Factoring Polynomials

Vocabulary

100

The largest factor that all the numbers share in an equation.

Greatest common factor

200

To express a number as a product of other whole numbers.

Factoring

300

containing one term.

monomial

400

Containing three terms.

Trinomial

500

Containing two monomials.

Binomial

Grouping Method

100

What is step three for the grouping method?

Group the first two terms together and then the last two terms together.

200

 3a³ + 12a² + a + 4 

(Solve using grouping method)

(a + 4)(3a² + 1)

300

What is step one for the grouping method?

Group the first two terms together and then the last two terms together.

400

What is step two of the grouping method?

Factor out a GCF from each separate binomial.

500

3n³ + 2n² - 3n - 2

(Solve using grouping method)

(n + 1)(n - 1)(3n + 2)

Greatest Common Factor Method

100

What is step three when using find the greatest common factor method?

Factor by grouping.

200

4x³−2x²+6x

(solve using the greatest common factor method.)

2x(2x²−x+3)

300

What is step one of the greatest common factor methods?

Find the greatest common factor of two or more expressions

400

x² + 9x + 14

(solve using greatest common factor method)

(x + 7)(x + 2)

500

What is step two of the greatest common factor method?

Factor the greatest common factor from a polynomial.

Word Problems

100

The top of a cosmetics case is a rectangle in which the width is 2 centimetres greater than the length. The expression x²+26x+168 represents the are of the top of the case. Factor the expression.

(x+14)(x+12)

200

A square has an area of 9x²+30xy+25y² square inches. The dimensions are binomials with positive integer coefficient What is the perimeter of the square.

4(3x+5y) or (12x+20y)

300

A rectangular garden is being separated into 6 equal sections for different types of flowers. The area of the garden is (12x+30) square meters. What is the area of each section of the garden

(2x+5)

400

A ticketing company for sporting events analyzes the ticket purchasing patterns. The expression 9a²-4b² is developed to help officials calculated the likely number of people who will buy tickets for a certain sporting event. Factor the expression.

(3a+2b)(3a-2b)

500

The area of a rectangular parking lot is represented by the expression a²-25, where the length is longer  than the width. Factor the expression to determine the possible dimensions of the length and width of the parking lot. If the length of the parking lot is 105 yards, what is the width of the parking lot?

(a-5)(a+5) 

95 yards

Challenge

100

which expression does not belong?

x²+2x-24

x²+11x+24

x²-10-24

x²-12x 24

x²+12x+24

200

16x³−48x²+32x

16x(x−2)(x−1)

300

a³b²+a⁴b+a²bc³−a³b³c²

a²b(ab+a²+c³−ab²c²)

400

x²y³z²+x⁴y³z

x²y³z(z+x²)

500

x²+20x+96

(x+12)(x+8)