Question
Identify the factors of the polynomial 6x2 - 18x - 24 when factored completely.
3
(x - 1)
(x + 1)
(x - 4)
(6x + 6)
(x + 4)
(x + 6)
6
3
(x - 1)
(x + 1)
(x - 4)
(6x + 6)
(x + 4)
(x + 6)
6
Answers
GPT-4o mini
To factor the polynomial \( 6x^2 - 18x - 24 \) completely, we can start by factoring out the greatest common factor (GCF). The GCF of the coefficients 6, -18, and -24 is 6.
So we can factor out 6:
\[
6(x^2 - 3x - 4)
\]
Next, we will factor the quadratic \( x^2 - 3x - 4 \). We look for two numbers that multiply to \(-4\) (the constant term) and add to \(-3\) (the coefficient of \(x\)). The numbers that meet these criteria are \(-4\) and \(1\).
Thus, we can factor \( x^2 - 3x - 4 \) as:
\[
(x - 4)(x + 1)
\]
Putting it all together, we have:
\[
6(x - 4)(x + 1)
\]
So the completely factored form of the polynomial \( 6x^2 - 18x - 24 \) is:
\[
6(x - 4)(x + 1)
\]
Therefore, the factors of the polynomial are \(6\), \( (x - 4) \), and \( (x + 1) \).
So we can factor out 6:
\[
6(x^2 - 3x - 4)
\]
Next, we will factor the quadratic \( x^2 - 3x - 4 \). We look for two numbers that multiply to \(-4\) (the constant term) and add to \(-3\) (the coefficient of \(x\)). The numbers that meet these criteria are \(-4\) and \(1\).
Thus, we can factor \( x^2 - 3x - 4 \) as:
\[
(x - 4)(x + 1)
\]
Putting it all together, we have:
\[
6(x - 4)(x + 1)
\]
So the completely factored form of the polynomial \( 6x^2 - 18x - 24 \) is:
\[
6(x - 4)(x + 1)
\]
Therefore, the factors of the polynomial are \(6\), \( (x - 4) \), and \( (x + 1) \).