Free Printable Solving Polynomial Equations

1.

Factor: x³+ 1

a)

(x + 1)³

b)

(x+1)(x²- x + 1)

c)

(x - 1) (x² + x - 1)

d)

(x + 1)(x² - 2x + 1)

2.

Factor by grouping:
4p³+8p²+3p+6

a)

(2p²+3)(p+2)

b)

(2p²+6)(p+4)

c)

(4p²+3)(p+2)

d)

(4p²+8p)(3p+6)

3.

Find the zeros of the function $f\left(x\right)=-2x^5+2x^4+40x^3$ and describe the end behavior of the graph.

a)

0, 5,-4 and as x $\rightarrow\infty$ , f(x) $\rightarrow-\infty$ and as x $\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

b)

0,-5,4 and as x $\rightarrow\infty$ , f(x) $\rightarrow-\infty$ and as x $\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

c)

0,5,-4 and as $x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty\ and\ as\ x\rightarrow-\infty,\ f\left(x\right)\ -\infty$

d)

0, 5,4 and as $x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty\ and\ as\ x\rightarrow-\infty,\ f\left(x\right)\ -\infty$

4.

Write a polynomial function of least degree that has a leading coefficient of 1 and zeros at 1,4, and -2.

a)

(x-1)(x-4)(x+2)

b)

$x^3+3x^2+6x+8$

c)

$x^3-3x^2-6x+8$

d)

(x+1)(x+4)(x-2)

5.

$2x^3-12x^2+18x=0$

Solve the equation

a)

x=0, x= -3

b)

x=0, x=3

c)

x=0, x=6

d)

x=0, x= -6

6.

$3x^6-11x^5-20x^4$

Factor

a)

$x^4\left(3x^2-11x-20\right)$

b)

$x^4\left(3x-4\right)\left(x+5\right)$

c)

$x^4\left(3x+5\right)\left(x-4\right)$

d)

$x^4\left(3x+4\right)\left(x-5\right)$

7.

Determine if x-5 is a factor of $x^3-5x^2-9x+45$

a)

Factor

b)

Not a Factor

8.

The standard equation of a circle with radius r and center (h,k) is $\left(x-h\right)^2+\left(y-k\right)^2=r^2$ Rewrite the equation of the circle in standard form and identify the center and radius. $x^2-2x+1+y^2=25$

a)

$\left(x+1\right)^2+\left(y+0\right)^2=5^2$ Center: (-1, 0) Radius: 5

b)

$\left(x-1\right)^2+\left(y-0\right)^2=5^2$ Center: (1,0) Radius: 5

c)

$\left(x-1\right)^2+\left(y-0\right)^2=25$ Center: (1,0) Radius: 5

d)

$\left(x+1\right)^2+\left(y+0\right)^2=25$ Center (-1,0) Radius: 5

9.

$x^3-125$

a)

$\left(x+5\right)\left(x^2-5x+25\right)$

b)

$\left(x+5\right)^3$

c)

$\left(x-5\right)\left(x^2-5x-25\right)$

d)

$\left(x-5\right)\left(x^2+5x+25\right)$

Solving Polynomial Equations

Total questions: 9

Worksheet time: 25mins

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