Operations with Polynomials
Find the sum:
(2x2 + 6x) + (-x2 -9x)
x2 - 3x
Given: f(x) = x2 - 10x + 19, find the range in interval notation.
[-6, infty)
Factor: 3x2 - 12
3(x + 2)(x - 2)
Solve for x:
3(x – 4) = 6(2x + 10)
x = -8
If (x+1) is a factor of P(x)=x3+1, what will the remainder be when you divide P(x) by (x+1)?
The remainder will be ZERO.
How can we find the remainder quickly when P(x) is divided by (x - 7)?
Evaluate P(7)
Find the difference:
(2x3 + 5x – 4) – (-x3 + x2 – 3x – 4)
3x3 - x2 + 8x
What is the domain for g(x) = x3 - 1?
All real numbers OR
(-infty, infty)
Factor Completely:
3x2 + 15x – 18
3(x + 6)(x – 1)
Solve for x:
x2 - 39 = 10
x = 7, x = -7
Find the quotient:
(3x^2-5x+2)/(x+1)
3x-8+10/(x+1)
What is the remainder when (x3 - 2x2 - 11) is divided by (x + 10)?
-1211
Find the product in simplest form:
(2x – 9)(2x + 5)
4x2 - 8x - 45
You know f(x) has a domain that is all real numbers and a range that is {y|y > 5}. What kind of function could f(x) be? Give 2 answers.
Quadratic, Absolute Value
Factor Completely:
8x2 + 10x - 12
2(4x - 3)(x + 2)
Solve for x:
2x2 - 36 = -x
x = -9/2, x = 4
(x^3+2x-3)divide (x-3)
x^2+3x+11+30/(x-3)
What is the remainder when (x3 - 3x2 + 6x + 8) is divided by (x + 1)?
-2
Find the product: (5x – 6)2
25x2 - 60x + 36
The domain of g(x) is given as {x| x > 11}. How is this written in interval notation?
(11, infty)
x3 + 125y3
(x + 5y)(x2 - 5xy + 25y2)
Jenna was asked to solve the equation below using the quadratic formula.
3x2 + 5x = 6
If she made no mistakes in her work, what would the value of the number under the radical equal?
97
Divide:
g(x) = x4 + 3x3 - 6x2 - 6x + 8 by (x + 4)
x3 - x2 - 2x + 2
Is (x+5) a factor of P(x)=2x2 - 3x - 10?
no
P(-5)=55, which means when P(x) is divided by (x+5) it would have a remainder of 55
What is the product of (x - 7) and (x2 - 3x + 1)?
x3 - 10x2 + 22x - 7
The range of a function is given as (-7, 12]. How is this written in set-builder notation?
{y| -7 < y le12}
Factor Completely:
2x3 + 7x2 - 18x - 63
(2x + 7)(x + 3)(x - 3)
Solve for x:
36x2 - 21x + 3 = 0
x = 1/3, x = 1/4
If P(x) = x4 - 3x3 - 6x + 1,
what is P(x) divided by (x + 3)?
x3 - 6x2 + 18x - 60 +
181/ (x + 3)
Is (x - 4) a factor of x3 - 4x2 - 2x + 1? Justify your answer.
NO - the remainder is -7
(substitute x=4 into the function OR show the division)