How do you factor x² + bx + c?

Find two numbers that multiply to c and add to b; those numbers are p and q in (x + p)(x + q).

How do I check a factorisation?

Expand it back out (FOIL). You should recover the original trinomial.

Factoring Quadratics · Grades 10–10

Factoring Quadratics Worksheets

List the factor pairs of c, then find the pair that adds to b. Grade 10 worksheets for factoring x² + bx + c into two binomials.

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What it is

Factoring a trinomial x² + bx + c means writing it as (x + p)(x + q), where p and q multiply to c and add to b.

Why it matters

Factoring is the gateway to solving quadratics, simplifying rational expressions, and analysing polynomial functions throughout Grades 10–12.

How to do it

Find two numbers that multiply to c.
Of those, pick the pair that adds to b.
Write the factors as (x + p)(x + q).

Examples by level

BeginnerFactor x² + 2x + 1 =(x + 1)(x + 1)
IntermediateFactor x² − 1 =(x + 1)(x − 1)
AdvancedFactor x² + 12x + 20 =(x + 10)(x + 2)

Examples are generated by the same engine as the worksheets, so they're always mathematically correct. Built to avoid repeats, not reshuffle the same handful of questions.

Common mistakes

Finding numbers that add to b but don't multiply to c (or vice-versa).
Sign errors when c is negative.
Not checking by expanding.

Tips

Check by expanding (FOIL), you should get the original.
Watch the signs: a negative c means the factors have opposite signs.

For parents

List the factor pairs of c first, then pick the pair that adds to b, it turns guessing into a method.

For teachers

Insist on the FOIL check; it makes factoring self-correcting.

Key vocabulary

trinomial: a three-term polynomial
factor: an expression multiplied to form another

Frequently asked questions

How do you factor x² + bx + c?: Find two numbers that multiply to c and add to b; those numbers are p and q in (x + p)(x + q).
How do I check a factorisation?: Expand it back out (FOIL). You should recover the original trinomial.

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