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Answer :
To factor the expression [tex]\(10r - 15\)[/tex], let's follow these steps:
1. Identify the Greatest Common Factor (GCF):
- Look at the coefficients of the terms [tex]\(10r\)[/tex] and [tex]\(-15\)[/tex].
- The GCF of 10 and 15 is 5.
2. Factor out the GCF:
- Divide each term by the GCF.
- [tex]\(10r \div 5 = 2r\)[/tex]
- [tex]\(-15 \div 5 = -3\)[/tex]
3. Write the expression in factored form:
- Once you've divided each term by the GCF, factor the expression as:
[tex]\[
10r - 15 = 5(2r - 3)
\][/tex]
4. Verify the factorization:
- Distribute the factor 5 throughout the terms in the parenthesis:
[tex]\[
5(2r) = 10r \quad \text{and} \quad 5(-3) = -15
\][/tex]
- The distributed expression [tex]\(10r - 15\)[/tex] matches the original expression, confirming that the factorization is correct.
So the factored form of the expression [tex]\(10r - 15\)[/tex] is [tex]\(5(2r - 3)\)[/tex].
1. Identify the Greatest Common Factor (GCF):
- Look at the coefficients of the terms [tex]\(10r\)[/tex] and [tex]\(-15\)[/tex].
- The GCF of 10 and 15 is 5.
2. Factor out the GCF:
- Divide each term by the GCF.
- [tex]\(10r \div 5 = 2r\)[/tex]
- [tex]\(-15 \div 5 = -3\)[/tex]
3. Write the expression in factored form:
- Once you've divided each term by the GCF, factor the expression as:
[tex]\[
10r - 15 = 5(2r - 3)
\][/tex]
4. Verify the factorization:
- Distribute the factor 5 throughout the terms in the parenthesis:
[tex]\[
5(2r) = 10r \quad \text{and} \quad 5(-3) = -15
\][/tex]
- The distributed expression [tex]\(10r - 15\)[/tex] matches the original expression, confirming that the factorization is correct.
So the factored form of the expression [tex]\(10r - 15\)[/tex] is [tex]\(5(2r - 3)\)[/tex].
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