p(x)+q(x) and p(x)-q(x),where p(x)=x3-2x2(square)-3 and p(x)=x4+x3+x2-7x
Yes
To find the expressions p(x) + q(x) and p(x) - q(x), we need to substitute the given expressions p(x) into the respective formulas and perform the required operations.
Let's first find p(x) + q(x):
p(x) + q(x) = (x^3 - 2x^2 - 3) + (x^4 + x^3 + x^2 - 7x)
To add these polynomials, we combine like terms by adding the coefficients of the same powers of x.
(x^3 + x^3) + (x^4) + (-2x^2 + x^2) + (-7x) - 3
This simplifies to:
x^4 + 2x^3 - x^2 - 7x - 3
Now let's find p(x) - q(x):
p(x) - q(x) = (x^3 - 2x^2 - 3) - (x^4 + x^3 + x^2 - 7x)
To subtract these polynomials, we distribute the negative sign to each term in q(x) and combine like terms.
x^3 - 2x^2 - 3 - x^4 - x^3 - x^2 + 7x
This simplifies to:
-x^4 - 2x^3 - 3x^2 + 7x - 3
Therefore, p(x) + q(x) = x^4 + 2x^3 - x^2 - 7x - 3 and p(x) - q(x) = -x^4 - 2x^3 - 3x^2 + 7x - 3.