Free Printable Polynomial Theorem

Worksheets

Polynomial Theorem

Total questions: 20

Worksheet time: 20mins

Name

Class

Date

A polynomial function with rational coefficients has the following zeros.
$-1, 1+3i$

Determine all the additional zeros.

$1-3i$

$-3i$

$1$

No additional zeros

Explain why it makes sense that a third degree polynomial must have at least one rational zero.

4 lines

Find all the rational zeros for the following polynomial: Mark all that apply.

$f\left(x\right)=2x^3-5x^2+4x-1$

$-1$

$1$

$2$

$\frac{1}{2}$

$-\frac{1}{2}$

Find all the real zeros of the function f(x) = 2x³ - 19x² + 38x + 24 given that x-4 is a factor.

x = 4, -1/2, -6

x = 4, -3, 2

x = 4, -1/2, 6

x = 4, 1/2, -6

Is (x-4) a factor of (x³ +x² -16x-16)?

YES

If (x + 3) is a factor of p(x), then p(- 3) = (a) .

Choose from the below words

-3

None of these.

Is (x-3) a factor of
(x³- 3x²+ 2x + 2)?

Yes

Is (x-4) a factor of (x³ +x² -16x-16)?

YES

If 𝒙²−𝟓 is divided by 𝒙−𝟐, then what is the remainder?

(a)

10.

If 𝟐x²+𝟏𝟎 is divided by 𝒙−𝟏, then what is the remainder?

(a)

11.

Use synthetic division to determine f(-3), if f(x)= (3x³ -5x² -4x +1).

(a)

12.

Find all the zeros, given that f(-3) = 0

f(x) = 2x³+5x²-6x-9

-3, 1, 3/2

-3, -1, 3/2

-3, 1, 2/3

-3,-1, 2/3

13.

The largest exponent determines the degree of the polynomial.

True

False

14.

According to the Rational Root Theorem, what are the all possible rational roots?
2x³ - 11x² + 12x + 9 = 0

±1,±2

±1,±3,±9

±1,±3±9,±1/2,±3/2,±9/2

±1,±2,±1/3,±2/3,±1/9,±2/9

15.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = x³ + 2x² - 6x + 8

±1, ±8

±1, ±2, ±4, ±8

±1, ±2, ±4

1, 2, 4, 8

16.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = 3x³ + 2x² - 6x + 7

±1, ±7, ±1/3, ±7/3

±1, 7

±1, ±3, ±7, ±7/3

±1, ±3, ±7, ±1/3, ±7/3

17.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = 2x³ + 5x² - 9x + 5

±1, ±5, ±1/2, ±5/2

±1, ±2, ±5, ±1/2, ±5/2

±1, ±5

±1, ±2, ±5, ±1/2, ±5/2, ±2/5

18.

Is (x-2) a factor of $f\left(x\right)=x^3-8x^2+14x-4?$

Yes, (x-2) is a factor. There is a remainder.

No, (x-2) is not a factor. The remainder is zero.

Yes, (x-2) is a factor. The remainder is zero.

No, (x-2) is not a factor. There is a remainder.

19.

What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x³- 5x²+ 2x - 10

2x-10

-2x-10

2x+10

20.

$p\left(x\right)=x^4-2x^3+kx-4$ , where k is an unknown integer.
p(x) divided by (x-1) has a remainder of 0.
What is the value of k?

(a)

100 %

Polynomial Theorem

Total questions: 20

Worksheet time: 20mins

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