Factoring Trinomials - Algebra Step by Step

Factor x^2 + bx + c by finding two numbers r1, r2 such that r1 + r2 = b and r1 * r2 = c. Then the factored form is (x + r1)(x + r2). Verify by multiplying the factors back out.

Example

Find the factor pair whose sum and product match the trinomial.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

x^{2} + 5x + 6

Step 2 — Find factor pair

Choose the pair: 2 + 3 = 5 and 2 x 3 = 6.

\hl{2} + \hl{3} = 5 \quad 2 \times 3 = 6

Step 3 — Factored form

Use the pair as binomials: x + 2 and x + 3.

(x+ \hl{2} )(x+ \hl{3} )

Step 4 — Check

Check by expanding back to the original.

(x+ 2 )(x+ 3 )= x^{2} + 5x + 6

trinomial List factor pairs of c; pick the pair whose sum is b. The factored form is immediate. Always expand to confirm the coefficient equality holds.