Algebra 1a Unit 1-2 review

Simplifying Radicals

100

sqrt(75)

5sqrt3

200

sqrt169

13

300

sqrt384

8sqrt6

400

sqrt160

4sqrt10

500

-4sqrt567

-36sqrt7

Solve for a variable

100

x +3 = 13

x = 10

200

x - 12 = -14

x = -2

300

2x - 4 = x + 2

x = 6

400

-4(2x + 8) = -16

x=-2

500

3/(x+3) =2/(x 

x=6

Add / Subtract polynomials

100

(3x^3+2x^2-4x-8) + (-2x^3+7x^2-2x+1)

(x^3+9x^2-6x-7)

200

(2x^3-6x-10)+(2x^3+2x^2-12x-8)

(4x^3+2x^2-18x-18)

300

(-2x^3+2x^2-12x+2) - (x^3+x^2-x)

(-3x^3+x^2-11x+2)

400

(3x^3+2x^2-4x-8) - 2(2x^2-8)

(3x^3-2x^2-4x-8)

500

2(3x^3+2x^2-4x-8)-3(x^3+2)+2(x+2)

(3x^3+4x^2-6x-10)

Multiplying Polynomials

100

(x+2)(x-1)

x^2+x-2

200

(x+4)(2x+1)

(2x^2+9x+4)

300

(2x-1)(3x-2)

(6x^2-7x+2)

400

(x + 2)(x^3 + 3x^2 + 4x – 17)

x^4 + 5x^3 + 10x^2 – 9x – 34

500

(3x^2 – 9x + 5)(2x^2 + 4x – 7)

6x^4 – 6x^3 – 47x^2 + 83x – 35

Pythagorean Theorem

100

Is a triangle with side lengths of 3 cm, 4 cm, and 5 cm a right triangle?

Yes. 25 = 25

200

Is a triangle with side lengths of 12 cm, 13 cm, and 5 cm a right triangle?

Yes. 169 = 169

300

Is a triangle with side lengths of 13 cm, 14 cm, and 25 cm a right triangle?

No. 365 does not equal 625

400

Find the hypotenuse of a triangle with leg lengths of 5 and 7. Round to the nearest 10th. 

Hypotenuse = 8.6 

500

What are the lengths of the legs of an isosceles right triangle with a hypotenuse of 16? In simplest radical form and rounded to the nearest 10th.  

legs = 11.3 and 

8sqrt2