Review - QUIZ 1.3-1.4

Review: Quiz 1.3-1.4

Quotient rule simply states that as long as the base is the same, we can just divide two powers by subtracting the exponents. 

Review quotient rule for exponents:

1.3: Division with Polynomials

Multiple Choice

Quotient Rule for exponents states: keep the base the same and do this to the exponents.

• Subtract

• Add

• Divide

• Multiply

Draw

Write your answer.

Multiple Choice

Evaluate the expression using quotient rule for exponents.

• a¹⁵b³⁰

• a²b⁷

• a⁸b¹³

​Division of a Polynomial by a Monomial

1. Create separate fractions for each term of the numerator having the original denominator for each fraction's denominator.

2. Reduce each fraction.

1.3: Division with Polynomials

Demostrative video:

https://youtu.be/UquFdMg6Z_U

1.3: Division with Polynomials

Draw

Write your calculations here.

Multiple Choice

Divide.

• -5x¹⁰

• 4x⁴ + 18x⁶

• -6x⁴ + 16x²

• 4x⁴ - 9x²

Multiple Choice

Divide.

• 3abc − 4abc 

• $$3a^3b^2c^4−4b$$

• 3abc +4b 

• $$3abc^3−4b$$

​Division of a Polynomial by a Binomial

1.3: Division with Polynomials

Long division of a polynomial by a binomial is carried out in essentially the same manner as long division of two integers with no variables:

1. Divide the highest degree term of the polynomial by the highest degree term of the binomial. Write the result above the division line.

2. Multiply this result by the divisor, and subtract the resulting binomial from the polynomial.

3. Divide the highest degree term of the remaining polynomial by the highest degree term of the binomial.

4. Repeat this process until the remaining polynomial has lower degree than the binomial.

Demostrative videos:

https://youtu.be/_FSXJmESFmQ

https://youtu.be/8lT00iLntFc

1.3: Division with Polynomials

More explanation:

https://www.chilimath.com/lessons/intermediate-algebra/polynomial-long-division/

Multiple Choice

Divide using long division method.

• A

• B

• C

• D

Multiple Choice

Solve by using long division method.

• A

• B

• C

• D

Fill in the Blanks

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

Multiple Choice

Which term is missing in this problem?

(2x³ + 5x² + 9) ÷ (x + 3)

• x⁴

• x

• x³

• x²

Multiple Choice

Divide:

(3x³ + 5x - 1) ÷ (x + 1)

• 3x³ - 3x² + 8x - 9

• $$3x^2-3x+8-\frac{9}{x+1}$$

• $$3x^2+3x+8+\frac{7}{x+1}$$

• 3x³ + 3x² + 8x + 7

Multiple Choice

Is this division problem worked correctly?

• This is incorrect, and the error occurs on the 3rd line!

• This is correct!

• This is incorrect, and error occurs on the 2nd line!

• This is incorrect, and the error occurs on the 4th line!

Division with Polynimials Book Practice:

• Page 18: exercises 1-14 (done in classroom)

• Page 34: exercises 9-12

• Page 39: exercises 29-32

• Page 49: exercises 11-14

1.4: Factoring Special Form Polynomials

Common Factors (pages 19-20)

• Example 1.4A

Definitions

• Factor: numbers we can multiply together to get another number.

• Common Factor: A factor of a number is an exact divisor of the given number or when a number is exactly divided by a divisor that divisor is known as a factor of that number.

• Greatest Common Factor: The greatest common factor is the largest possible number that divides both of the terms.​

• Factoring: Factoring is the opposite of distributing. Instead of putting numbers together we are going to take them apart. We will do this by finding out what number divides both of our terms.

1.4: Factoring Special Form Polynomials

Factor Polynomials using GCF Method:

1.4: Factoring Special Form Polynomials

​In order to factor Polynomials, you find the GCF (Greatest Common Factor) and use it to find the factors.

​* The lowest power of x is your GCF for the variable part.

Watch these videos:

• https://youtu.be/Y1Vd5wb0rnM

• https://www.youtube.com/watch?v=fEZWqLxViUM

Multiple Choice

Which of the following is a good definition for the Greatest Common Factor of a polynomial?

• The largest combination of constants and variables you can "pull out" of a polynomial

• The constants and variables that are the smallest

• The constants and variables that are the largest

• The common factor that is the greatest

Multiple Choice

What is the GCF of 24 and 36?

• 8

• 12

• 6

• 4

Multiple Choice

What is the Greatest Common Factor of 3, 24, 12?

• 3

• 6

• 12

• 4

Fill in the Blanks

What is the GCF of 5 and 7?

Multiple Choice

What is the GCF of the expression:

$$2x^4+8x^3$$

• 2x

• $$2x^3$$

• 2

• $$4x^2$$

Multiple Choice

What is the GCF of

  $$4x^{2\ }-12x+36$$ ?

• 2x

• 4x

• $$2x^2$$

• 4

• $$4x^2$$

Multiple Choice

What is the greatest common factor of 48x²and 32x³?

• 8x²

• 16x²

• 16x

• 96x³

Multiple Choice

Factor 12x + 9

• not factorable

• 3 (4x + 3)

• x (12+9)

• 3 (4x - 3)

Multiple Choice

Factor: 2n³+16n+12

• 3(n³+8n+6)

• 2n(n³+8n+6)

• 2(n³+8n+6)

• 2n(n³+24n+6)

Multiple Choice

Factor 5ab²c¹¹ + 2bc⁵

• bc⁵(5ab²c⁶ + 2b)

• bc⁵(5abc⁶ + 2)

• b²c⁵(5bc⁶ + 2)

• c⁴(5a²b²c⁷ + 2bc)

Fill in the Blanks

Factor:

$5y(x-3)-8(x-3)$

Multiple Choice

Factor:

-10xy⁹z + 8y³z⁵

• 2y⁴z(-20xy⁶ + 4z⁴)

• 2y³z(-5xy⁶ + 4z⁴)

• 2y³z(-5xy⁶z + 4z⁵)

• 2y³z(-5xy⁶z + 8z⁴)

Multiple Choice

Factor:

12j²k³ - 20hj

• 4j²(24j²k³ - 20h)

• 4j(3jk³ - 5h)

• 4j(6jk³ - 10h)

• 4j(3jk² - 5h)