Unit 5 Review Day

Unit 5 Review Day

I can review unit 5 knowledge for my final.

Let's start by previewing this chapter. Answer each question as best you can.

Open Ended

 Factor Completely: $3x^2+18x+15$  

Open Ended

 Simplify
 $\left(4+7i\right)-\left(3+2i\right)$  

Open Ended

Evaluate
 $125^{\frac{1}{3}}$  

Poll

How confident do you feel in your ability to factor quadratics completely?

• I don't know how to factor.

• I feel okay about it.

• I can factor almost anything!

Factoring Review

Factoring

 $x^2+7x-18$  

• Use an area model and diamond

• Place the squared term and constant diagonal from one another

Multiple Choice

What will go on the top of our diamond problem?

• $-7x$

• $-18x^2$

• $18x^2$

• $7x$

Solving the diamond

• We need values that multiply to the top and add to the bottom.

• You can list out factors of the top number to help find the side values

Multiple Choice

Which values should we use to solve our diamond?

• 3 & 6

• 2 & 9

• -2 & 9

• -3 & 6

Finishing Factoring

• Find the outside values

• Pay attention to the signs of the inside values

Write your answer

• Once you have the outsides, you can write your answer

• each side is a set of parenthesis

Multiple Choice

Factor:
x² - 8x - 128

• (x - 16)²
• (x - 16)(x + 8)
• (x + 16)(x - 8)
• (x - 16)(x - 8)

Multiple Choice

Factor:
x² -15x + 36

• (x - 18)(x + 2)
• (x - 12)(x - 3)
• (x - 12)(x + 3)
• (x + 18)(x - 2)

Poll

How confident do you feel in your ability to simplify complex numbers?

• I don't know how to simplify complex numbers.

• I feel okay about it.

• I can simplify complex numbers with no issue!

Things we know about complex numbers

• we use i to represent imaginary numbers

•  $i=\sqrt{-1}$  

•  $i^2=-1$  

• We can add, subtract and multiply complex numbers

Complex Numbers

• Complex numbers are made up of 2 parts - real part & imaginary part

Add like terms

• Combine the real parts together

• Combine the imaginary parts together

• Make sure you pay attention to the signs!

•  $6-4i$  

Subtraction

• To subtract complex numbers, start by distributing the negative (minus sign) into the second set of triangles

•  $\left(2+6i\right)-\left(5+i\right)$  

Add like terms

•  $-3+5i$  

Multiple Choice

Find the sum.
(5-2i) + (-7+8i)

• -2+6i
• 12+6i
• -35-16i²
• -35 -16i

Multiple Choice

Simplify:

(7 + 2i)(9 - 6i)

• 75-24i

• 63 - 24i - 12i²

• 51 - 24i

• 58 + 60i

Multiple Choice

Simplify:

(10+ 15i) - (48 - 30i)

• 58 - 45i

• 58 - 15i

• -38 - 15i

• -38 + 45i

Poll

How confident do you feel in your ability to rewrite and evaluate rational exponents?

• I don't know how to rewrite or find the value.

• I can do one but not the other.

• I am able to rewrite and evaluate rational exponents with little to no help!

Rewriting expressions

We can rewrite this exprssion into a rational exponent

Multiple Choice

Which value goes in the numerator (top of fraction)

• a

• b

• x

Multiple Choice

 Write in exponential form
 ∛x⁷

• x⁷∕ ³
• x3⁄7
• 3x⁷
• 7x³

Multiple Choice

Write the following expression in radical form:

• a.)
• b.)
• c.)
• d.)