Question

Pls answer this for me, this is the remainder theorem for grade 9 so help me.

1) x^3 +5x^2+ 2x +1 divided by x+1
2) x^3 - 6x^2 + 5x + 2 divided by x - 5

Answer 1

1. 3

2. 2

Explanation:

| |

x | + | 1 | | x^2 | + | 4 x | - | 2

x^3 | + | 5 x^2 | + | 2 x | + | 1

x^3 | + | x^2 | | | |

| | 4 x^2 | + | 2 x | |

| | 4 x^2 | + | 4 x | |

| | | | -2 x | + | 1

| | | | -2 x | - | 2

| | | | | | 3

__________________________________________

| |

x | - | 5 | | x^2 | - | x | + | 0

x^3 | - | 6 x^2 | + | 5 x | + | 2

x^3 | - | 5 x^2 | | | |

| | -x^2 | + | 5 x | |

| | -x^2 | + | 5 x | |

| | | | | | 2

| | | | | | 0

| | | | | | 2

Answer 2

Explanation:

1) x + 1 = 0

x = -1

P(x) = x³ + 5x² + 2x + 1

P(-1) = (-1)³ + 5(-1)² + 2*(-1) + 1

= -1 + 5*1 -2 +1

= - 1 +5 - 2 +1

P(-1) = 3

2)x -5 =0

x = 5

P(x) = x³ - 6x² + 5x + 2

P(5) =5³ -6*(5)² + 5*5 + 2

= 125 - 6*25 + 25 + 2

= 125 - 150 + 25 +2

P(5) = 2