Question
Match the polynomial with it's factorization.
x²-36
x²-16
x²-9
x²-36
x²-16
x²-9
Answers
GPT-4o mini
To factor the polynomial \( x^2 - 36 \), we can recognize that it is a difference of squares:
\[
x^2 - 36 = (x - 6)(x + 6)
\]
Now, let's look at the other polynomials you provided:
1. \( x^2 - 16 = (x - 4)(x + 4) \)
2. \( x^2 - 9 = (x - 3)(x + 3) \)
Based on the factorizations:
- \( x^2 - 36 \) matches with \( (x - 6)(x + 6) \)
- \( x^2 - 16 \) matches with \( (x - 4)(x + 4) \)
- \( x^2 - 9 \) matches with \( (x - 3)(x + 3) \)
So the polynomial \( x^2 - 36 \) does not directly match with either \( x^2 - 16 \) or \( x^2 - 9 \); instead, these are separate polynomials with their own factorizations.
In summary, each polynomial's factorization is:
- \( x^2 - 36 = (x - 6)(x + 6) \)
- \( x^2 - 16 = (x - 4)(x + 4) \)
- \( x^2 - 9 = (x - 3)(x + 3) \)
\[
x^2 - 36 = (x - 6)(x + 6)
\]
Now, let's look at the other polynomials you provided:
1. \( x^2 - 16 = (x - 4)(x + 4) \)
2. \( x^2 - 9 = (x - 3)(x + 3) \)
Based on the factorizations:
- \( x^2 - 36 \) matches with \( (x - 6)(x + 6) \)
- \( x^2 - 16 \) matches with \( (x - 4)(x + 4) \)
- \( x^2 - 9 \) matches with \( (x - 3)(x + 3) \)
So the polynomial \( x^2 - 36 \) does not directly match with either \( x^2 - 16 \) or \( x^2 - 9 \); instead, these are separate polynomials with their own factorizations.
In summary, each polynomial's factorization is:
- \( x^2 - 36 = (x - 6)(x + 6) \)
- \( x^2 - 16 = (x - 4)(x + 4) \)
- \( x^2 - 9 = (x - 3)(x + 3) \)