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)

1) 8

2) 5

3) False

4) Option B

Step-by-step 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) =

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.

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step-by-step explanation: