Task Sets: Extend polynomial identities to complex numbers - Common Core Math - HS Number and Quantity

1.

Factor $x^2 + 9$ over the complex numbers.

A.

$(x + 3)(x - 3)$

B.

$(x + 3i)(x - 3i)$

C.

$(x + 3i)^2$

D.

Prime over complex numbers

2.

The canonical example: factor $x^2 + 4$ over the complex numbers.

A.

$(x + 2)(x - 2)$

B.

$(x + 2i)^2$

C.

$(x + 2i)(x - 2i)$

D.

$(x + 4i)(x - i)$

3.

Factor $x^2 + 5$ over the complex numbers.

A.

Cannot be factored because $5$ is not a perfect square

B.

$(x + \sqrt{5}\,i)(x - \sqrt{5}\,i)$

C.

$(x + \sqrt{5})(x - \sqrt{5})$

D.

$(x + 5i)(x - i)$

4.

The quadratic $x^2 + 2x + 5 = 0$ has roots $-1 + 2i$ and $-1 - 2i$ .

Write the factored form: $x^2 + 2x + 5 = (x - $ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ $)(x - $ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ )$.

Enter the two roots (the numbers being subtracted), separated.

first root (with sign):

second root (with sign):

5.

Factor $4x^2 + 25$ over the complex numbers.

A.

$(2x + 5)(2x - 5)$

B.

$(2x + 5i)(2x - 5i)$

C.

$(4x + 25i)(x - i)$

D.

Cannot be factored

Exercises: Extend Polynomial Identities to Complex Numbers

Warm-Up: Review What You Know

Fluency Practice