RANGER Math practice · Algebra · ages 14+
Free factoring quadratics practice
Ranger's Math Trail practices quadratics in the form x² + bx + c: first factoring them into two brackets, then solving x² + bx + c = 0 by factoring.
Show me how names the two numbers that multiply to c and add to b, writes the brackets, then sets each bracket to 0.
Practice factoring quadratics now
Pick a level
Free, no sign-up. The game asks your age once, then every answer comes with a hint and a step-by-step Show me how.
How to do it
- Look for two numbers that multiply to c and add to b.
- For x² + 5x + 6, that's 2 and 3, so it factors to (x + 2)(x + 3).
- To solve x² + bx + c = 0, factor it, then set each bracket equal to 0.
- (x + 2)(x + 3) = 0 gives x = −2 or x = −3.
Worked examples
Example 1Factor: x2 − 6x − 27
- Look for two numbers that MULTIPLY to −27 and ADD to −6.
- They are −9 and 3: (−9) × 3 = −27 and (−9) + 3 = −6.
- So x2 − 6x − 27 = (x − 9)(x + 3).
Answer: (x − 9)(x + 3)
Try one like it →Example 2Solve: x2 − 5x − 36 = 0
- Factor: two numbers that multiply to −36 and add to −5 are 4 and −9.
- x2 − 5x − 36 = (x + 4)(x − 9) = 0.
- A product is 0 only if one part is 0: x + 4 = 0 or x − 9 = 0.
- So x = −4 or x = 9.
Answer: x = −4 or x = 9
Try one like it →Mistakes to watch for
- If c is negative, one number is positive and one is negative.
- If c is positive and b is negative, both numbers are negative.
- Check by multiplying the brackets back out.
The game
Questions
How do I enter two answers?
Separate them with a comma: 3, −2. The order doesn't matter.
What age is it for?
Factoring usually comes in Algebra 1 (around age 14 or 15).
More math practice: Addition · Subtraction · Multiplication facts · Division and long division · Place value and rounding · Fractions · Decimals · Percents and ratios · Negative numbers · Order of operations · Exponents and square roots · Solving equations · Slope and linear equations · Systems of equations · Area, perimeter and volume · Angles · Pythagorean theorem · Circles · Mean, median, mode and range · All math topics