IDNLearn.com is committed to providing high-quality answers to your questions. Whether it's a simple query or a complex problem, our community has the answers you need.
Sagot :
To understand the transition from Step 1 to Step 2, let's carefully examine the operations performed:
Step 1:
[tex]\[ -c = a x^2 + b x \][/tex]
In Step 1, we have a quadratic equation set up in a standard form, where the right-hand side is a polynomial expression.
Step 2:
[tex]\[ -c = a\left(x^2 + \frac{b}{a} x\right) \][/tex]
For Step 2, let's rewrite the equation to understand the transformation. The expression [tex]\( a x^2 + b x \)[/tex] is factored, with [tex]\( a \)[/tex] being factored out from the terms involving [tex]\( x \)[/tex].
The factored form changes as follows:
[tex]\[ a x^2 + b x = a \left( x^2 + \frac{b}{a} x \right) \][/tex]
Here, each term in the polynomial [tex]\( a x^2 + b x \)[/tex] is divided by [tex]\( a \)[/tex]:
- From [tex]\( a x^2 \)[/tex], when divided by [tex]\( a \)[/tex], we get [tex]\( x^2 \)[/tex].
- From [tex]\( b x \)[/tex], when divided by [tex]\( a \)[/tex], we get [tex]\( \frac{b}{a} x \)[/tex].
Thus, pulling the factor [tex]\( a \)[/tex] out and placing it in front of the parenthesis, we get:
[tex]\[ -c = a \left(x^2 + \frac{b}{a} x \right) \][/tex]
This operation is specifically the process of factoring the common factor [tex]\( a \)[/tex] out of the terms involving [tex]\( x \)[/tex].
Therefore, the best explanation or justification for Step 2 is:
Factoring the binomial.
This approach simplifies the equation and prepares it for further steps, such as completing the square or deriving the quadratic formula.
Step 1:
[tex]\[ -c = a x^2 + b x \][/tex]
In Step 1, we have a quadratic equation set up in a standard form, where the right-hand side is a polynomial expression.
Step 2:
[tex]\[ -c = a\left(x^2 + \frac{b}{a} x\right) \][/tex]
For Step 2, let's rewrite the equation to understand the transformation. The expression [tex]\( a x^2 + b x \)[/tex] is factored, with [tex]\( a \)[/tex] being factored out from the terms involving [tex]\( x \)[/tex].
The factored form changes as follows:
[tex]\[ a x^2 + b x = a \left( x^2 + \frac{b}{a} x \right) \][/tex]
Here, each term in the polynomial [tex]\( a x^2 + b x \)[/tex] is divided by [tex]\( a \)[/tex]:
- From [tex]\( a x^2 \)[/tex], when divided by [tex]\( a \)[/tex], we get [tex]\( x^2 \)[/tex].
- From [tex]\( b x \)[/tex], when divided by [tex]\( a \)[/tex], we get [tex]\( \frac{b}{a} x \)[/tex].
Thus, pulling the factor [tex]\( a \)[/tex] out and placing it in front of the parenthesis, we get:
[tex]\[ -c = a \left(x^2 + \frac{b}{a} x \right) \][/tex]
This operation is specifically the process of factoring the common factor [tex]\( a \)[/tex] out of the terms involving [tex]\( x \)[/tex].
Therefore, the best explanation or justification for Step 2 is:
Factoring the binomial.
This approach simplifies the equation and prepares it for further steps, such as completing the square or deriving the quadratic formula.
We are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. IDNLearn.com is your go-to source for accurate answers. Thanks for stopping by, and come back for more helpful information.