How do you divide #(3x^3 - 2x^2 - 12x - 2)/(x-7)#?

Question

Isaiah Anthony · Accepted Answer

#3x^2+19x+121+845/(x-7)# #"one way is to use the divisor as a factor in the numerator"# #"consider the numerator"# #color(red)(3x^2)(x-7)color(magenta)(+21x^2)-2x^2-12x-2# #=color(red)(3x^2)(x-7)color(red)(+19x)(x-7)color(magenta)(+133x)-12x-2# #=color(red)(3x^2)(x-7)color(red)(+19x)(x-7)color(red)(+121)(x-7)color(magenta)(+847)-2# #=color(red)(3x^2)(x-7)color(red)(+19x)(x-7)color(red)(+121)(x-7)+845# #"quotient "=color(red)(3x^2+19x+121),"remainder "=845# #rArr(3x^3-2x^2-12x-2)/(x-7)=3x^2+19x+121+845/(x-7)#

Isaiah Anthony · Answer

undefined To divide (3x^3 - 2x^2 - 12x - 2) by (x-7), you can use long division. Here are the steps:

1. Start by dividing the highest degree term of the dividend (3x^3) by the divisor (x-7). This gives you 3x^2.

2. Multiply the divisor (x-7) by the quotient obtained in step 1 (3x^2). This gives you 3x^3 - 21x^2.

3. Subtract the result obtained in step 2 from the original dividend (3x^3 - 2x^2 - 12x - 2) to get a new polynomial: -19x^2 - 12x - 2.

4. Repeat steps 1-3 with the new polynomial (-19x^2 - 12x - 2).

5. Divide the highest degree term of the new polynomial (-19x^2) by the divisor (x-7). This gives you -19x.

6. Multiply the divisor (x-7) by the quotient obtained in step 5 (-19x). This gives you -19x^2 + 133x.

7. Subtract the result obtained in step 6 from the new polynomial (-19x^2 - 12x - 2) to get a new polynomial: -145x - 2.

8. Repeat steps 1-3 with the new polynomial (-145x - 2).

9. Divide the highest degree term of the new polynomial (-145x) by the divisor (x-7). This gives you -145.

10. Multiply the divisor (x-7) by the quotient obtained in step 9 (-145). This gives you -145x + 1015.

11. Subtract the result obtained in step 10 from the new polynomial (-145x - 2) to get a remainder of 1013.

Therefore, the division of (3x^3 - 2x^2 - 12x - 2) by (x-7) is equal to 3x^2 - 19x - 145 with a remainder of 1013.