8.1.1
What do we call a quadratic expression that cannot be factored?
Nonfactorable
What two things do we need in order to factor a quadratic expression?
We need a Diamond Problem and a Generic Rectangle.
What are we missing in each of the following expressions. You do not need to solve just write down what is missing.
a. 9x2-4
b. 12x2-16x
c. 40-100m
a. bx term is missing
b. ones term (c term) is missing
c. x2 term is missing
Use (x-3)(x+2) and a generic rectangle to find the standard form.
x2-x-6
Factor if possible.
l. 9x2-1
l. (3x-1)(3x+1)
Use a generic rectangle to multiply (6x-1)(3x+2). Write your solution as a sum.
18x2+9x-2
Factor if possible, if not explain why.
a. x2+9x+18
(x+3)(x+6)
Factor the following quadratic expression, if possible.
a. k2-12k+20
a. (k-2)(k-10)
Factor the expression, if possible.
a. 2x2+3x-5
a. (2x+5)(x-1)
Factor each polynomial
a. x2-64
b. y2-6y+9
a. (x+8)(x-8)
b. (y-3)2
Use the greatest common factor to rewrite each sum as a product.
a. 4x+8
b. 10x+25y+5
c. 2x2-8x
a. 4(x+2)
b. 5(2x+5y+1)
c. 2x(x-4)
Factor if possible, if not explain why.
d. 3x2+5x-3
Not factorable, 9 has factors 1,9 and 3,3 and neither add up to 5.
Factor the following expression, if possible.
b. 6x2+17x-14
b. (2x+7)(3x-2)
Factor if possible.
d. 2x2+5x+7
d. Not factorable because no integers have a product of 14 and sum of 5.
Factor, if possible.
d. 9x2+12x+4
k. x2+4
d. (3x+2)2
k. not factorable
Multiply the expression below using a generic rectangle. Then verify Casey's pattern.
a. (4x-1)(3x+5)
12x2+17x-5
Factor if possible, if not explain why.
b. 4x2+4x+1
b. (2x+1)2
What is the standard form of a quadratic expression?
ax2+bx+c
Factor, if possible.
d. x2y-3xy-10y
d. y(x-5)(x+2)
Factor if possible, remember to factor out greatest common factors first.
d. 5x2-45
d. 5(x+3)(x-3)
Fill in the missing pieces of the Diamond Problems.
a. top: -80, bottom:2
b. top: 12, bottom: -7
c. top: 0, bottom:10
a. 10, -8
b. -3, -4
c. 0, 10
Factor the expressions completely. Remember to remove any common factors first!
a. 4x2-10x-6
(2x-6)(2x+1)
(x-3)(4x+2)
Factor the following expressions, if possible.
b. 2x2+5x+3
c. x2+5x-7
d. 3m2+m-14
b. (2x+3)(x+1)
c. not factorable
d. (3m+7)(m-2)
Without factoring, predict which quadratic expression will have more than one factored form.
a. 12t2-10t+2
b. 5p2-23p-10
c. 10x2+25x-15
a. Common factors so it could have more than one factored form
b. No common factors
c. Common factors so it could have more than one factored form
Factor each of the following expressions below.
a. 25x2-1
f. 9x2-100
Bonus: What are these called?
a. (5x-1)(5x+1)
f.(3x-10)(3x+10)
Bonus: Difference of squares