How To Factorize X²+12X+35: A Simple Guide With Examples

x²+12x+35

(x+7)(x+5)

To factorize x²+12x+35, we need to find two numbers that multiply to 35 and add up to 12 (the coefficient of x).

Let’s list all the possible pairs of factors of 35:

1 x 35

5 x 7

Out of these pairs, which ones add up to 12? Only 5 and 7 do.

So, we can rewrite x²+12x+35 as:

x²+5x+7x+35

Now, we group the first two terms together and the last two terms together:

(x²+5x) + (7x+35)

We can factor out x from the first group and 7 from the second group:

x(x+5) + 7(x+5)

Notice that we now have a common factor of (x+5). We can factor it out:

(x+5)(x+7)

So, the fully factored form of x²+12x+35 is (x+5)(x+7).

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