MIni Lesson Factoring with Complex Numbers

https://www.youtube.com/watch?v=xXPnR4MIH0A

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​Sum of Squares...Why do we need complex numbers to correctly factor?

Multiple Choice

$$\left(25x^2+121\right)$$ is considered ____?

• A difference of squares

• A sum of squares

Multiple Choice

The only way to correctly factor $$\left(25x^2+121\right)$$ is to ____?

• Distribute a negative 1 and change all signs

• Use i when factoring

• You do not have to do anything special in order to correctly factor this polynomial.

Multiple Select

Select all factors for $$\left(25x^2+121\right)$$

• (5x +11)

• (5x+11i)

• (5x-11)

• (5x-11i)

Multiple Select

$$\left(x^4-16\right)\ initially\ can\ be\ factored\ into\ \left(select\ all\ that\ apply\right)$$

• $$\left(x^2-4\right)$$

• (x-4)

• $$\left(x^2+4\right)$$

• (x+4)

• $$\left(x^2-8\right)\left(x^2-2\right)$$

Multiple Select

In order to further factor $$\left(x^2-4\right)\$$ you will need what two factors?

• $$\left(x\ -2i\right)$$

• (x-2)

• $$\left(x+2i\right)$$

• (x+2)

• None of these

Multiple Select

In order to further factor $$\left(x^2+4\right)$$ you will need what two factors?

• $$\left(x\ -2i\right)$$

• (x-2)

• $$\left(x+2i\right)$$

• (x+2)

• None of these

Multiple Select

If $$\left(x^4-16\right)\$$ can be factored into $$\left(x^2-4\right)\left(x^2+4\right)$$ select all the factors needed, in order to factor completely.

• $$\left(x\ -2i\right)$$

• (x-2)

• $$\left(x+2i\right)$$

• (x+2)

• None of these

Multiple Select

Work it out on paper before answering.

Select all that are factors of

$$\left(x^4-81\right)$$ .

• $$\left(x^2+9\right)$$

• $$\left(x-9\right)$$

• $$\left(x+3i\right)$$

• $$\left(x^2-9i\right)$$

• $$\left(x^2-3i\right)$$