Question

1. Find f(x) + g(x) and determine the degree and numer of different terms for g(x)

f(x)=6x^2+7x ; gx=-2x6^2+9x+5
2. Find h(x)-j(x)
h(x)=4x^3+6x^2+1; j(x)=-8x^4+5x^2+6

Answer 1

To find f(x) + g(x), add the two polynomials. The resulting polynomial has a degree of 6 and 4 different terms. To find h(x) - j(x), subtract the two polynomials. The resulting polynomial has a degree of 4 and 4 different terms.

Step-by-step explanation:

To find f(x) + g(x), we simply add the two given functions.

Given:

• f(x) = 6x^2 + 7x
• g(x) = -2x^6 + 9x + 5

Adding them together:

f(x) + g(x) = (6x^2 + 7x) + (-2x^6 + 9x + 5)

Simplifying further, we combine like terms:

f(x) + g(x) = -2x^6 + 6x^2 + 16x + 5

The degree of the polynomial -2x^6 + 6x^2 + 16x + 5 is 6. The number of different terms is 4.

To find h(x) - j(x), we subtract the two given functions.

Given:

• h(x) = 4x^3 + 6x^2 + 1
• j(x) = -8x^4 + 5x^2 + 6

Subtracting them:

h(x) - j(x) = (4x^3 + 6x^2 + 1) - (-8x^4 + 5x^2 + 6)

Simplifying further, we combine like terms:

h(x) - j(x) = 8x^4 - 4x^3 + x^2 - 5

The degree of the polynomial 8x^4 - 4x^3 + x^2 - 5 is 4. The number of different terms is 4.