Question

recap add and subtract polynomials- complete in your notebook this shows two functions. $f(x) = 2x^4 - x + 1$ $g(x) = x^4 - 3x^3 + 5x - 1$ a). what is the result of $f(x)+g(x)$? b). what is the result of $f(x)-g(x)$?

Explanation:

Step1: Substitute functions for f(x)+g(x)

$
f(x)+g(x) = (2x^4 - x + 1) + (x^4 - 3x^3 + 5x - 1)
$

Step2: Group like terms

$
f(x)+g(x) = (2x^4 + x^4) - 3x^3 + (-x + 5x) + (1 - 1)
$

Step3: Combine like terms

$
f(x)+g(x) = 3x^4 - 3x^3 + 4x
$

Step4: Substitute functions for f(x)-g(x)

$
f(x)-g(x) = (2x^4 - x + 1) - (x^4 - 3x^3 + 5x - 1)
$

Step5: Distribute the negative sign

$
f(x)-g(x) = 2x^4 - x + 1 - x^4 + 3x^3 - 5x + 1
$

Step6: Group like terms

$
f(x)-g(x) = (2x^4 - x^4) + 3x^3 + (-x - 5x) + (1 + 1)
$

Step7: Combine like terms

$
f(x)-g(x) = x^4 + 3x^3 - 6x + 2
$

Answer:

a). $3x^4 - 3x^3 + 4x$
b). $x^4 + 3x^3 - 6x + 2$