divide 5x^3-5x+1/x-3?

(5x^3 - 5x +1 )/(x-3)
= (5x^3 -15x^2 +15x^2-45x +40x - 120 + 121)/(x-3)
= 5x^2+15x+40 + 121/(x-3)
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You can also use sythetic division or long division.

3 | 5____0____-5____1
_ |_____15___45____120
_ | 5___ 15___40____121

5x² + 15x + 40 Rem 121

= (5x³ - 5x + 1)/(x - 3)
= 5x² + 15x + 40 rem 121

Answer: 5x² + 15x + 40 & 121/(x - 3)

Checking back to 5x³ - 5x + 1:
= ([5x² + 15x+ 40][x - 3]) + 121
= 5x³ - 15x² + 15x² - 45x + 40x - 120 + 121
= 5x³ - 5x + 1

..............5x^2 + 15x + 40
......__________________
x - 3)5x^3 + 0x^2 - 5x + 1
.......5x^3 - 15x^2
--------------------------------------
................15x^2 - 5x
................15x^2 - 45x
--------------------------------------
..........................40x + 1
.......................40x - 120
--------------------------------------
................................121

(5x^3 - 5x + 1)/(x - 3)
= (5x^2 + 15x + 40) + 121/(x - 3)
= 5(x^2 + 3x + 8) + 121/(x - 3)

you detect zeros for (x + a million)(x - 2)(x - 3) very certainly: If everybody bracket includes 0, no remember what's in the different brackets, the total term will replace into 0. So seem on the 1st bracket (x + a million). What x would make x+a million=0? attempt (-a million). Do an identical exercising for the subsequent 2 brackets and you have your answer (for this and all destiny projects of this manner). (3x^3 + 4x^2 – 5x – 2) ÷ (x + 2). as quickly as you think of, you have the answer, multiply it by utilising (x+2). If the effect is 3x^3+4x^2-5x-2 then your answer is o.ok. attempt (x+2)*(3*x^2-2*x-a million). that's stable prepare to place in writing polynomials in a undeniable order, often with the utmost exponent of the self sufficient variable first. y = 5x^3 – 2x^2 + x – 13 is in that time-honored. wish it facilitates.

you can't multiply 5 by nothing to the third root

Hey you can just use long division...see steps here:

http://www.mathanswerkey.com/solution.php?q=ld((5x'3-5x+1)/(x-3))

5x^3 - 5x + 1
= 5x^3 - 15x^2 + 15x^2 - 45x + 40x - 120 + 121
= 5x^2(x - 3) + 15x(x - 3) + 40(x - 3) + 121
= (x - 3)(5x^2 + 15x + 40) + 121

=> (5x^3 - 5x + 1) / (x - 3)
= 5x^2 + 15x + 40 + (121)/(x - 3)

5x^2+15x+40 +121/(x-3)

moms