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.

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.

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