What is the zero-product property?

If a product of factors equals zero, at least one factor must be zero. It's why factoring solves equations — but only when one side is exactly 0.

What if the quadratic doesn't factor nicely?

Use the quadratic formula — it works on every quadratic, factorable or not. Factoring is the fast path when the numbers cooperate.

Yes — this skill is one of the free ones. Every unit opens with free skills, no account needed. Premium ($6/month or $30/year) unlocks every skill plus the parent progress dashboard.

How is this different from IXL?

No punishing score. A wrong answer gives you a step-by-step explanation, not a number that drops — and every question is reviewed by a human before you see it.

Algebra 2 practice

Solving Quadratic Equations by Factoring — Practice

Solve equations like $x^2 + 5x + 6 = 0$ by factoring and applying the zero-product property — free, no account, with a worked explanation on every question.

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What you'll practice

Factoring turns a quadratic equation into a product equal to zero, and the zero-product property finishes the job: if $(x+2)(x+3) = 0$ , one of the factors must be zero. These questions cover monic and non-monic quadratics, equations that need rearranging into standard form first, and the classic lost-solution traps.

Worked example

Solve $x^2 + 5x + 6 = 0$ .

Factor the left side: two numbers with product $6$ and sum $5$ are $2$ and $3$ , so $(x+2)(x+3) = 0$ .
Apply the zero-product property: $x + 2 = 0$ or $x + 3 = 0$ .
Solve each: $x = -2$ or $x = -3$ .
Check one: $(-2)^2 + 5(-2) + 6 = 4 - 10 + 6 = 0$ . ✓

Common mistakes

Sign slip at the end: $(x+2)(x+3)=0$ gives $x = -2, -3$ — not $x = 2, 3$ .
Dividing both sides by $x$ : for $2x^2 - 8x = 0$ , dividing by $x$ silently throws away the solution $x = 0$ . Factor instead: $2x(x-4) = 0$ .
Applying the zero-product property when the right side isn't 0: $(x+1)(x+2) = 6$ does NOT mean $x+1=6$ or $x+2=6$ . Expand and rearrange to $=0$ first.

Try a few

1. Solve $x^2 - 7x + 12 = 0$ .

$x = 3$ or $x = 4$
$x = -3$ or $x = -4$
$x = 3$ or $x = -4$
$x = 2$ or $x = 6$

2. Solve $x^2 + x - 12 = 0$ .

$x = -4$ or $x = 3$
$x = 4$ or $x = -3$
$x = -4$ or $x = -3$
$x = -6$ or $x = 2$

3. Solve $2x^2 - 8x = 0$ .

$x = 0$ or $x = 4$
$x = 4$ only
$x = 0$ or $x = -4$
$x = 2$ or $x = 4$

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FAQ

What is the zero-product property?: If a product of factors equals zero, at least one factor must be zero. It's why factoring solves equations — but only when one side is exactly 0.
What if the quadratic doesn't factor nicely?: Use the quadratic formula — it works on every quadratic, factorable or not. Factoring is the fast path when the numbers cooperate.
Is Cramzoo free?: Yes — this skill is one of the free ones. Every unit opens with free skills, no account needed. Premium ($6/month or $30/year) unlocks every skill plus the parent progress dashboard.
How is this different from IXL?: No punishing score. A wrong answer gives you a step-by-step explanation, not a number that drops — and every question is reviewed by a human before you see it.

Related Algebra 2 skills

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No login, no card. Open Algebra 2 and pick the tile.