To factor the quadratic expression \(3x^2 + 7x - 6\) by grouping, follow these steps:
1. **Multiply the coefficient of \(x^2\) (which is 3) by the constant term (which is -6)**:
\[
3 \times -6 = -18
\]
2. **Find two numbers that multiply to -18 and add to the coefficient of \(x\) (which is 7)**:
\[
The numbers are 9 and -2 because 9 \times -2 = -18 \quad \text{and} \quad 9 + (-2) = 7
\]
3. **Rewrite the middle term (7x) using the two numbers found (9 and -2)**:
\[
3x^2 + 9x - 2x - 6
\]
4. **Group the terms in pairs**:
\[
(3x^2 + 9x) + (-2x - 6)
\]
5. **Factor out the greatest common factor (GCF) from each pair**:
\[
3x(x + 3) - 2(x + 3)
\]
6. **Factor out the common binomial factor \((x + 3)\)**:
\[
(3x - 2)(x + 3)
\]
So the correct factored form is:
\[
(3x - 2)(x + 3)
\]
Among the given choices, the correct choice is:
\[
(3x - 2)(x + 3)
\]
9.
Factor by grouping.
3x2 + 7x – 6
(3x – 2)(x – 3)
(3x + 2)(x – 3)
(x + 3)(3x + 2)
(3x – 2)(x + 3)
1 answer