Certainly! Let's go through the problem step by step.
### 1.1.1 List all the terms in the expression
The expression given is:
[tex]\[ 7x + 35 \][/tex]
The terms in this expression are:
- [tex]\( 7x \)[/tex]
- [tex]\( 35 \)[/tex]
### 1.1.2 Find the HCF of these terms
To find the Highest Common Factor (HCF), we need to consider the coefficients of the terms. The coefficients are 7 (from [tex]\( 7x \)[/tex]) and 35 (from the constant term).
Now, let’s break down the coefficients into their prime factors:
- [tex]\( 7 \)[/tex] is already a prime number.
- [tex]\( 35 \)[/tex] can be broken down into prime factors: [tex]\( 35 = 5 \times 7 \)[/tex].
The common prime factor is [tex]\( 7 \)[/tex]. Therefore, the HCF of [tex]\( 7 \)[/tex] and [tex]\( 35 \)[/tex] is [tex]\( 7 \)[/tex].
### 1.1.3 Divide all the terms by the HCF
Now, we’ll divide each term by the HCF, which is 7.
- Dividing the first term [tex]\( 7x \)[/tex] by 7:
[tex]\[ \frac{7x}{7} = x \][/tex]
- Dividing the second term [tex]\( 35 \)[/tex] by 7:
[tex]\[ \frac{35}{7} = 5 \][/tex]
So, when we factor out the HCF from the expression [tex]\( 7x + 35 \)[/tex], we get:
[tex]\[ 7x + 35 = 7(x + 5) \][/tex]
### Summary:
1. List of terms: [tex]\( 7x \)[/tex] and [tex]\( 35 \)[/tex].
2. HCF of the coefficients (7 and 35): [tex]\( 7 \)[/tex].
3. Expression after dividing each term by the HCF: [tex]\( 7(x + 5) \)[/tex].
This is the factorized form of the given expression.
