Ray
Lv 6
Ray asked in 科學及數學數學 · 1 decade ago

# F4 Maths Dividing Polynomials6

1. Divide the following polynomial.Find Q(x),R(x) No need the steps.

(x^4+2x^3-12x^2-4) / (x^2-2x-6)

2. When A is divided by x^2+x+1, the Q(x) is x^2-2 with R(x) 2x+7. Find the Q(x) and R(x) when A is divided by x^2-2x+4.

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• wkho28
Lv 7

1. Divide the following polynomial. Find Q(x), R(x) No need the steps.

(x^4+2x^3-12x^2-4) / (x^2-2x-6)

1+4+2

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

1-2-6 ) 1+2-12+0-4

1-2-6

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

4-6+0

4-8-24

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

2+24-4

2 - 4-12

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

28+8

Q(x) = x^2 + 4x + 2

R(x) = 28x + 8

2. When A is divided by x^2+x+1, the Q(x) is x^2-2 with R(x) 2x+7. Find the Q(x) and R(x) when A is divided by x^2-2x+4.

A = (x^2+x+1) Q(x) + R(x)

= (x^2+x+1)(x^2-2)+2x+7

= x^4+x^3-x^2-2x-2+2x+7

= x^4+x^3-x^2+5

1+3+1

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

1-2+4 ) 1+1-1+0+5

1-2+4

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

3-5+0

3-6+12

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

1-12+5

1 - 2+4

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

-10+1

Q(x) = x^2 + 3x + 1

R(x) = -10x + 1