Algebra II ch. 6 review

exponent rules

100

x⁷* x⁴

x¹¹

200

x²y⁵ * x³y

x⁵y⁶

300

x^-3/x^-4

x

400

(5x^-4y²)/(10x²y^-3)

y⁵/2x⁶

500

[(-2x²y³)/(3x^-3y)]^-2

9/(4x¹⁰y⁴)

polynomial long division

100

(x² + 4x + 3) divided by (x + 1)

x + 3

200

(3x³ - 7x² + 9x - 14) div. by (x - 2)

3x² - x + 7

300

(2x² - 5x - 4) div. by (x - 3)

2x + 1 R -1

400

(4g² - 9) div. by (2g + 3)

2g - 3

500

(a³ - 64) div by (a - 4)

a² +4a + 16

synthetic division

100

(x² + 3x - 15) div by (x - 2)

x + 5

200

(x³ - 8x² + 19x - 9) div by (x - 4)

x² - 4x + 3 R 3

300

(2x² + 13x + 15) div by (x + 5)

2x + 3

400

(2x³ + 4x - 6) div by (x + 3)

2x² - 6x + 22 R -72

500

(6x⁴ + 15x³ - 28x - 6) div by (x + 2)

6x³ + 3x² - 6x - 16 R 26

equations in standard form

100

y = x(x - 3)

y = x² - 3x

200

y = (x - 2)(x - 4)

y = x² - 6x + 8

300

y = x(x - 3)(x + 2)

y = x³ - x² - 6x

400

y = (x - 2)³

y = x³ - 6x² + 12x - 8

500

y = x(x + 2)³

y = x⁴+ 6x³ + 12x² + 8x

end behaviors, zeros and graphs

100

y = 7x⁵ - 3x⁴ + 1

What is the lead coefficient and the degree of the polynomial?

l.c. = 7 and degree = 5

200

y = 5x⁴ - 2x³ + 2x² - 3x + 1

What is the end behavior?

up, up

300

y = (x - 8)(x + 4)²(x - 3)³

What are the zeros and the multiplicity of each?

8, -4(2), 3(3)

400

y = x²(x - 5)³

What is the degree, sign of the lead coefficient and end behavior of the graph?

degree = 5

l.c. is positive

end behavior is down, up

500

Graph y = x³(x - 2)(x + 1)²(x + 6)⁴

See student graph