Polynomial Functions
Write the polynomial in standard form. Then classify it by its degree and number of terms.
x^2+3x-4x^3
3rd Degree (cubic) Trinomial
-4x^3+x^2+3x
Write the polynomial in factored form.
x^4-x^3-6x^2
x^2(x-3)(x+2)
Find the real or imaginary solutions of the equation.
x^3+10x^2+24x=0
x=0,-4,-6
Divide using long division.
(x^2-13x-48) div (x+3)
x-16
Write the polynomial in standard form. Then classify it by its degree and number of terms.
6-2x^2-4+x^2
2nd Degree (quadratic) Binomial
-x^2+2
Write the polynomial in factored form.
x^3-2x^2+x
x(x-1)(x-1)
Find the real or imaginary solutions of the equation.
x^4-3x^2=-2x^2
x=0,1,-1
Divide using long division.
(3x^3-x^2-7x+6) div (x+2)
3x^2-7x+7, R -8
Determine the end behavior of the polynomial function.
y=5x^3-2x^2+1
Down & Up
Find the zeros of the function. State the multiplicity of multiple zeros.
y=(x-3)(x+4)(x-2)^2
x = 3, -4, 2 mult. of 2
Find the real or imaginary solutions of the equation.
x^4-13x^2+36=0
x=+-2,+-3
Divide using synthetic division.
(x^3+5x^2-x-9) div (x+2)
x^2+3x-7, R 5
Determine the end behavior of the polynomial function.
y=3x+10+8x^4-x^2
Up & Up
Find the zeros of the function. State the multiplicity of multiple zeros.
y=x^3(3x-4)(2x+5)
x= 4/3, -5/2, 0 mult. of 3
Find the real or imaginary solutions of the equation.
x^3-125=0
x=5,(-5+-5isqrt3)/2
Divide using synthetic division.
(-2x^3+15x^2-22x-15) div (x-3)
-2x^2+9x+5
Use Desmos to determine the End Behavior, # of Turning Points, and Intervals for the polynomial function.
y=-x+x^3+2
Down & Up
2 Turning Points
Increasing: -infinity to -.058
Decreasing: -0.58 to 0.58
Increasing: 0.58 to infinity
Find the relative Maximum and Relative Minimum of each function.
y=x^3-7x^2+10x
Relative Max of 4.06 @ 0.88
Relative Min of -8.21 @ 3.79
Find the real or imaginary solutions of the equation.
x^3+64=0
x=-4,2+-2isqrt3
Determine whether (x+4) is a factor of
x^3+3x^2-10x-24
Yes, it is a factor of the polynomial.
Use Desmos to determine the End Behavior, # of Turning Points, and Intervals for the polynomial function.
y=4x^2+9-5x^4-x^3
Down & Down
3 Turning Points
Increasing: - infinity to -0.71
Decreasing: -0.71 to 0
Increasing: 0 to 0.56
Decreasing: 0.56 to infinity
Find the relative Maximum and Relative Minimum of each function.
y=x^3-x^2-9x+9
Relative Max of 16.90 @ -1.43
Relative Min of -5.05 @ 2.10
Find the real solutions of the equation by graphing.
36x^3+6x^2=9x
x=-0.59,0,0.42
Use synthetic division and the Remainder Theorem to find P(a).
P(x) = 2x^4-9x^3+7x^2-5x+11, a=4
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