Vocabulary
What is the DEGREE of 2x4+9x3-5x2+6
4
The sum of 3x2+4x-2 and x2-5x+3 is equal to
Combine like terms!
Answer: 4x2-x+1
When written in standard form, the product of (3+x) and (2x-5) is equal to:
(3+x)(2x-5) = 6x-15+2x2-5x -->
2x2+x-15
Factor the polynomial and write as the product of two binomials:
x2+5x-6
Answer: (x+6)(x-1)
Which is a factor of x2+5x-24?
1) (x+4)
2) (x-4)
3) (x+3)
4) (x-3)
x2+5x-24 = (x+8)(x-3)
The answer is choice (3) --> (x+3)
Name three factoring methods we have learned in class.
GCF
AM
Slide N Divide
The expression (x2-5x-2)-(-6x2-7x-3) is equivalent to
(x2-5x-2)-(-6x2-7x-3) Distribute the negative to each term!
Answer: 7x2+2x+1
When written in standard form, the expression
2x(x-4)-3(x+5)
is equal to
2x(x-4)-3(x+5)
Answer: 2x2-11x-15
Rewrite the polynomial as the product of two binomials
2x2+8x-10
Answer: 2(x+5)(x-1)
If 3x is a factor of 3x2-9x, what is the other factor?
3x2-9x = 3x(x-3)
The answer is (x-3)
Write an example of a polynomial with 4 terms and degree of 3.
Mr. Chatergoon/Ms. Patel/Mr. Genua will check!
3(x2+2x-3)-4(4x2-7x+5)
Distribute the "3" to (x2+2x-3) and
Distribute the "-4" to (4x2-7x+5)
Answer: -13x2+34x-29
The expression (m-3)2, when written in standard form, is equivalent to:
(m-3)2 = (m-3)(m-3)
Answer: m2-6m+9
Which expression is NOT equivalent to 2x2+10x+12?
1) (2x+4)(x+3)
2) (2x+6)(x+2)
3) (2x+3)(x+4)
4) 2(x+3)(x+2)
The answer is choice (3)
(2x+3)(x+4)
5x+4x2(2x+7)-6x2-9x Distribute to get
5x+8x3+28x2-6x2-9x Combine like terms
Answer: 8x3+22x2-4x
Write an example for the following:
"The product of two conjugate binomials"
Example: (x+4)(x-4)
Same variables/constants, but opposite signs!
When 4x2+7x-5 is subtracted from 9x2-2x+3, the result is
"subtracted from" means to FLIP the order!
(9x2-2x+3) - (4x2+7x-5) and distribute the negative
Answer: 5x2-9x+8
What is the product of x2-2x+3 and x+1?
(x2-2x+3)(x+1) = x3-x2+x+3
When factored completely, the expression 3x2-9x+6 is equivalent to:
Answer: 3(x-1)(x-2)
Answer:
(4x+9)(4x-9)
Which factoring methods would you use to simplify the following:
A. 2x2-3x-20
B. 4x2+5x-6
C. x2+6x+9
A. 2x2-3x-20 (GCF-We can divide each term by 2)
B. 4x2+5x-6 (Slide N Divide) Leading Coefficient > 1
C. x2+6x+9 (AM) - Leading Coefficient equals 1
If A= 3x2+5x-6 and B=-2x2-6x+7, then A-B equals
A-B equals:
(3x2+5x-6)-(-2x2-6x+7) #Always use parentheses
Answer: 5x2+11x-13
Which expression is NOT equivalent to -4x3+x2-6x+8
1) x2(-4x+1)-2(3x-4)
2) x(-4x2-x+6)+8
3) -4x3+(x-2)(x-4)
4) -4(x3-2)+x(x-6)
Original Polynomial: 4x3+x2-6x+8
The answer is choice (2)
x(-4x2-x+6)+8 = -4x3-x2+6x-8
Which product is equivalent to 4x2-3x-27?
1) (2x+9)(2x-3)
2) (2x-9)(2x+3)
3) (4x+9)(x-3)
4) (4x-9)(x+3)
The answer is choice (3)
(4x+9)(x-3)
Factor completely: 15x+3x2-42
3x2+15x-42
3(x2+5x-14)
3(x+7)(x-2)