00:01
In order to solve this equation by factoring, we first need to know the rule for factoring a quadratic of the form ax squared plus bx plus c.
00:12
This rule tells us that to start, i need to multiply a times c.
00:17
A times c is then going to equal m times p, and then b is going to equal m plus p.
00:25
Use this information to determine m and p, and this allows us to split up the middle term and rewrite the quadratic as ax squared plus mx plus px plus c.
00:39
We can then proceed with the process of grouping.
00:42
We'll start by multiplying a times c.
00:46
That's 6 times 5 and gives us 30, so i know my two numbers, m and p, multiply to 30.
00:52
I also know they're going to add to equal the coefficient of the linear term, which is 17.
00:59
Now if i think about what two numbers multiply to 30 and add to 17, i get m equals 15 and p equals 2.
01:08
This allows us to rewrite the quadratic as 6x squared plus 15x plus 2x plus 5 equals 0.
01:19
Now group together the first two terms and also the last two terms...