Question
Factor completely.
3q2–8q–3
3q2–8q–3
Answers
GPT-4o mini
To factor the quadratic expression \(3q^2 - 8q - 3\), we can use the factoring method for quadratics.
1. Start with the expression:
\[
3q^2 - 8q - 3
\]
2. Multiply the coefficient of \(q^2\) (which is 3) with the constant term (which is -3):
\[
3 \times (-3) = -9
\]
3. Now, we need to find two numbers that multiply to -9 and add up to the coefficient of \(q\) (which is -8). The numbers that satisfy this are -9 and 1 because:
\[
-9 \times 1 = -9 \quad \text{and} \quad -9 + 1 = -8
\]
4. Rewrite the middle term using -9 and 1:
\[
3q^2 - 9q + 1q - 3
\]
5. Now, group the terms:
\[
(3q^2 - 9q) + (1q - 3)
\]
6. Factor out the greatest common factor from each group:
\[
3q(q - 3) + 1(q - 3)
\]
7. Now factor out the common binomial \((q - 3)\):
\[
(3q + 1)(q - 3)
\]
Thus, the completely factored form of the expression \(3q^2 - 8q - 3\) is:
\[
(3q + 1)(q - 3)
\]
1. Start with the expression:
\[
3q^2 - 8q - 3
\]
2. Multiply the coefficient of \(q^2\) (which is 3) with the constant term (which is -3):
\[
3 \times (-3) = -9
\]
3. Now, we need to find two numbers that multiply to -9 and add up to the coefficient of \(q\) (which is -8). The numbers that satisfy this are -9 and 1 because:
\[
-9 \times 1 = -9 \quad \text{and} \quad -9 + 1 = -8
\]
4. Rewrite the middle term using -9 and 1:
\[
3q^2 - 9q + 1q - 3
\]
5. Now, group the terms:
\[
(3q^2 - 9q) + (1q - 3)
\]
6. Factor out the greatest common factor from each group:
\[
3q(q - 3) + 1(q - 3)
\]
7. Now factor out the common binomial \((q - 3)\):
\[
(3q + 1)(q - 3)
\]
Thus, the completely factored form of the expression \(3q^2 - 8q - 3\) is:
\[
(3q + 1)(q - 3)
\]