Polynomial Operations
Add the Polynomials
(4x + 9) +(x - 4)
5x + 5
What is the remainder after dividing:
(4x4 + 6x3 - 6x2 + 5) / (x - 1)
r = 9
What is the constant term of the expansion of
(4x + 3)3?
27
What is the degree of the polynomial:
6x5 - 2x4 + 4x2 - 5x3 + 15?
5th degree
Determine f(3) given f(x) = 2x3 + 9x2 - 4x - 3.
f(3) = 120
Add the polynomials:
(-5x2+3x6+5) + (-5x6-5-3x2)
-2x6-8x2
Is x + 4 a factor of x3 + 3x2 - x + 12? Show your work.
yes, (x + 4)(x2 - x + 12)
What is the constant term of the expansion of
(95x + 2)5?
32
Give an example of a trinomial with a leading coefficient of -5 and a constant term of 12.
-5xn +axm + 12
Determine f(-1/2) given
f(x) = 2x4 - 3/2x3 + 5/4x2 + 9/4x + 2.
f(-1/2) = 3/2
Add the polynomials:
(x2 +3x + 5) + ( -x2 +6x)
9x + 5
Divide: (12x3 + 15x2 + 11x + 17) / (x + 1)
12x2 + 3x + 8 + 9/(x + 1)
Give the coefficient of the cubic term of the expansion of (x - 4)3.
1
Put the polynomial in standard form:
6x - 9x3 + 5 + 11x2
-9x3 + 11x2 + 6x + 5
or
9x3 - 11x2 - 6x - 5
Evaluate f(x) = 5x3 - 2x2 - 14x + 5 at x = 3
f(3) = 80
Subtract the polynomials:
(-x2 + 5x - 11) - (x2 + x)
-2x3 + 4x - 11
Find two polynomials that, when multiplied, give
3x2 - 17x - 6 (factor).
(3x + 1)(x - 6)
Expand: (3x + 1)3.
27x3 + 27x2 + 9x + 1
What is the coefficient of the quadratic term:
6x3 - 2x5 + 4x4 - 5x2 + 15?
-5
Evaluate f(x) = x3 - 12x2 + 8x - 10 at x = - 1
f(-1) = -31
Add the polynomials:
(6x - 2) + (x2 + x - 6)
6x3 + 4x2 - 38x + 12
Divide: (2x3 - 9x + 5) / (x - 2)
2x2 + 4x - 1 + 3/(x - 2)
Expand: (x - 3)4.
x4 - 4x3 +54x2 - 108x + 81
Put the polynomial in standard form:
1/6x2 - 1/3x3 + 5/9x + 1
6x3 - 3x2 - 10x - 18
Evaluate f(x) = 2x4 + 3x3 - 4x2 - 8x + 11 at x = 2
f(2) = 35