Question

Given the functions (x)=x2-4 and h(x)=x+2, Express the following as the sum, difference, products, or quotient of the functions above
1. P(x)=x-2
2 .r(x)=x2+x-2
3.s(x)=x3+2x2-4x-8
4.t(x)=x2+x+6

Answer 1

1. (x)/h(x) [quotient]

=x²-4/x+2

=(x+2)(x-2)/(x+2)

=x-2

=P(x)

2. (x)+h(x) [sum]

= x²-4+x+2

=x²+x-2

=r(x)

3. (x)*h(x) [product]

=(x²-4)(x+2)

=x³+2x-4x-8

=s(x)

4. (x)-h(x) [difference]

=(x²-4)-(x+2)

=x²-4-x-2

=x²-x-6 (there seems to be a problem with the - signs. Did you enter the question correctly?)

Hope it helps

Answer 2

GIVEN : (x) = x²-4

h(x)= x+2

To find: value in form of sum,Product,quotient difference

Solution:

We have, (x) = x²-4

h(x) = x+2

Sum of (x) + h(x)

= x²-4+ x+2

= x²+x-2

Difference of (x )- h(x)

= x²-4-(x+2)

= x²-4 -x -2

= x² -x -6

Product of (x) * h (x)

= (x²-4)*(x+2)

= x³+2x²- 4x -8

Quotient of (x)/ h(x)

= (x²-4)/ (x+2)

= (x²-2²)/(x+2) [ using a²- b²= (a+b)(a-b)]

= (x+2)(x-2)/(x+2)

= (x-2) [(x+2) cancelled out]

Answer: Sum = x²+x-2

Difference = x²-x+6

Product = x³+2x²-4x-8

Quotient =x-2