Question
What is the factorization of the polynomial below?
-x^2-14x-48
0-1(x+8)(x+6)
01-x+8)(x-6)
0 (x+6)(x+8)
0(-x+ (-x+6)(x+8)
-x^2-14x-48
0-1(x+8)(x+6)
01-x+8)(x-6)
0 (x+6)(x+8)
0(-x+ (-x+6)(x+8)
Answers
GPT-4o mini
To factor the polynomial \(-x^2 - 14x - 48\), we can first factor out -1 for easier handling:
\[
-x^2 - 14x - 48 = -1(x^2 + 14x + 48)
\]
Next, we need to factor the quadratic \(x^2 + 14x + 48\). We are looking for two numbers that multiply to \(48\) and add up to \(14\). The numbers that satisfy this are \(6\) and \(8\), since:
\[
6 \times 8 = 48
\]
\[
6 + 8 = 14
\]
So we can express the quadratic as:
\[
x^2 + 14x + 48 = (x + 6)(x + 8)
\]
Putting it all together, the complete factorization of the original polynomial is:
\[
-x^2 - 14x - 48 = -1(x + 6)(x + 8)
\]
Thus, the final factorization is:
\[
-(x + 6)(x + 8)
\]
\[
-x^2 - 14x - 48 = -1(x^2 + 14x + 48)
\]
Next, we need to factor the quadratic \(x^2 + 14x + 48\). We are looking for two numbers that multiply to \(48\) and add up to \(14\). The numbers that satisfy this are \(6\) and \(8\), since:
\[
6 \times 8 = 48
\]
\[
6 + 8 = 14
\]
So we can express the quadratic as:
\[
x^2 + 14x + 48 = (x + 6)(x + 8)
\]
Putting it all together, the complete factorization of the original polynomial is:
\[
-x^2 - 14x - 48 = -1(x + 6)(x + 8)
\]
Thus, the final factorization is:
\[
-(x + 6)(x + 8)
\]