Math

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Algebra II Unit 7– Polynomial Functions - Remediation

Obj 07c – I can understand the fundamental theorem of Algebra and its effects on multiplicity.

1.

Identify the number of zeros for the polynomial shown.

𝑓(𝑥) = (𝑥 − 3)2(𝑥 + 2)(𝑥 − 1)3

2.

What degree polynomial has 2 imaginary solutions and 3 real solutions?

3. The polynomial below has at least 1 imaginary solution. What could the minimum degree of the polynomial be?

4. For the 7th degree polynomial below find the number of real and imaginary solutions.

Real: ___________ Imaginary: ________

5. Determine the number of real and imaginary solutions for the polynomial shown.

ℎ(𝑥) = 𝑥5 − 4𝑥3 + 3𝑥

Real: ___________ Imaginary: ________

Obj 07c – I can understand the fundamental theorem of Algebra and its effects on multiplicity. Remediation

Divide the polynomials.

6.

(30𝑚3 − 21𝑚2 + 24𝑚 − 90) ÷ (6𝑚 − 9)

7.

(24𝑥3 − 32𝑥2 − 64𝑥 + 65)

8𝑥 − 8

9. 𝒙𝟑 + 𝟐𝒙𝟐 + 𝟑

𝒙 + 𝟐

10. (3 + 13𝑥2 + 7𝑥3 + 15𝑥 + 𝑥4) ÷ (𝑥 + 1)

Obj 07e – I can write the equation of a polynomial function given a graph or the zeros. Remediation

Write the equation of the polynomial with the least degree from the information given in standard form.

10.

Zeros: 4, -1, √2, −√2

11.

Roots: -4, 3i, -3i

Write the equation of the polynomial with the least degree from the information given in any form.

12.

13.