Zero Product Property - Algebra Step by Step

Solve a quadratic by factoring and applying the zero product property: if (x+a)(x+b)=0 then x=-a or x=-b. Verify each root by substituting back into the original equation.

zero-product If a product equals zero, at least one factor must be zero. Factor the quadratic, set each factor to zero, and solve.

Example

Factor the quadratic and set each factor equal to zero.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

x^{2} + 5x + 6 = 0

Step 2 — Factor

Factor the trinomial using 2 and 3.

(x+ \hl{2} )(x+ \hl{3} )= 0

Step 3 — Set factors to zero

Set each factor to zero: x + 2 = 0 and x + 3 = 0.

x+ 2 = \hl{0} \quad x+ 3 = \hl{0}

Step 4 — Roots

Read the roots: x = -2 or x = -3.

x= \hl{-2} \quad \text{or}\quad x= \hl{-3}