Question

I need help on these two problems please!

Answer 1

14.a. (2x+2)(5-x^2)
2x+2=0
2x=-2
x=-1

5-x^2=0
x^2=5
x=square root of 5

Therefore x=-1, square root of 5

14.b. f(x)= (2x+2)(5-x^2)
=10x+10-2x^3-2x^2
=-2x^3-2x^2+10x+10

Answer 2

The answer to your question is below

Explanation:

14a f(x) = (2x + 2)(5 - x²)

Process

1.- Factor (5 - x²)

(5 - x²) = (
`(√(5) - x)(√(5) + x)`

Then f(x) = (2x + 2) (
`(√(5) - x)(√(5) + x)`

2.- Equal each factor to zero

2x₁ + 2 = 0
`√(5)` - x₂ = 0
`√(5) + x`₃ = 0

2x₁ = -2 x₂ =
`√(5)` x₃ = -
`√(5)`

x₁ = -2/2

x₁ = -1

3.- Conclusion

The roots of the function are

x₁ = -1

x₂ =
`√(5)`

x₃ = -
`√(5)`

14b.Expand the function

(2x + 2) (5 - x²) = 10x - 2x³ + 10 - 2x²

or -2x³ - 2x² + 10x + 10