Question
Factor this expression
2x^2 + 9x + 9
2x^2 + 9x + 9
Answers
Answered by
GPT-4o mini
To factor the expression \( 2x^2 + 9x + 9 \), we need to find two numbers that multiply to \( 2 \times 9 = 18 \) (the product of the coefficient of \( x^2 \) and the constant term) and add to \( 9 \) (the coefficient of \( x \)).
The two numbers that satisfy these conditions are \( 6 \) and \( 3 \), since \( 6 \times 3 = 18 \) and \( 6 + 3 = 9 \).
We can now rewrite the middle term of the expression using these two numbers:
\[
2x^2 + 6x + 3x + 9
\]
Next, we can group the terms:
\[
(2x^2 + 6x) + (3x + 9)
\]
Now, we can factor out the common factors from each group:
\[
2x(x + 3) + 3(x + 3)
\]
Now we see that \( (x + 3) \) is a common factor:
\[
(2x + 3)(x + 3)
\]
Thus, the factored form of the expression \( 2x^2 + 9x + 9 \) is:
\[
(2x + 3)(x + 3)
\]
The two numbers that satisfy these conditions are \( 6 \) and \( 3 \), since \( 6 \times 3 = 18 \) and \( 6 + 3 = 9 \).
We can now rewrite the middle term of the expression using these two numbers:
\[
2x^2 + 6x + 3x + 9
\]
Next, we can group the terms:
\[
(2x^2 + 6x) + (3x + 9)
\]
Now, we can factor out the common factors from each group:
\[
2x(x + 3) + 3(x + 3)
\]
Now we see that \( (x + 3) \) is a common factor:
\[
(2x + 3)(x + 3)
\]
Thus, the factored form of the expression \( 2x^2 + 9x + 9 \) is:
\[
(2x + 3)(x + 3)
\]