+152 1) Let f(x)= x4−3x2+2 and g(x)= 2x4+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)=x4−3x+2 and g(x)= 2x4−6x2+2x−1. What is the degree of f(x)*g(x)?
4) Find t if the expansion of the product of x3−4x2+2x−5 and x2+tx−7 has no x2 term.
5) There is a polynomial which, when multiplied by x2+2x+3, gives 2x5+3x4+8x3+8x2+18x+9. What is that polynomial?
Im sorry for the long list of questions. Thank you!!!
+130466 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
+130466 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
