GCF
Find the GCF of the expression below. Factor out the GCF.
x2+x
x(x+1)
Completely factor the expression below (HINT: Look for a GCF first).
x2-100
(x+10)(x-10)
Completely factor the expression below (HINT: Look for a GCF first).
x2+7x+12
(x+3)(x+4)
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
What two things do we have to look for if I want to find the GCF of an expression?
The coefficients and the variables.
Find the GCF of the expression below. Factor out the GCF.
25x2+50x4
25x2(1+2x2)
Completely factor the expression below (HINT: Look for a GCF first).
a2+36
Prime!
Completely factor the expression below (HINT: Look for a GCF first).
y2-5y+6
(y-2)(y-3)
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)
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.
Find the GCF of the expression below. Factor out the GCF.
a4b3-a3b+6a2b
a2b(a2b2-a+6)
Completely factor the expression below (HINT: Look for a GCF first).
9z2-25
(3z+5)(3z-5)
Completely factor the expression below (HINT: Look for a GCF first).
4x2-12x-40
4(x-5)(x+2)
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
What is Mr. Sirwell's first name?
Carter
Find the GCF of the expression below. Factor out the GCF.
15x7-30x3+12x4
3x3(5x4-10+4x)
Completely factor the expression below (HINT: Look for a GCF first).
4a4-16a2
4a2(a+2)(a-2)
Completely factor the expression below (HINT: Look for a GCF first).
6x3-18x2-48x
6x(x-4)(x+2)
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.
How old is Mr. Sirwell?
22
Find the GCF of the expression below. Factor out the GCF.
34x7y3z4-17x3y5z8+51x4y2
17x3y2(2x4yz4-1y3z8+3x)
Completely factor the expression below (HINT: Look for a GCF first).
6x4y2-24x2y4
6x2y2(x+2y)(x-2y)
Completely factor the expression below (HINT: Look for a GCF first).
2a2−7a−12
(2a+3)(a-4)
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.