Answer :
To factor the expression [tex]\(10r - 15\)[/tex], we need to find the greatest common factor (GCF) of the terms in the expression.
1. Identify the terms: The expression [tex]\(10r - 15\)[/tex] consists of two terms: [tex]\(10r\)[/tex] and [tex]\(-15\)[/tex].
2. Find the GCF:
- The coefficients of the terms are 10 and 15.
- Determine the GCF of 10 and 15. Both numbers can be divided by 5, which is the largest number that can divide both without leaving a remainder. So, the GCF is 5.
3. Factor using the GCF:
- Take the GCF, which is 5, and factor it out of each term.
- When you factor 5 out of [tex]\(10r\)[/tex], you're left with [tex]\( \frac{10r}{5} = 2r \)[/tex].
- When you factor 5 out of [tex]\(-15\)[/tex], you're left with [tex]\( \frac{-15}{5} = -3 \)[/tex].
4. Write the expression as a product:
- Combine these results in the format of factored expression: [tex]\(5(2r - 3)\)[/tex].
So, the factored form of the expression [tex]\(10r - 15\)[/tex] is [tex]\(5(2r - 3)\)[/tex].
1. Identify the terms: The expression [tex]\(10r - 15\)[/tex] consists of two terms: [tex]\(10r\)[/tex] and [tex]\(-15\)[/tex].
2. Find the GCF:
- The coefficients of the terms are 10 and 15.
- Determine the GCF of 10 and 15. Both numbers can be divided by 5, which is the largest number that can divide both without leaving a remainder. So, the GCF is 5.
3. Factor using the GCF:
- Take the GCF, which is 5, and factor it out of each term.
- When you factor 5 out of [tex]\(10r\)[/tex], you're left with [tex]\( \frac{10r}{5} = 2r \)[/tex].
- When you factor 5 out of [tex]\(-15\)[/tex], you're left with [tex]\( \frac{-15}{5} = -3 \)[/tex].
4. Write the expression as a product:
- Combine these results in the format of factored expression: [tex]\(5(2r - 3)\)[/tex].
So, the factored form of the expression [tex]\(10r - 15\)[/tex] is [tex]\(5(2r - 3)\)[/tex].
