QuestionFactorise
Studdy Solution
STEP 1
What is this asking?
We need to find two expressions that multiply together to give us .
Watch out!
Don't forget to check your answer by multiplying the factors back together!
It's super easy to make a small mistake, so checking is key!
STEP 2
1. Set up the factors
2. Find the constant terms
3. Find the x terms
STEP 3
Alright, let's **kick things off**!
We know our answer will look like , where , , , and are numbers we need to **hunt down**!
Since when we multiply the first terms together we get , and is a **prime number** (meaning its only factors are and itself), we can confidently say our factors will look like .
STEP 4
Now, let's **crack the code** of those constant terms!
When we multiply the last terms in each factor, we should get .
Since is also a **prime number**, its only factors are and .
This means and could be and (in either order!).
STEP 5
Let's **test out** the combination .
Multiplying this out gives us .
Hmm, close, but not quite!
The term is , not .
STEP 6
Let's **flip the script** and try .
Multiplying this out gives us . **Bingo!** That's exactly what we're looking for!
STEP 7
We've already found the correct factors in the previous step, but let's **dive a little deeper** into *why* this works.
Notice that the middle term, , comes from adding the product of the outer terms () and the product of the inner terms ().
So, , which **nails it**!
STEP 8
The factored form of is .
Was this helpful?
