what is the degree of the polynomial p(x)+q(x) let p(x)=x^4-7x+14 and q(x)=x^2-5
To find the degree of the polynomial p(x) + q(x), we first need to understand what a degree of a polynomial means. The degree of a polynomial is the highest exponent of the variable in the polynomial.
Given that p(x) = x^4 - 7x + 14 and q(x) = x^2 - 5, we can see that p(x) is a 4th degree polynomial because the highest exponent of x is 4, which is the exponent in the term x^4. Similarly, q(x) is a 2nd degree polynomial because the highest exponent of x is 2, which is the exponent in the term x^2.
To find the degree of p(x) + q(x), we need to add the two polynomials together. When we add two polynomials, we combine like terms. In this case, the highest exponent of x in the sum will determine the degree of the resulting polynomial.
So, let's add p(x) and q(x):
p(x) + q(x) = (x^4 - 7x + 14) + (x^2 - 5)
Combining like terms, we get:
p(x) + q(x) = x^4 + x^2 - 7x - 5 + 14
Simplifying further:
p(x) + q(x) = x^4 + x^2 - 7x + 9
Now, looking at the resulting polynomial, we can see that the highest exponent of x is 4, which means that the degree of p(x) + q(x) is 4.