Factoring Quadratics with Leading Coefficient One

Algebra Foundation

Algebra 1

Study expressions, equations, inequalities, functions, linear models, systems, polynomials, quadratics, and exponential growth with original explanations and worked examples.

Learn with original explanations and worked examples. OpenStax Elementary Algebra 2e was consulted for topic coverage.

Study every current unit through original concept lessons, formula derivations, experiments, quizzes, and practice sets.

Algebra 1 · Unit 8 · Topic 8.2

Factoring Quadratics with Leading Coefficient One

To factor x² + bx + c into (x + r)(x + s), find r and s with r + s = b and rs = c.

Definition and explanation

To factor x² + bx + c into (x + r)(x + s), find r and s with r + s = b and rs = c. Integer pairs are useful when an integer factorization exists.

Worked example

Factor x² + x − 12. The integers 4 and −3 add to 1 and multiply to −12, so the factors are (x + 4)(x − 3). Expanding gives x² + x − 12.

Common mistake

Matching the product alone is insufficient; the sum must match the middle coefficient too.

Key takeaway

To factor x² + bx + c into (x + r)(x + s), find r and s with r + s = b and rs = c.

Explain each step of the worked example, then check the units, signs, and conditions that apply.

Further reading

Topic coverage was checked against the openly available OpenStax Elementary Algebra 2e and Algebra and Trigonometry 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.