Question

How do you factor `3x ^ { 2} + 15x + 21= 0`?

Answer 1

`3(x^2+5x+7)=0`

Explanation:

`3x^2+15x+21=0`+

Since all terms are divisible by 3, we take 3 as a common factor:
`3(x^2+5x+7)=0`

We can further go and simplify the equation:

We divide the whole equation by 3:
`(3x^2+15x+21=0)/3`
`rarrx^2+5x+7=0`

Then we use the reverse of `(a+b)^2=a^2+2ab+b^2`, in our case `a=x`
`2ab=5x`
`rarr 2(x)b=5x`

Dividing the equation by `x` and then by 2:
`(2cancelxb)/cancelx=(5cancelx)/cancelx`
`(cancel2b)/cancel2=5/2`
`b=2.5`

Now we can write the equation in form `a^2+2ab+b^2`:
`x^2+5x+(2.5)^2-(2.5)^2+7=0`
`(x+2.5)^2-6.25+7=(x+2.5)^2+0.25`
`(x+2.5)^2cancel(+0.25)cancel(-0.25)=0-0.25`
`(x+2.5)^2=-0.25`