Solving a Quadratic by Factoring
Question
Answer choices
- x = -2 or x = -3
- x = 3 only
- x = 3 or x = 3
- x = 2 only
- x = 2 or x = 3
E Correct answer: E) x = 2 or x = 3
Set up the problem carefully before computing. For x^2 + bx + c, find two numbers that add to b and multiply to c. Set each linear factor equal to zero.
Carry the arithmetic through one step at a time, double-checking signs and units. The ACT writes wrong answers to catch the most common slips, so an answer that "looks right" without verification is risky.
Plug the answer back into the original expression as a sanity check whenever the problem allows. If the substitution does not balance, you have made an arithmetic mistake earlier in the work.
The underlying rule
Factor: (x - 2)(x - 3) = 0 because 2 + 3 = 5 (matches -b) and 2 · 3 = 6 (matches c). Set each factor to zero: x = 2 or x = 3.
Why each wrong answer is wrong
- A) x = -2 or x = -3: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- B) x = 3 only: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- C) x = 3 or x = 3: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- D) x = 2 only: A common arithmetic or sign error leads to this value; carefully redo the calculation.
Study tip
For x^2 + bx + c = 0, look for two integers that multiply to c and add to b. The roots are the negatives of those integers (since (x - r1)(x - r2) = x^2 - (r1+r2)x + r1·r2).
More Easy Intermediate Algebra
- Solving a Quadratic by FactoringSolve for x: x^2 - 5 x + 4 = 0.
- Function EvaluationIf f(x) = 3x^2 - 1, what is f(3)?
- System of Linear EquationsSolve the system: 2x + 2y = 14 and x + y = 7. Express your answer as (x, y).
- Exponent RulesSimplify (x^2)^2 · x^1.
- Solving a Quadratic by FactoringSolve for x: x^2 - 6 x + 5 = 0.