+152 1) Let f(x)= \(x^4-3x^2+2\) and g(x)= \(2x^4+2x-1\). Let a be a constant. What is the largest possible degree of f(x)+a*g(x)?
1b.) Using the same equations as before, let b be a constant. what is the smallest possible degree of the polynomial f(x)+b*g(x)?
2) Suppose f is a polynomial such that f(0)=47, f(1)=32, f(2)=-13, and f(3)=16. What is the sum of the coefficients of f?
3) Let f(x)=\(x^4-3x+2\) and g(x)= \(2x^4-6x^2+2x-1\). What is the degree of f(x)*g(x)?
4) Find t if the expansion of the product of \(x^3-4x^2+2x-5\) and \(x^2+tx-7\) has no \(x^2\) term.
5) There is a polynomial which, when multiplied by \(x^2+2x+3\), gives \(2x^5+3x^4+8x^3+8x^2+18x+9\). What is that polynomial?
Im sorry for the long list of questions. Thank you!!!
+128474 Here's a few, BigChungus
1a) Multiplying a polynomial by a constant doesnot change its degree
So....adding two 4th power polynomial together still produces a 4th power polynomial
1b ) Let b = -1/2
So (1/2) g(x) produces -x^4 - x + 1/2
Adding this to f(x) will produce -3x^2 - x + 5/2
So....the smallest that f + b*g can be is degree 2
+128474 2) Suppose f is a polynomial such that f(0)=47, f(1)=32, f(2)=-13, and f(3)=16. What is the sum of the coefficients of f?
If f(0) = 47....then the constant term must be 47
And if f(1) = 32.....then the sum of the coefficients and the constant term = 32
Therefore
sum of coefficients + constant term = 32
sum of coefficients + 47 = 32 subtract 47 from both sides
sum of coefficients = -15
+152 Thank you for your hard work!!! Unfortunately, the site just started maintenance and its likely my class will end. Sorry for causing trouble
