precalc2-algebra

# precalc2-algebra - Often in calculus the diﬃcult part is...

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Algebra Review Problems 1. Factoring You should be comfortable solving equations by factoring them. Solve for x in each of the following equations: (a) 6 x - x 2 = 0 (b) 4 x 2 + 4 x + 1 = 0 (c) x 2 + 2 x = 8 (d) 2 x 2 + 6 = 7 x 2. Solving Quadratic Equations You should be comfortable solving quadratic equations that you cannot factor. Solve for x in each of the following equations: (a) 1 - 3 x - x 2 = 0 (b) 4 x 2 + 6 x + 1 = 0 (c) x 2 - 6 = 2 x 3. Sometimes the quadratic expressions are disguised as more complicated equations. Solve for x in the following equations: (a) 1 x - x = 1 (b) x - 2 x = - 2 x (c) x 3 + 3 x 2 - 5 x = 0 (d) x x - 2 = x + 1 (e) x - 2 x = 1 (f) x 4 - 5 x 2 + 4 = 0 4. Simplifying Expressions
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Unformatted text preview: Often in calculus the diﬃcult part is the algebra required to simplify complicated expressions. In each of these expressions, simplify to a point where the h in the denominator will cancel with a similar factor in the numerator. (a) ( x + h ) 3-x 3 h (b) √ x + h-√ x h (c) 1 x + h-1 x h 5. Simplifying Fractions Write the following fractions as a single fraction, with neither the numerator or denominator as a fraction: (a) 3 / 2 6 / 7 (b) 1 2-1 3 1 4 + 1 6 (c) 1 x +1-1 x-1 x 2-2 x...
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