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Reverse expansion

Start with a quadratic

x² + 5x + 6
x22x3xx2 + 5x + 62 and 3 make 5 and 6(x + 2)(x + 3)

A quadratic like x² + 5x + 6 can be built from two binomial factors.

Detailed notes

Worked Example

Factor x² + 5x + 6 by finding the two bracket numbers.

Step 1: Start with the quadratic

For x² + bx + c, we look for two numbers that build the middle and constant terms.

x2 + 5x + 6

Step 2: Find numbers that multiply to the constant

The constant is 6, so list factor pairs of 6.

1×6=6
2×3=6

Step 3: Choose the pair that adds to the x coefficient

The middle coefficient is 5. The pair 2 and 3 multiplies to 6 and adds to 5.

2+3=5

Step 4: Write the factors

Use the two numbers as the constants in the two brackets.

x2 + 5x + 6 = (x + 2)(x + 3)