Factoring trinomials

Japanese school year: Junior high 3

What you learn

Learn how to factor quadratic trinomials of the form x^2+(a+b)x+ab into (x+a)(x+b) by finding pairs with matching sums and products. You will practice fundamental problems where constants a and b are integers. Prior familiarity with expanding binomial expressions will help you grasp this technique quickly.

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Key points

Use this to factor a quadratic expression with leading coefficient 1 into two linear factors. Find two numbers, $a$ and $b$ , whose sum is the $x$ coefficient and whose product is the constant term.

x^2 + (a + b)x + ab = (x + a)(x + b)

Use this to factor a quadratic expression with a negative middle coefficient and a positive constant term. Find two positive numbers, $a$ and $b$ , whose sum is the absolute middle coefficient and whose product is the constant term.

x^2 - (a + b)x + ab = (x - a)(x - b)

Use this to factor quadratic expressions containing two variables, $x$ and $y$ . Find two numbers $a$ and $b$ using their sum and product, just as with a single variable.

x^2 + (a + b)xy + aby^2 = (x + ay)(x + by)

Worked example

x^2 + 7x + 10

The two integers that multiply to 10 and add to 7 are 2 and 5.

Choose a set to practice.

Practice 1Basic 1, Standard 4