Question

Explain how to factor when the leading coefficient is 1.

A) Find the factors of b that add up to c.

B) Find the factors of b that multiply to c.

C) Find the factors of c that add up to b.

D) Find the factors of c that multiply to b.

Answer 1

Answer: C) Find the factors of c that add up to b.

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Step-by-step explanation:

If we want to factor something in the form x^2+bx+c, then we look for two numbers that

• Multiply to c
• Add to b

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Let's look at a specific example

Consider factoring x^2+5x+6

We need to find two numbers that...

• Multiply to c = 6
• Add to b = 5

Through trial and error, you should find the two numbers to be 3 and 2. This means it factors to (x+3)(x+2). The order of the factors doesn't matter.

You can use the FOIL rule or the box method to expand out (x+3)(x+2). You should get x^2+5x+6 again.