Question

How do you factor the trinomial `c^2 + 9c +18`?

Answer 1

`(c+3)(c+6)`

Explanation:

`c^2+9c+18`

Before solving this let us consider the general form of a quadratic equation.i.e. `" "ax^2+bx+c.`

Here `a=1.` Since `a^2` has no numerical coefficient,

`b=9 and c=18.`

So let's start.f First write all the factors of `c` (here 18) and identify the two factors which sum up to `b` (here 9).

Factors of `18 " are " 1,2,3,6,9 and 18`.

Have a close look. `3+6=9=b.`

Now you can split the expression as:

`c^2+3c+6c+18.`

Now factorize the equation into groups by taking out the common factors. Here as you can see, `c` is common in the first two terms.so take `c` out. In the `3 rd and 4th` terms `6` is common.

Now the expression is:

`c(c+3)+6(c+3).` take the common bracket out.
Here is your answer.(`c+3)(c+6).`

NB:this method of factorization is only possible when `b^2+4ac>=0.`

Answer 2

`(c+6)(c+3)`

Explanation:

`"the factors of + 18 which sum to + 9 are + 6 and + 3"`

`rArrc^2+9c+18=(c+6)(c+3)`