Question
\large x^2+10x+25
a
(x + 10)(x + 15)
b
(x + 5)(x + 2)
c
(x - 5)(x - 5)
d
(x + 5)(x + 5)
a
(x + 10)(x + 15)
b
(x + 5)(x + 2)
c
(x - 5)(x - 5)
d
(x + 5)(x + 5)
Answers
GPT-4o mini
To factor the quadratic expression \( x^2 + 10x + 25 \), we first recognize that it is a perfect square trinomial.
We can rewrite the expression as:
\[
x^2 + 2(5)x + 5^2
\]
This matches the pattern \( a^2 + 2ab + b^2 = (a + b)^2 \), where \( a = x \) and \( b = 5 \). Therefore, we can express the quadratic as:
\[
(x + 5)^2
\]
Now we can check the provided options:
- Option **a**: \( (x + 10)(x + 15) \) is not correct.
- Option **b**: \( (x + 5)(x + 2) \) is also not correct.
- Option **c**: \( (x - 5)(x - 5) \) is incorrect as well.
- Option **d**: \( (x + 5)(x + 5) \) is the correct factorization since it equals \( (x + 5)^2 \).
Thus, the correct answer is:
**d** \( (x + 5)(x + 5) \)
We can rewrite the expression as:
\[
x^2 + 2(5)x + 5^2
\]
This matches the pattern \( a^2 + 2ab + b^2 = (a + b)^2 \), where \( a = x \) and \( b = 5 \). Therefore, we can express the quadratic as:
\[
(x + 5)^2
\]
Now we can check the provided options:
- Option **a**: \( (x + 10)(x + 15) \) is not correct.
- Option **b**: \( (x + 5)(x + 2) \) is also not correct.
- Option **c**: \( (x - 5)(x - 5) \) is incorrect as well.
- Option **d**: \( (x + 5)(x + 5) \) is the correct factorization since it equals \( (x + 5)^2 \).
Thus, the correct answer is:
**d** \( (x + 5)(x + 5) \)