PC - Polynomial Function Unit Review
Give the y-intercept of y=-3x⁴-2x³+2x-1.
-1
Find the zeros and their multiplicities. y = -3(x+1)²(x-4)³
-1 (mult. of 2) 4 (mult. of 3)
Give the y-intercept of y=3x⁶-4x⁵+7x²-3.
-3
Find the zeros and their multiplicities. y = (x+3)²(x-1)³
-3 (mult. of 2) 1 (mult of 3)
Give the y-intercept of y=4x-3x³.
0
Find the zeros and their multiplicities. y = -3x(x+2)(x-5)
0 (mult of 1) -2 (mult of 1) 5 (mult of 1)
Find the zeros and their multiplicities. y = -2x(x-4)²
0 (mult of 1) 4 (mult of 2)
For a polynomial of degree 4, what would be the maximum number of real zeros and what would be the minimum number of real zeros possible?
The maximum would be 4 real zeros. The minimum would be 0 real zeros.
For a polynomial function of degree 5, what is the maximum number of real zeros and what is the minimum number of real zeros possible?
The maximum would be 5 real zeros. The minimum would be 1 real zero.
Approximate the real zero(s) to the nearest hundredth. y=3x³-2x²+1
x≈-.53
Approximate the real zero(s) to the nearest hundredth. y=-2x⁴+3x²+5
x≈-1.58 or x≈1.58
Approximate the real zero(s) to the nearest hundredth. y=x³+2x-1
x≈.45
Approximate the real zero(s) to the nearest hundredth. y=x⁴-2x+1
x≈.54 or x=1
Solve x⁴-5x²-36=0.
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Solve x³-1=0.
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Solve, writing your solutions in interval notation. (x+3)(x-2)²≤0
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Solve, writing your solutions in interval notation. (x²+7)(2x²+1)>0
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Solve, writing your solutions in interval notation. 25-x²≥0
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Solve, writing your solutions in interval notation. x²+4x≥5
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Solve, writing your solutions in interval notation. x⁴-5x²+4≤0
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Solve, writing your solutions in interval notation. x⁴<4x²
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Solve, writing your solutions in interval notation. x⁵+9x≥10x³
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Use synthetic division to divide. (5x³-3x²-6) ÷ (x-1)
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Use synthetic division to divide. (8x⁴+75x³+21x²-48x+53) ÷ (x+9)
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Use synthetic division to divide. (x³+5) ÷ (x+2)
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Use synthetic division to divide. (x³+6x²-21x-18) ÷ (x-3)
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Use synthetic division to divide. (x³-13x²+24x+18) ÷ (x-3)
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What is the remainder when 3x²+7x-20 is divided by x+1?
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What is the remainder when 3x²+7x-20 is divided by x-1?
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What is the remainder when 3x²+7x-20 is divided by x-2?
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What is the remainder when 4x²-x+3 is divided by x-4?
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What is the remainder when 7x²-3x+2 is divided by x+4?
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What would be the linear factorization of x³+6x²-x-30?
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What would be the linear factorization of x⁴+5x³-15x²-5x+14?
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What would be the linear factorization of x⁴-6x³+5x²+12x?
Answer:
Give the y-intercept of y=8x⁵-3x³+2.
2
Find the zeros and their multiplicities. y = (x-2)(x+5)(x+1)(x-4)
2 (mult of 1) -5 (mult of 1) -1 (mult of 1) 4 (mult of 1)
If 2+3i is a zero of a polynomial function, what other zero must exist for the function?
2-3i (from the Complex Conjugates Theorem)
Give the y-intercept of y=2x³-3x²+4x+3.
3
If -4i is a zero of a polynomial functions, what other zero must exist for the function?
4i (from the Complex Conjugates Theorem)
Describe the end-behavior of y=-3x⁴-2x³+2x-1.
Answer:
Describe the end-behavior of y=2x³-3x²+4x+3.
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Describe the end-behavior of y=3x⁶-4x⁵+7x²-3.
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Describe the end-behavior of y=4x-3x³.
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Describe the end-behavior of y=8x⁵-3x³+2.
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Find all possible rational zeros for 10x⁴+x³+7x²+x-3=0
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Find all possible rational zeros for 12x³-32x²+25x-6=0
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Find all possible rational zeros for 2x³-9x²-11x+8=0
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Find all possible rational zeros for x³-x²+2x-2=0
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Find the exact values for all the zeros of f(x)=2x⁴-5x³-9x²+15x+9.
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Find the exact values for all the zeros of f(x)=2x⁴-9x³-22x²+18x+36.
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Find the exact values for all the zeros of f(x)=x³-3x²-5x+15.
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Find the exact values for all the zeros of f(x)=x³-5x²+2x-10.
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Find the exact values for all the zeros of f(x)=x⁴-6x³+10x²-6x+9.
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Find the exact values for all the zeros of f(x)=x⁴-6x³+6x²+24x-40.
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Find the zeros of f(x)=x³+x²-6x.
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Find the zeros of f(x)=x³-2x²-8x.
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Find the zeros of f(x)=x³-7x²-8x.
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Find where f(x) is 0, positive, or negative. f(x)=(x+2)²(x-1)²
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Find where f(x) is 0, positive, or negative. f(x)=(x+3)(x-1)
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Find where f(x) is 0, positive, or negative. f(x)=(x+3)(x-1)(x+2)
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Find where f(x) is 0, positive, or negative. f(x)=(x-3)²(x+2)³
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Find where f(x) is 0, positive, or negative. f(x)=x(x+2)²
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Find where f(x) is 0, positive, or negative. f(x)=x(x+3)(x-3)
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Graph y = (x+3)²(x-1)³.
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Graph y = (x-2)(x+5)(x+1)(x-4).
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Graph y = -2x(x-4)².
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Graph y = -3(x+1)²(x-4)³.
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Graph y = -3x(x+2)(x-5).
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Graph y = 2x(x-3)(x+4).
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Is (x+2) a factor of x³+4x²+x-6?
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Is (x+3) a factor of x³+4x²+x-6?
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Is (x-1) a factor of x³+4x²+x-6?
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Is (x-2) a factor of x³+4x²+x-6?
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Is (x-3) a factor of x³+4x²+x-6?
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Solve x³+3x²-14x-20=0.
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Solve x³-2x²-3x+6=0.
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Solve x⁴+6x²+8=0.
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Solve x⁴-14x²+45=0.
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