Question

1. What is the remainder when x^2+4 is divided by x-2?

2. Evaluate f(-1) using substitution: f(x)=2x^3-3x^2-18x-8

3. The point (1,0) lies on the graph of p(x)=x^4-2x^3-x+2
True or false

4. If x-1 is a factor of p(x)=x^3-7x^2+15x-9, which of the following represents the complete factorization for p(x)?
A. (x-3)(x+4)(x+1)
B. (x-3)(x-3)(x-1)
C. (x-3)(x+3)(x-1)
D. (x-3)(x+3)(x+1)

Answer 1

1.The remainder is 8. (x2 + 4)/(x - 2) = (x + 2) + 8/(x - 2) or x2 + 4 = (x - 2)(x + + 8
2. 5
3.not sure but maybe true
4.divide P(x) by (x-1) to get the quadratic equation... from which can be solve using any method in finding the roots of quadratic equation....

Answer 2

1) 8

2) 5

3) False

4) Option B

Explanation:

1) We have to find the remainder when we divide (x² + 4) by (x - 2)

To get the remainder we will put x = 2 in (x² + 4)

= (2)² + 4

= 8

2). We have to evaluate f(-1) using substitution in f(x) = 2x³ - 3x² - 18x - 8

f(-1) = 2(-1)³ - 3(-1)²- 18(-1) - 8

= 2(-1) - 3 + 18 -8

= -2 - 3 + 18 - 8

= 5

3) The point (1, 0) lies on the graph of p(x) =
`x^(4)-2x^(3)-x+2`

If this point lies on the graph then p(1) should be equal to zero.

p(1) = 1³ - 7(1)² + 7(1) - 9

= 1 - 7 + 7 - 9

= -8 ≠ 0

Therefore, It's false.

4). (x - 1) is a factor of p(x) = x³ - 7x² + 15x - 9

Now we will factorize it further when (x - 1) is a zero factor.

By Synthetic division

1 | 1 - 7 15 -9

1 -6 9

-----------------------------

1 -6 9 0

Now we have got the expression as (x - 1)(x²- 6x + 9)

Or (x -1)(x² - 6x + 9) = (x - 1)(x - 3)(x - 3)

Therefore, Option B. is the answer.