Operations with Polynomials
Find the sum:
(2x2 + 6x) + (-x2 -9x)
x2 - 3x
Factor: 4x2 - 400
4(x + 10)(x - 10)
Solve for x:
3(x – 4) = 6(2x + 10)
x = -8
What important information does the degree of a polynomial equation tell you?
The number of solutions/roots.
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
Factor Completely:
3x2 + 15x – 18
3(x + 6)(x – 1)
Solve for x: x2 - 39 = 10
x = 7, x = -7
Solve for x:
x2 + 6x + 2 = 0
(-6 +- sqrt(24))/2
Is (x - 4) a factor of x3 - 4x2 - 2x + 1? Justify your answer.
NO - the remainder is -7
Find the product in simplest form:
(2x – 9)(2x + 5)
4x2 - 8x - 45
Factor Completely:
8x2 + 10x - 12
2(4x - 3)(x + 2)
Solve for x: 2x2 - 36 = -x
x = -9/2, x = 4
Find all roots and their corresponding multiplicity:
(x2 - 16)(x2 + 3x - 28) = 0
4 (multiplicity of 2)
-4
7
What is the remainder when (x3 - 2x2 - 11) is divided by (x + 10)?
789
Find the product: (5x – 6)2
25x2 - 60x + 36
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
Factor: x3 - 27y3
(x - 3y)(x2 + 3xy + 9y2)
Divide g(x) = x4 + 3x3 - 6x2 - 6x + 8 by (x + 4)
x3 - x2 - 2x + 2 (remainder = 0)
What is the product of (x - 7) and (x2 - 3x + 1)?
x3 - 10x2 + 22x - 7
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
Factor Completely: 3x4 - 24x3 - 6x2 + 48x
3x(x2 - 6)(x - 8)
P(x) = x4 - 3x3 - 6x + 1
What is P(x) divided by (x + 3)?
x3 - 6x2 + 18x - 60 +
181/ (x + 3)