Question

How can I factor the following trinomial?
a) x^2+7x+10

Answer 1

x² + 7x + 10 = (x + 5)(x + 2)

Explanation:

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Rule:

To factor a trinomial of the form

x² + ax + b,

find two numbers whose product is b and whose sum is a.

Call these numbers, if they exist, p and q.

Then the factorization is

(x + p)(x + q).

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Let's apply the rule to this problem.

To factor

x² + 7x + 10.

Here, a = 7, and b = 10, so we need to find two numbers that multiply to 10 and add to 7.

The numbers are 5 and 2 since 5 × 2 = 10, and 5 + 2 = 7.

The factorization is

(x + 5)(x + 2)

Answer: x² + 7x + 10 = (x + 5)(x + 2)