Question
Fill in the blank to show what the quadratic expression would look like when factored.(5 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. x2−3x−10x2−3x−10 = (x−x−3x)(x+x+2) 3x2−6x+93x2−6x+9 = 1(x2−2x+3)(x2−2x+3) 9x2−259x2−25 = (3x−3x−2)(5+5+5)
Answers
GPT-4o mini
To factor the given quadratic expressions, here are the correct factorizations:
1. For the expression \( x^2 - 3x - 10 \), the factorization is:
\[
(x - 5)(x + 2)
\]
2. For the expression \( 3x^2 - 6x + 9 \), it factors to:
\[
3(x^2 - 2x + 3)
\]
However, this polynomial does not factor neatly into linear factors with real coefficients since it has no real roots.
3. For the expression \( 9x^2 - 25 \), the factorization is:
\[
(3x - 5)(3x + 5)
\]
Here's what the blanks would look like filled:
1. \( x^2 - 3x - 10 = (x - 5)(x + 2) \)
2. \( 3x^2 - 6x + 9 = 3(x^2 - 2x + 3) \)
3. \( 9x^2 - 25 = (3x - 5)(3x + 5) \)
For the inputs you have described, place the correct response into the appropriate slots based on the structure of your query.
1. For the expression \( x^2 - 3x - 10 \), the factorization is:
\[
(x - 5)(x + 2)
\]
2. For the expression \( 3x^2 - 6x + 9 \), it factors to:
\[
3(x^2 - 2x + 3)
\]
However, this polynomial does not factor neatly into linear factors with real coefficients since it has no real roots.
3. For the expression \( 9x^2 - 25 \), the factorization is:
\[
(3x - 5)(3x + 5)
\]
Here's what the blanks would look like filled:
1. \( x^2 - 3x - 10 = (x - 5)(x + 2) \)
2. \( 3x^2 - 6x + 9 = 3(x^2 - 2x + 3) \)
3. \( 9x^2 - 25 = (3x - 5)(3x + 5) \)
For the inputs you have described, place the correct response into the appropriate slots based on the structure of your query.