9th
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12th
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Mathematics

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Shayla Bushhousen

4 years

Mathematics

9th -

12thgrade

5.2pc Real Zeros of a Polynomial

Shayla Bushhousen

20
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12 questions

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1. Multiple Choice
1 minute
1 pt
The degree of the polynomial determines the max number of roots.
True
False
2. Multiple Choice
3 minutes
1 pt
The Rational Zeros Theorem states $\frac{p}{q}$ is a rational zero of $f\left(x\right)$ if $p$ is a factor of the constant term and $q$ is a factor of the leading coefficient .

Is -3 a possible rational zero for the polynomial $f\left(x\right)$ ?

$f\left(x\right)=3x^3+2x^2-5x+2$

Why or why not?
Yes, because 3 is a factor of p, the constant term of the polynomial.
Yes, because 3 is a factor of q, the leading coefficient.
No, because 3 is not a factor of p, the constant term of the polynomial.
No, because 3 is not a factor of p, the constant term of the polynomial.
3. Multiple Choice
5 minutes
1 pt
Using the Rational Zeros Theorem, which is the complete list of the possible rational zeros for the polynomial function?

$f\left(x\right)=\ 2x^5+x^3-16$
$\pm2,\ \pm4,\ \pm8$
$\pm1,\pm2,\pm4,\pm8,\pm16$
$\pm\frac{1}{4}\pm\frac{1}{2}\pm1,\pm2,\pm4,\ \pm8$
$\pm\frac{1}{2}\pm1,\pm2,\pm4,\pm8,\pm16$
4. Multiple Choice
20 seconds
1 pt
Select 2 ways you can tell if $x-2$ is a factor of a polynomial function $f\left(x\right)$ .
Substitute -2 for x in $f\left(x\right)$ to see if the end result is 0.
Substitute 2 for x in $f\left(x\right)$ to see if the end result is 0.
Synthetically divide $f\left(x\right)$ by -2 to see if the end result is zero.
Synthetically divide $f\left(x\right)$ by 2 to see if the end result is zero.
5. Multiple Choice
30 seconds
1 pt
Select 2 of the following statements that imply a zero of a polynomial function could have a multiplicity 4?
The polynomials' graph has a bounce at the x intercept.
One of the polynomials' factors has an exponent of 4.
Example: $\left(x-1\right)^4$
The highest degree of the polynomial is 4.
The polynomials' graph crosses the x- axis..
6. Multiple Choice
1 minute
1 pt
What are the maximum number of real solutions the polynomial function could have?

$f\left(x\right)=-4x^5-4x^3-4x^2-4$

5
4
3
2
7. Multiple Choice
20 seconds
1 pt
Select 2 of the following statements that explain if $\left(x+2\right)$ is a factor of $f\left(x\right)=\ x^2+3x+7$ and why or why not.
Yes, the function has a remainder of 0 when I synthetically divide by -2.
Yes, because the function equals 0 when I substitute -2 in for x.
No, the function has a remainder of 5 when I synthetically divide by -2
No, because the function equals 5 when I substitute -2 in for x.
8. Multiple Choice
5 minutes
1 pt
When synthetically dividing $f\left(x\right)=-8x^4+x^2-5x^6$
by some factor of x, how must I list my coefficients?
-8, 1, -5
-5, -8, 1
-8, 0, 1, -5, 0, 0
-5, 0, -8, 0, 1, 0, 0
9. Multiple Choice
5 minutes
1 pt
What is a list of all the possible rational roots of the polynomial function?

$f\left(x\right)=\ x^3-4x^2+5x-12$
$\pm1,\ \pm2,\pm3,\pm4,\pm6,\pm12$
$\pm\frac{1}{2},\pm1,\ \pm2,\pm3,\pm4,\pm6,\pm12$
$\pm\frac{1}{2},\pm\frac{3}{4}\pm1,\pm2,\pm3,\pm4,\pm6,\pm12$
$\pm\frac{1}{12},\pm\frac{1}{2},\pm\frac{3}{4}\pm1,\pm2,\pm3,\pm4,\pm6,\pm12$
10. Multiple Choice
15 minutes
1 pt
Find all zeros for the polynomial function given one of the factors of the function is (x+3).

$f\left(x\right)=2x^3+5x^2-6x-9$

$x=-3,-1$
$x=-3,\ -1,\ \frac{3}{2}$
$x=1,\ 3$
$x=\ \frac{-3}{2},\ 1,\ 3,\$
11. Multiple Choice
1 minute
1 pt
Which statement is NOT TRUE regarding the graphed polynomial function?

Check all that apply.
The factors are $\left(x+1\right)\left(x-1\right)^2\left(x-2\right)$
The factors are $\left(x-1\right)\left(x+1\right)\left(x+1\right)\left(x+2\right)$
The solutions are:
-2 (multiplicity of 1)
-1 (multiplicity of 2)
1 (multiplicity of 1)
The intercepts are

(-1, 0), (0, 1), (1, 0), (2, 0)
12. Multiple Choice
3 minutes
1 pt
The Rational Zeros Theorem states $\frac{p}{q}$ is a rational zero of $f\left(x\right)$ if $p$ is a factor of the constant term and $q$ is a factor of the leading coefficient . Is -2 a possible rational zero for the polynomial $f\left(x\right)$ ? $f\left(x\right)=3x^3+2x^2-5x+2$ Why or why not?
Yes, because 2 is a factor of p, the constant term of the polynomial.
Yes, because 2 is a factor of q, the leading coefficient.
No, because 2 is not a factor of p, the constant term of the polynomial.
No, because 2 is not a factor of p, the constant term of the polynomial.
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5.2pc Real Zeros of a Polynomial

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