Question

Learning Task 1. Perform what is asked.
1. Evaluate 3x4 + 2x2 - 5x + 1 when x = 3202
2. What is the remainder if x3 + 2x2 - 4x + 3 is divided by (x - 3)?
3. Given P(x)
2x3 + 5x2 – 3, find P(-1).
4. If f(x) = x3 + 4x2 + 3x - 2, what will be the value of f(x) at x = 3?
5. Use synthetic division to find the remainder when (5x2 - 2x + 1) is divided
by (x + 2).​

Answer 1

Step-by-step explanation:

Learning Task 1. Perform what is asked.

1. Evaluate 3x4 + 2x2 - 5x + 1 when x = 3202

2. What is the remainder if x3 + 2x2 - 4x + 3 is divided by (x - 3)?

3. Given P(x)

2x3 + 5x2 – 3, find P(-1).

4. If f(x) = x3 + 4x2 + 3x - 2, what will be the value of f(x) at x = 3?

5. Use synthetic division to find the remainder when (5x2 - 2x + 1) is divided

by (x + 2).​

Answer 2

Answer:

1) $3.15 * 10^{14}$

2) 36

3) 0

4) 70

5) 25

Step-by-step explanation:

1)  Evaluate $3x^{4} + 2x^{2} - 5x + 1$ when x = 3202

Solution:

Given,

x = 3202

$3x^{4} + 2x^{2} - 5x + 1$  ...............(1)

Substitute the value of x in equation (1) we get,

$3(3202)^{4} + 2(3202)^{2} - 5(3202) + 1$  = $(3.15 *10^{14} ) + (20505608) - (16010) +1$

                                       Answer  = $3.15 * 10^{14}$

2. What is the remainder if $x^{3} + 2 x^{2} - 4x + 3$  is divided by (x - 3)?

Solution:

Given,

x - 3 = 0

x = 3

$x^{3} + 2 x^{2} - 4x + 3$    ...............(1)

Substitute x = 3 in equation (1) we get:

$x^{3} + 2 x^{2} - 4x + 3 = 3^{3} + 2 (3)^{2} - 4 (3) + 3$

                            = 27 + 18 - 12 + 3

                            = 36

The remainder of $x^{3} + 2 x^{2} - 4x + 3$ is 36.

By using synthetic division also method the remainder is 36.

3. Given P(x) = $2 x^{3} + 5x^{2} - 3$ , find P(-1).

Solution:

P(x) = $2 x^{3} + 5x^{2} - 3$     ................(1)

x = -1

Substitute the value of x in equation (1) we get,

P(-1) = $2 (-1)^{3} + 5(-1)^{2} - 3$

P(-1) = -2 + 5 -3

P(-1) = -5 + 5

P(-1) = 0

4. If f(x) = $x^{3} + 4x^{2} +3x-2$, what will be the value of f(x) at x = 3?

Solution:

Given:

$f(x) = x^{3} + 4x^{2} +3x-2$    .................(1)

x = 3

Substitute the value of x in equation (1) we get,

$f(3) = 3^{3} + 4(3)^{2} +3(3) -2$

f(3) = 27 + 36 + 9 - 2

f(3) = 72 - 2

f(3) = 70

5. Use synthetic division to find the remainder when $(5x^{2} - 2x + 1)$ is divided by (x + 2).​

Solution:

Given,

x + 2

Therefore x = -2

Equation = $5x^{2} - 2x + 1$

By using synthetic division,

-2 ║ 5        -2         1

       0        -10       24

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

       5         -12        25

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

The remainder = 25

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