

(3a² + 1)(4a − 3)

200

Factoring by grouping results in this kind of answer

Two binomials

300

m³ − m² + 2m − 2

(m² + 2)(m − 1)

400

192x² y + 72x³ − 24rxy − 9rx²

3x(8x − r)(8y + 3x)

500

105xuv + 60xv − 70xu − 90xv²

5x(7u − 6v)(3v − 2)

Factor Mix

100

Factor completely 

9x^2 +25

(3x+5)(3x+5)

200

Factor Completely 

x^2+4x+3

(x+1)(x+3)

300

Factor completely 

8a^2x-2b^2x

2x(4a^2 -b^2)

2x(2a-b)(2a+b)

400

Factor completely 

20x^2y^2+15x^3y^2z-30x^2y^3z^2

5x^2y^2(4y^3+3xz-6yz^2)

500

2a^2+5a-12

(a+4)(2a-3)

Trivia!

100

what does is mean when a polynomial is prime?

A polynomial with integer coefficients that cannot be factored into polynomials of lower degree

200

What does it mean to factor a polynomial

Factoring polynomials involves breaking up a polynomial into simpler terms so when  the terms are multiplied together they equal the original polynomial.  

300

What are the four things included in factoring polynomials

• Grouping like terms

• Finding the difference of perfect squares:

• Factoring quadratic trinomials

• Finding the greatest common factor

400

What number am I think of?

77

500

what is the inverse process of factoring polynomials

multiplying polynomials

Solve

100

Solve by factoring, Check your solution 

x^2-x-20=0

(x+4)(x-5)=0

x={-4,5}

200

Solve by factoring, Check your solution. 

2x^2-2x=4

(x+2/2)(x-4/2)

x:{-1, 2)

300

Solve by factoring, Check you answer 

3x^2=x+4

(x+3/3)(x-4/3)

x={-1, 4/3}

400

Solve using the quadratic formula.  Round answers to three decimal places if necessary.  

y^2 +10y+11=0

(-b +- sqrt(b^2-4ac))/(2a)

-3.268

500

Simplify.  

(x^2+4x+4)/(x+2)

x+2