POLYNOMIAL OPERATIONS
5.1
5.1
Simplify the expression. Assume that no variable equals 0.
((3a^3)/(b^4))^2
(9a^6)/(b^8
Use long division to find the quotient.
(x^2-13x+12)div(x-1)
x-12
State the degree and leading coefficient of the polynomial.
3x^5+2x^2-4-8x^6
degree=6
leading coefficient=-8
Factor the polynomial. If the polynomial cannot be factored, write prime.
x^3+5x^2-2x-10
(x+5)(x^2-2)
If f(x)=2x4-5x2+8x-7, find f(6).
2453
State the possible number of positive real zeros and imaginary zeros of the function.
f(x)=x^4-5x^3+2x^2+5x+7
postive zeros: 2 or 0
imaginary zeros: 4, 2, or 0
Simply the expression.
(4x^2-9x+3)+(-2x^2-5x-6)
2x^2-14x-3
Use synthetic division to find
(x^3-4x^2+6x-4)div(x-2)
x^2-2x+2
Find b(2x-1)-3b(x) if b(m)=2m2+m-1
2x^2-9x+3
Factor the polynomial. If the polynomial cannot be factored, write prime.
a^2+3ay+2ay^2+6y^3
(a+3y)(a+2y^2)
Given a polynomial and one of its factors, Find the remaining factors of the polynomial.
x^3-x^2-10x-8;x+2
x-4, x+1
List all of the possible rational zeros for the function.
f(x)=x^3-6x^2-8x+24
+-1, +-2, +-3, +-4, +-6, +-8, +-12, +-24
Simplify the expression.
(2a^3+5a-7)-(a^3-3a+2)
a^3+8a-9
Use synthetic division to find
(4y^3-6y^2+4y-1)div(2y-1)
2y^2-2y+1
Graph f(x)=x3-3x2+5. Estimate the relative maxima and relative minima. (Where the x value is closest to)
relative max: near x=0
relative min: near x=2
Factor the polynomial. If the polynomial cannot be factored, write prime.
x^3-400
prime
Given a polynomial and one of its factors, Find the remaining factors of the polynomial.
2x^3+17x^2+23x-42;x-1
x+6,2x+7
List all of the possible rational zeros for the function.
f(x)=2x^4+3x^2-x+15
+-1, +-3, +-5, +-15, +-1/2, +-3/2, +-5/2, +-15/2
Find
4/3x^2(6x^2+9x-12)
8x^4+12x^3-16x^2
Simplify
(24a^3b^2-16a^2b^3)/(8ab
3a^2b-2ab^2
Determine the consecutive integer values of x between which each real zero of the function is located.
f(x)=x^3-2x^2+5
between x=-2 and x=-1
Factor the polynomial. If the polynomial cannot be factored, write prime.
24x^5+3x^2y^3
3x^2(2x+y)(4x^2-2xy+y^2)
Given a polynomial and one of its factors, Find the remaining factors of the polynomial.
x^4+2x^3+2x^2-2x-3;x-1
x+1, x^2+2x+3
Find all the rational zeros for the function.
f(x)=2x^3+4x^2-6x
0, -3, 1
Find
(a^2+3a-4)(a+2)
a^3+5a^2+2a-8
Use synthetic division to find
(12b^2+23b+15)div(3b+8)
4b-3+39/(3b+8)
If a polynomial function has a degree of 6, at most how many turning points can that polynomial function have?
5
Solve
x^4-29x^2+100=0
-5, -2, 2, 5
Given a polynomial and one of its factors, Find the remaining factors of the polynomial.
x^4+2x^3-8x-16; x+2
x-2, x^2+2x+4
GIVEN x=4 is a solution to the equation, Find the remaining rational zeros for the function.
f(x)=x^4-4x^3-7x^2+22x+24
-2, -1, 3