Question

7k^2+9+2 factoring?

Answer 1

\(\large\rm \color{royalblue}{\text{Hello and welcome to OpenStudy! :)}}\)

Answer 2

Did you mean to put this for your expression?
7k^2+9k+2

The 9 is supposed to be 9k, yes?

Answer 3

yes it is suppose to be 9k

Answer 4

\[\large\rm 7k^2+\color{orangered}{9k}+2 \]Notice that the coefficients on the ends add up to 9.
7 + 2 = 9, yes?
So let's break down this middle 9k into 7k and 2k.\[\large\rm 7k^2+\color{orangered}{7k+2k}+2\]

Answer 5

From this point, we can factor `by grouping`.

Answer 6

\[\large\rm (7k^2+7k)+(2k+2)\]So we have two groups.
What do 7k^2 and 7k have in common?
We want to factor something out of that first set of brackets.

Answer 7

Ok that makes sense

Answer 8

What do 7k^2 and 7k have in common?

Answer 9

k or 1 ?

Answer 10

Well they certainly have k in common.
They both have k. Good.
But they both also have a 7, yes?

Answer 11

yes they do

Answer 12

\[\large\rm (7k^2+7k)+(2k+2)\]So what we'll attempt to do is, take out (divide out), 7k from each term.\[\large\rm 7k(~~?~~+~~?~~)+(2k+2)\]Ok so be careful when factoring.
When you take 7k out of 7k, we're talking about division,
so we're not left with 0 in the second slot.
We're left with 1, ya?
\[\large\rm 7k(~~?~~+1)+(2k+2)\]We had 7k and we divided 7k out of it.

Answer 13

How bout the other term?
What are we left with... when we take 7k out of 7k^2?

Answer 14

2 k

Answer 15

2 square

Answer 16

Hmm close! :)
Remember the square means we're multiplying the k by itself.
So we think of \(7k^2\) as \(7kk\).

So if we divide 7k out of 7kk, we're left with just k, right?

Answer 17

\[\large\rm 7k(k+1)+(2k+2)\]

Answer 18

How bout the second set of brackets?
Looks like both have a 2 in common, ya?

Answer 19

\[\large\rm 7k(k+1)+2(~~?~~+~~?~~)\]So what happens if we take a 2 out of each term?
What are we left with in the second set of brackets?
Any ideas? :)

Answer 20

would it be k ?

Answer 21

You're taking 2 out of 2k.
So you 're left with k for the first slot,yes,\[\large\rm 7k(k+1)+2(k+~~?~~)\]But what happens when you divide 2 out of 2?
You're not left with 0, you're left with 1, right?\[\large\rm 7k(k+1)+2(k+1)\]

Answer 22

From this point,\[\large\rm 7k\color{orangered}{(k+1)}+2\color{orangered}{(k+1)}\]notice that these two terms have something in common: The (k+1).
So let's artificially put some brackets on the outside of everything,\[\large\rm [7k\color{orangered}{(k+1)}+2\color{orangered}{(k+1)}]\]And from here, we'll pull the common factor (k+1) out of each term,\[\large\rm \color{orangered}{(k+1)}[7k+2]\]Hopefully that last step makes sense.
You're taking the orange part out of each term.
So your 7k(k+1) loses (k+1) becoming 7k.
Similarly the other term 2(k+1) becomes 2 when you take (k+1) out of it.

Answer 23

And that would be your final answer.\[\large\rm (k+1)(7k+2)\]I hope it makes some sense to you.
I know factoring can be a little difficult at first.
Keep practicing! :)

Answer 24

Ok I will keep practicing thanks!! :)