How do you divide #(-x^4-3x^3-2x^2+7x+3)/(x^2+3) #?

Question

How do you divide #(-x^4-3x^3-2x^2+7x+3)/(x^2+3)  #?

Savannah Anderson · Accepted Answer

#-x^2-3x+1+(16x)/(x^2+3)# Using place keepers of zero value. Example: #0x^3# # color(white)("dddddddddddddd")+x^4-3x^3-2x^2+7x+3# #color(magenta)(-x^2)(x^2+3)->color(white)("d") ul(-x^4+0x^3-3x^2larr" Subtract")# #color(white)("dddddddddddddddd")0 -3x^3+x^2+7x+3# #color(magenta)(-3x)(x^2+3) -> color(white)("dddd")ul(-3x^3+0x^2-9xlarr" Subtract")# #color(white)("ddddddddddddddddddddd")0+x^2+16x+3# #color(magenta)(+1)(x^2+3)->color(white)("dddddddddddd")ul(x^2+color(white)("..")0x+3larr" Subtract")# #color(magenta)("Remainder "->color(white)("dddddddddddd.")0+16x+0)# #color(white)()# #-x^2-3x+1+(16x)/(x^2+3)#

Kennedy Adams · Answer

undefined To divide (-x^4-3x^3-2x^2+7x+3) by (x^2+3), you can use long division. Here are the steps:

1. Divide the first term of the numerator (-x^4) by the first term of the denominator (x^2). The result is -x^2.

2. Multiply the entire denominator (x^2+3) by -x^2, and subtract the result from the numerator. This gives you a new numerator: (-x^4-3x^3-2x^2+7x+3) - (-x^2)(x^2+3).

3. Simplify the new numerator: -x^4-3x^3-2x^2+7x+3 + (x^4+3x^2).

4. Combine like terms in the numerator: -3x^3+7x+3.

5. Repeat the process by dividing the first term of the simplified numerator (-3x^3) by the first term of the denominator (x^2). The result is -3x.

6. Multiply the entire denominator (x^2+3) by -3x, and subtract the result from the simplified numerator. This gives you a new numerator: -3x^3+7x+3 - (-3x)(x^2+3).

7. Simplify the new numerator: -3x^3+7x+3 + (3x^3+9x).

8. Combine like terms in the numerator: 16x+3.

9. Repeat the process by dividing the first term of the simplified numerator (16x) by the first term of the denominator (x^2). The result is 16.

10. Multiply the entire denominator (x^2+3) by 16, and subtract the result from the simplified numerator. This gives you a new numerator: 16x+3 - 16(x^2+3).

11. Simplify the new numerator: 16x+3 - 16x^2-48.

12. Combine like terms in the numerator: -16x^2+16x-45.

The final result of the division is: -x^2 - 3x - 3 + (-3x + 7)/(x^2+3) + 16/(x^2+3) - 45/(x^2+3).