Butte High Algebra 1 Chapter 7 Review

Polynomials in General

100

Write the polynomial in standard form:

-4x + 3x⁶ - 17x⁵ + 6 - x⁷

-x⁷ + 3x⁶ - 17x⁵ - 4x +6

200

What do you call a polynomial to the 0, 1st, 2nd, and 3rd degree?

constant, linear, quadratic, cubic

300

What do you call a polynomial with a degree of 4 or more?

You name it by degree OR quartic & quintic

400

What do you call a polynomial with 1, 2, 3, and 4 or more terms?

monomial, binomial, trinomial, polynomial

500

Name the polynomial according to the degree and number of terms:

3x³ + 4x² - x - 14

Cubic Polynomial

Adding Polynomials

100

When adding polynomials, you have to combine like terms.  What two things make terms "like terms"?

Same variable raised to the same power. 

200

Add the polynomials:

(5n³ + 6n⁴) + (7n⁴ - 5n³)

13n⁴

300

Add the polynomials:

(5 + x) + (x² + 7x + 3)

x² + 8x + 8

400

Add the polynomials:

(3x² + 6x³ + 5x) + (x³ - 2x - 4x⁴)

-4x⁴ + 7x³ + 3x² + 3x

500

Add the polynomials:

(2n⁴ - 7n³) + (4n - 5n⁴) + (6n - 8n³)

-3n⁴ - 15n³ + 10n

Subtracting Polynomials

100

Like addition, when subtracting polynomials you only have to combine ____ ______.

like terms

200

Subtract the polynomials:

(8a⁴ - 6a) - (8a - 8a⁴)

16a⁴ - 14a

300

Subtract the polynomials:

(2k² - 6k³) - (8k³ - 5k²)

-14k³ + 7k²

400

Subtract the polynomials:

(8m² + 5m) - (4m² - m)

4m² + 6m

500

Subtract the polynomials:

(2 - 6x - 2x⁴) - (3x - 3 + x⁴)

-3x⁴ - 9x + 5

Multiplying Polynomials

100

When multiplying polynomials, what do you do with the coefficients? What do you do with the exponents?

multiply; add

200

Multiply the polynomials:

3(5x + 5)

15x + 15

300

Multiply the polynomials:

4p(5p² - 8p - 3)

20p³ - 32p² - 12p

400

Multiply the polynomials:

(6n + 1)(7n + 8)

42n² + 55n + 8

500

Multiply the polynomials:

(7n + 2)(3n² + 8n + 8)

21n³ + 62n² + 72n + 16

Factoring Polynomials (Part 1)

100

Factor the polynomial by finding the greatest common factor:

18x³ + 21x² - 6x

3x(6x² + 7x - 2)

200

Factor the polynomial by grouping:

r² + 14r + 48

(r + 8)(r + 6)

300

Factor the polynomial by first factoring out the greatest common factor then by grouping:

3v² + 18v - 21

3(v + 7)(v - 1)

400

Factor the polynomial using "advanced" grouping:

7n² - 67n - 30

(7n + 3)(n - 10)

500

Factor the polynomial by first removing the GCF then by "advanced" grouping:

53x² - 240x - 320

5(7x + 8)(x - 8)

Factoring Polynomials (Part 2)

100

Factor the polynomial by finding the greatest common factor:

-35x⁶ - 45k² + 50

5(-7k⁶ - 9k² + 10)

200

Factor the polynomial by grouping:

p² - 16p + 63 

(p - 9)(p - 7)

300

Factor the polynomial by first factoring out the greatest common factor then by grouping:

4v² - 20v + 24

4(v - 3)(v - 2)

400

Factor the polynomial using "advanced" grouping:

5x² - 29x - 42

(5x + 6)(x - 7)

500

Factor the polynomial by first removing the GCF then by "advanced" grouping:

28x² + 212x - 360

4(7x - 10)(x + 9)