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?

Guest Nov 18, 2019

#1**+1 **

also

Let f(x) = x^4-3x^2 + 2 and g(x) = 2x^4 - 6x^2 + 2x -1 . What is the degree of \(f(x) \cdot g(x)\)?

Guest Nov 18, 2019

#2**+1 **

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

ElectricPavlov Nov 18, 2019

#3**+1 **

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

CPhill Nov 18, 2019