1. Let f(x) = x^3 + 3x ^2 + 4x - 7 and g(x) = -7x^4 + 5x^3 +x^2 - 7. What is the coefficient of x^3 in the sum f(x) + g(x)?
2. Let f(x) = x^4-3x^2 + 2 and g(x) = 2x^4 - 6x^2 + 2x -1. Let a be a constant. What is the largest possible degree of \(f(x) + a\cdot g(x)?\)
3. Let f(x) = x^4-3x^2 + 2 and g(x) = 2x^4 - 6x^2 + 2x -1. Let b be a constant. What is the smallest possible degree of the polynomial \(f(x) + b\cdot g(x)\)?
4. 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?
also
Let f(x) = x^4-3x^2 + 2 and g(x) = 2x^4 - 6x^2 + 2x -1 . What is the degree of \(f(x) \cdot g(x)\)?
1> Well, yo would just add the x^3 tems in the two fxns 1 + 5 = 6
2> If a is a constant, it will only change the coefficients of the functions, not the degree of the terms
so the greatest degree will still be 4 form the x^4 and 2x^4 in the two fxns
3> Similar to 2 except the lowest degree will be 1 from the 2x term
4> not sure
the constant will be 47
5> when the two functions are multiplied you will have a x^4 * 2x^4 = 2 x^8 term in the final answer.... dgree 8
1. Let f(x) = x^3 + 3x ^2 + 4x - 7 and g(x) = -7x^4 + 5x^3 +x^2 - 7. What is the coefficient of x^3 in the sum f(x) + g(x)?
The coefficient is just the sum of 1x^3 + 5x^3 = 6x^3 = 6
2. Let f(x) = x^4-3x^2 + 2 and g(x) = 2x^4 - 6x^2 + 2x -1. Let a be a constant. What is the largest possible degree of
f(x) + a* g(x)
As long as "a" is not -1/2 , the sum will result in a polynomial of degree 4
3. Let f(x) = x^4-3x^2 + 2 and g(x) = 2x^4 - 6x^2 + 2x -1. Let b be a constant. What is the smallest possible degree of the polynomial f(x) + b * g(x) ?
If "b" is -1/2 the resulting sum will be a first power polynomial....this is the smallest possible degree
4. 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 of the polynomial must just be 47
If f(1) = 32
Then the sum of the coefficients is just 32 - 47 = - 15