Question
Factor completely.
6m2–10m+4
6m2–10m+4
Answers
GPT-4o mini
To factor the expression \( 6m^2 - 10m + 4 \), we will first find the greatest common factor (GCF) of the terms in the polynomial.
1. **Identify the GCF**: The GCF of the coefficients (6, -10, and 4) is 2. We factor out 2 from the entire expression:
\[
6m^2 - 10m + 4 = 2(3m^2 - 5m + 2)
\]
2. **Factor the quadratic expression**: Now we need to factor \( 3m^2 - 5m + 2 \). We can use the method of factoring by grouping or the quadratic formula to find two numbers that multiply to \( 3 \times 2 = 6 \) and add to \( -5 \). The numbers are \( -3 \) and \( -2 \).
3. **Rewrite the middle term**:
\[
3m^2 - 3m - 2m + 2
\]
4. **Group the terms**:
\[
(3m^2 - 3m) + (-2m + 2)
\]
5. **Factor out the common factors in each group**:
\[
3m(m - 1) - 2(m - 1)
\]
6. **Factor out the common binomial factor**:
\[
(3m - 2)(m - 1)
\]
7. **Combine everything**:
\[
6m^2 - 10m + 4 = 2(3m - 2)(m - 1)
\]
So the completely factored form of the expression \( 6m^2 - 10m + 4 \) is:
\[
\boxed{2(3m - 2)(m - 1)}
\]
1. **Identify the GCF**: The GCF of the coefficients (6, -10, and 4) is 2. We factor out 2 from the entire expression:
\[
6m^2 - 10m + 4 = 2(3m^2 - 5m + 2)
\]
2. **Factor the quadratic expression**: Now we need to factor \( 3m^2 - 5m + 2 \). We can use the method of factoring by grouping or the quadratic formula to find two numbers that multiply to \( 3 \times 2 = 6 \) and add to \( -5 \). The numbers are \( -3 \) and \( -2 \).
3. **Rewrite the middle term**:
\[
3m^2 - 3m - 2m + 2
\]
4. **Group the terms**:
\[
(3m^2 - 3m) + (-2m + 2)
\]
5. **Factor out the common factors in each group**:
\[
3m(m - 1) - 2(m - 1)
\]
6. **Factor out the common binomial factor**:
\[
(3m - 2)(m - 1)
\]
7. **Combine everything**:
\[
6m^2 - 10m + 4 = 2(3m - 2)(m - 1)
\]
So the completely factored form of the expression \( 6m^2 - 10m + 4 \) is:
\[
\boxed{2(3m - 2)(m - 1)}
\]