Ch. 10 Preview

Ch. 10Preview

by Kimberly Gordiany

​Simplifying Radicals

​We will also need to remember how to simplify radicals in chapter 5. A factor tree is a good method, as long as you remember to keep the square root symbols over the factors of the square roots.

​Then, circle the numbers at the end of each branch to

​multiply them for your answer.

Draw

Simplify $$\sqrt[]{27}$$  

Multiple Choice

Simplify $$\sqrt[]{28}$$  

• $$4\sqrt[]{7}$$  

• $$7\sqrt[]{4}$$  

• $$7\sqrt[]{2}$$  

• $$2\sqrt[]{7}$$  

Multiple Choice

Simplify $$\sqrt[]{24}$$  

• $$6\sqrt[]{2}$$  

• $$2\sqrt[]{6}$$  

• $$4\sqrt[]{6}$$  

• $$2\sqrt[]{12}$$  

Multiple Choice

Any number that can be expressed as a quotient of two integers, where the denominator is not zero

• Asymptote

• Rational Number

• Reflection

• Translation

Multiple Choice

A transformation that flips a figure across a line

• Rational Number

• Reflection

• Translation

• Zero of a Function

Multiple Choice

Any number x, such that f(x)=0

• Rational Number

• Reflection

• Translation

• Zero of a Function

Multiple Choice

A line that a curve approaches as the value of x and y become very large or very small

• Zero of a Function

• Asymptote

• Reflection

• Translation

Multiple Choice

A transformation that moves each point in a figure the same distance in the same direction

• Asymptote

• Rational Number

• Reflection

• Translation

​Exponent Rules:

​

​

​

​

​

​

To multiply same bases, you add the exponents

​To divide same bases, you subtract the exponents

​To raise exponents to another power, you multiply exponents

​Negative exponents give the reciprocal

​

​

​

Fill in the Blanks

Assume all variables are nonzero. Simplify $\frac{x^{11}y^5}{x^4y^7}$  

Do not use negative exponents for your answer

Fill in the Blanks

Assume that all variables are nonzero. Simplify with no negative exponents. $\left(2x^{-4}\right)^3$  

Multiple Choice

Combine Like Terms

$$5x^2+10x-4x+6$$  

• $$5x^2-6x+6$$  

• $$5x^2-6x-6$$  

• $$5x^2+6x+6$$  

• $$5x^2+6x-6$$  

Fill in the Blanks

Assume that all variables are nonzero. Simplify without using negative exponents. $\left(x^3\right)^{-2}$  

Fill in the Blanks

Assume that all variables are nonzero. Simplify using no negative exponents. $\left(\frac{3x^2y}{z}\right)^4$  

Multiple Choice

Combine like terms.

$$3x+12-10x$$  

• 15x - 10

• 7x + 12

• 3x + 2

• -7x + 12

Multiple Choice

Combine like terms.

$$x^2+x+3x^2-4x$$  

• $$4x^2-3x$$  

• $$4x^2-3x+1$$  

• $$x^3+3x^2-4x$$  

• $$x^3-3x^2+4x$$  

​Greatest Common Factor

We use GCF to simplify fractions and rational

expressions.

​

​Look for the largest number that is a factor of

​both terms.

​

​When looking at variables, look for the highest exponent that is a factor of both terms.

Multiple Choice

Find the GCF of

3a² and 12a

• 3

• $$3a^2$$  

• 3a

• a

Multiple Choice

Find the GCF of

c²d and cd²

• cd

• c²d²

• cd²

• c²d

Multiple Choice

Find the GCF of

16x⁴ and 40x³

• $$4x^3$$  

• $$8x^2$$  

• $$4x$$  

• $$8x^3$$  

​Factoring Trinomials

​We factored trinomials in chapter 2. When we have a quadratic trinomial, we look for factors of c (the number with no variable) that add or subtract to b (the number in the middle).

​The factors of a quadratic trinomial will be 2 pairs of binomials written in parentheses. The parentheses is the way that we show multiplication because factors are numbers we multiply.

Multiple Choice

Factor the trinomial

x² - 4x - 5

• (x-5)(x+1)

• (x-5)(x-1)

• (x+5)(x-1)

• (x+5)(x+1)

Multiple Choice

Factor the Trinomial

x² + 2x - 24

• (x+4)(x-6)

• (x-4)(x+6)

• (x-3)(x+8)

• (x+3)(x-8)

Multiple Choice

Factor the Trinomial

x² + 12x + 32

• (x+9)(x+3)

• (x-9)(x-3)

• (x+4)(x+8)

• (x-4)(x-8)

Multiple Choice

Factor the Trinomial

x² + 9x + 18

• (x+6)(x+3)

• (x+9)(x+2)

• (x+4)(x+5)

• (x+2)(x+7)

Multiple Choice

Factor the Trinomial

x² -6x + 9

• (x+3)²

• (x-3)²

• (x-3)(x+3)

• (x+3)(x-3)

Multiple Choice

Factor the Trinomial

x² -8x - 20

• (x-4)(x-5)

• (x+4)(x-5)

• (x+10)(x-2)

• (x+2)(x-10)

Fill in the Blanks

Solve: 5x² = 45

x = +/-

Fill in the Blanks

Solve: 4x² - 7 = 93

x = +/-

Draw

Solve: 2(x-2)² = 32