p(x)+q(x) and p(x)-q(x),where p(x)=x3-2x2(square)-3 and p(x)=x4+x3+x2-7x
To find the expression for p(x)+q(x), we need to add the two given polynomials:
p(x) = x^3 - 2x^2 - 3
q(x) = x^4 + x^3 + x^2 - 7x
To add the two polynomials, we combine like terms. Let's start by writing down the terms with the highest exponent first:
p(x) + q(x) = (x^4) + (x^3 + x^3) + (-2x^2) + (x^2) + (-7x) + (-3)
Next, we group the terms with the same exponent:
p(x) + q(x) = x^4 + (2x^3) + (-x^2) + (-7x) + (-3)
So, p(x) + q(x) is equal to x^4 + 2x^3 - x^2 - 7x - 3.
Now, let's find the expression for p(x)-q(x). To subtract the two polynomials, we distribute a negative sign to the terms of q(x):
p(x) - q(x) = (x^3 - 2x^2 - 3) - (x^4 + x^3 + x^2 - 7x)
Distribute the negative sign:
p(x) - q(x) = x^3 - 2x^2 - 3 - x^4 - x^3 - x^2 + 7x
Combine like terms:
p(x) - q(x) = (-x^4) + (x^3 - x^3) + (-2x^2 - x^2) + 7x - 3
Simplify:
p(x) - q(x) = -x^4 - 3x^2 + 7x - 3
Therefore, p(x) - q(x) is equal to -x^4 - 3x^2 + 7x - 3.