Question

Learning Task 1. Perform what is asked.
1. Evaluate 3x4 + 2x - 5x + 1 when x 3202
2. What is the remainder if x8+2x44x+ 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).

Para po yan sa gr 10
topic:Remainder Theorem and Factor Theorem​​

Answer 1

1. 3x^4 + 2x^ - 5x + 1 when x = 3202 is 3(3202)⁴ + 20489599.

2. Remainder if x^8 + 2x^4 + 4x + 3 is divided by ( x - 3 ) is 6414.

3. P( -1 ) = 0.

4. The value of f(x) at x = 3 is 70.

5.  The remainder when ( 5x^2 - 2x + 1 ) is divided by ( x + 2 ) is 25.

Given:

1.    Evaluate 3x^4 + 2x^ - 5x + 1 when x = 3202

2.   x^8 + 2x^4 + 4x + 3 is divided by ( x - 3 )

3.   P(x) = 2x^3 + 5x^2 -3

4.   f(x) = x^3 + 4x^2 + 3x - 2

5.   ( 5x^2 - 2x + 1 ) is divided by ( x + 2 )

To Find:

1.  Result after evaluating 3x^4 + 2x^ - 5x + 1 when x = 3202.

2. Remainder if x^8 + 2x^4 + 4x + 3 is divided by ( x - 3 ).

3. P(-1)

4. The value of f(x) at x = 3.

5. The remainder when ( 5x^2 - 2x + 1 ) is divided by ( x + 2 ).

Solution:

1.

The given expression is 3x^4 + 2x^ - 5x + 1

Substitute x = 3202 in the above expression, and we get

3x^4 + 2x^ - 5x + 1 = 3(3202)⁴ + 2(3202)² - 5(3202) + 1

=  3(3202)⁴ + 2(10252804) - 16010 + 1

= 3(3202)⁴ + 20505608 -16009

= 3(3202)⁴ + 20489599

2.

When x^8 + 2x^4 + 4x + 3 is divided by ( x - 3 ), the remainder is 6414 and the quotient is x⁷ + 3x⁶ + 9x⁵ + 27x⁴ - 79x³ + 237x² + 711x + 2137.

3.

Given that P(x) = 2x^3 + 5x^2 - 3. Substitute x = -1. We get,

P(-1 ) = 2(-1)³ + 5(-1)² - 3

        = 2(-1) + 5(1) - 3

        = -2 + 5 - 3

        = 5 - 5

 P(-1) = 0

4.

Given that  f(x) = x^3 + 4x^2 + 3x - 2. Now substitute x = 3. We get,

f(3) = (3)^3 + 4(3)^2 + 3(3) - 2

= 27 + 4(9) + 9 - 2

= 27 + 36 + 7

= 70

The value of f(x) at x = 3 is 70

5.

When ( 5x^2 - 2x + 1 ) is divided by ( x + 2 ), the remainder is 25 and the quotient is 5x - 12.

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