Processing math: 100%
- Evaluate each expression without using a calculator. solution
(a) (−3)4 (b) −34 (c) 3−4 (d) 523521 (e) (23)−2 (f) 16−3/4
- Simplify each expression. Write your answer without negative exponents. solution
(a) √200−√32 (b) (3a3b3)(4ab2)2
(c) (3x3/2y3x2y−1/2)−2
- Expand and simplify. solution
(a) 3(x+6)+4(2x−5) (b) (x+3)(4x−5) (c) (√a+√b)(√a−√b)
(d) (2x+3)2 (e) (x+2)3
- Multiply or divide to simplify as a sum/difference of terms. solution
(a) √x(x2−1) (b) √x+xx2 (c) t2−3t+3√t√t
- Factor the expression. solution
(a) x2+3x (b) 2x3+4x (c) x3−4x (d) x3+9x (e) x2−5x+6 (f) x2−x−6
- Factor the expression. solution
(a) x2+7x+3 (b) x2−x−6 (c) 6x2+x−1 (d) 3x2−14x+8
- Solve the following equations. solution
(a) 1−1x2=0 (b) √x−1+3=5 (c) √x+2=x (d) |2x−3|=4
- Simplify the rational expression. solution
(a) x2+3x+2x2−x−2 (b) 2x2−x−1x2−9⋅x+32x+1
(c) yx−xy1y−1x
- Simplify each expression. solution
(a) x3−9x2x−6 (b) 12+h−12h (c) (5+h)2−25h
- Rationalize the numerator. solution
(a) √9+h−3h (b) √x−2x−4
- Evaluate the difference quotient as indicated.
(a) f(a+h)−f(a)h for f(x)=x2 solution
(b) f(4+h)−f(4)h for f(x)=√x solution
(c) f(x+h)−f(x)h for f(x)=1√x solution
- Decompse the rational function as a sum of partial fractions. solution
(a) 6x2−9 (b) x2−2xx−1 (c) xx2+x−2
- Compute the ratio |an+1an|, and simplify. solution
(a) an=(−1)n12n+3 (b) an=(−2)nn! (c) an=(−1)n−11(2n+1)!