Answer :

Sure! Let's solve the problem step-by-step.

We are given two functions:
- [tex]\( f(x) = 2x^3 + x^2 + 8x + 7 \)[/tex]
- [tex]\( g(x) = -5x^3 - 10x - 19 \)[/tex]

We need to find [tex]\( (f-g)(x) \)[/tex], which means subtracting [tex]\( g(x) \)[/tex] from [tex]\( f(x) \)[/tex].

Step 1: Write Down the Expression for [tex]\( (f-g)(x) \)[/tex].

[tex]\[
(f-g)(x) = f(x) - g(x)
\][/tex]

[tex]\[
(f-g)(x) = (2x^3 + x^2 + 8x + 7) - (-5x^3 - 10x - 19)
\][/tex]

Step 2: Simplify the Expression by Distributing the Negative Sign to [tex]\( g(x) \)[/tex].

Apply the negative sign to each term in [tex]\( g(x) \)[/tex]:

- The expression becomes:

[tex]\[
2x^3 + x^2 + 8x + 7 + 5x^3 + 10x + 19
\][/tex]

Step 3: Combine Like Terms.

- Combine the [tex]\( x^3 \)[/tex] terms:

[tex]\( 2x^3 + 5x^3 = 7x^3 \)[/tex]

- Combine the [tex]\( x^2 \)[/tex] terms:

[tex]\( x^2 = x^2 \)[/tex] (no other [tex]\( x^2 \)[/tex] term to combine with)

- Combine the [tex]\( x \)[/tex] terms:

[tex]\( 8x + 10x = 18x \)[/tex]

- Combine the constant terms:

[tex]\( 7 + 19 = 26 \)[/tex]

Step 4: Write the Resulting Polynomial.

Putting it all together, the expression for [tex]\( (f-g)(x) \)[/tex] is:

[tex]\[
(f-g)(x) = 7x^3 + x^2 + 18x + 26
\][/tex]

So, the polynomial for [tex]\( (f-g)(x) \)[/tex] is [tex]\( 7x^3 + x^2 + 18x + 26 \)[/tex].

Thanks for taking the time to read Given the functions tex f x 2x 3 x 2 8x 7 tex and tex g x 5x 3 10x 19 tex find tex f. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada