Polynomial Factoring

GCF

Difference of Two Squares

Factoring Trinomials

Real-World Applications

Random!

100

Find the GCF of the expression below. Factor out the GCF.

x²+x

x(x+1)

100

Completely factor the expression below (HINT: Look for a GCF first).

x²-100

(x+10)(x-10)

100

Completely factor the expression below (HINT: Look for a GCF first).

x²+7x+12

(x+3)(x+4)

100

A soccer ball is kicked into the air, and its height h (in meters) after t seconds is modeled by the equation:

h=t²−5t+6

At what times does the ball hit the ground?

2 and 3 seconds

100

What two things do we have to look for if I want to find the GCF of an expression?

The coefficients and the variables.

200

Find the GCF of the expression below. Factor out the GCF.

25x²+50x⁴

25x²(1+2x²)

200

Completely factor the expression below (HINT: Look for a GCF first).

a²+36

Prime!

200

Completely factor the expression below (HINT: Look for a GCF first).

y²-5y+6

(y-2)(y-3)

200

A rectangular garden has an area modeled by the equation:

A=y²+8y+15

Since the length is y+3, what is the width?

(y+5)

200

What two things do you need to utilize the difference of two squares?

A subtraction sign between the two terms and able to take the square-root of both terms.

300

Find the GCF of the expression below. Factor out the GCF.

a⁴b³-a³b+6a²b

a²b(a²b²-a+6)

300

Completely factor the expression below (HINT: Look for a GCF first).

9z²-25

(3z+5)(3z-5)

300

Completely factor the expression below (HINT: Look for a GCF first).

4x²-12x-40

4(x-5)(x+2)

300

A company sells a product, and its profit function (in dollars) is given by:

P(x)=x²−14x+45

where x is the number of items sold (in hundreds). At what sales levels does the company break even?

500 units and 900 units

300

What is Mr. Sirwell's first name?

Carter

400

Find the GCF of the expression below. Factor out the GCF.

15x⁷-30x³+12x⁴

3x³(5x⁴-10+4x)

400

Completely factor the expression below (HINT: Look for a GCF first).

4a⁴-16a²

4a²(a+2)(a-2)

400

Completely factor the expression below (HINT: Look for a GCF first).

6x³-18x²-48x

6x(x-4)(x+2)

400

Scientists are studying the population of a species of fish in a lake. The number of fish, P(t), t years after 2000, is modeled by the equation:

P(t)=t²-12t+35

Find when the fish population reaches zero, meaning the species either was introduced or went extinct.

In 2005 the fish was introduced and in 2007 the fish went extinct.

400

How old is Mr. Sirwell?

500

Find the GCF of the expression below. Factor out the GCF.

34x⁷y³z⁴-17x³y⁵z⁸+51x⁴y²

17x³y²(2x⁴yz⁴-1y³z⁸+3x)

500

Completely factor the expression below (HINT: Look for a GCF first).

6x⁴y²-24x²y⁴

6x²y²(x+2y)(x-2y)

500

Completely factor the expression below (HINT: Look for a GCF first).

2a²−7a−12

(2a+3)(a-4)

500

Doctors are studying how a drug is absorbed into a patient's bloodstream. The concentration of the drug (in mg/L) at time t (in hours) is modeled by:

C(t)=3t²−18t

Where t represents the time after the drug was administered. Find when the drug starts working and when it completely stops being effective.

The drug starts working right away at t=0 hours and the drug stops being effective at t=6 hours.