SOLUTION: Solve the equation 15x^3+14x^2-3x-2=0given that -1 is a zero of f(x)15x^3+14x^2-3x-2=0 where does the (x+1) come from? what is the best way to solve 15x^3+14x^2-3x-2=0

Algebra ->  Sequences-and-series -> SOLUTION: Solve the equation 15x^3+14x^2-3x-2=0given that -1 is a zero of f(x)15x^3+14x^2-3x-2=0 where does the (x+1) come from? what is the best way to solve 15x^3+14x^2-3x-2=0      Log On


   

Question 1155004: Solve the equation 15x^3+14x^2-3x-2=0given that -1 is a zero of f(x)15x^3+14x^2-3x-2=0
where does the (x+1) come from?

what is the best way to solve
15x^3+14x^2-3x-2=0
Found 3 solutions by ewatrrr, MathLover1, MathTherapy:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi  

given that -1 is a zero of f(x)

That tells You 

( x -(-1)) is a factor  of 15x^3+14x^2-3x-2=0

Use traditional division to find %2815x%5E3%2B14x%5E2-3x-2%29+%2F%28x%2B1%29

%2815x%5E3%2B14x%5E2-3x-2%29+%2F%28x%2B1%29 = 15x^2 - x - 2

15x^2 - x - 2 = (5x-2)(3x+1)

(5x-2)=0

(3x+1)=0

Roots are:  -1, -1/3, 2/5

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the equation 15x%5E3%2B14x%5E2-3x-2=0
given that -1 is a zero of f%28x%29=15x%5E3%2B14x%5E2-3x-2=0
recall zero product theorem:
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29 where x%5B1%5D,x%5B2%5D, and x%5B3%5D are zeros

if x%5B1%5D=-1 is a zero, than %28x-x%5B1%5D%29=x-%28-1%29=x%2B1
that is where the (x+1) comes from, and it means that 15x%5E3%2B14x%5E2-3x-2=0 is divisible by x%2B1 or x%2B1 is one of the factors

the best way to solve is try to factor completely
since you know x%2B1 is a factor, try to make groups that will factor out x%2B1
15x%5E3%2B14x%5E2-3x-2=0......write 14x%5E2 as -x%5E2%2B15x%5E2 and -3x as -2x-x

15x%5E3-x%5E2%2B15x%5E2-2x-x-2=0...group
%2815x%5E3%2B15x%5E2%29-%28x%5E2%2Bx%29-%282x%2B2%29=0
15x%5E2%28x%2B1%29-x%28x%2B1%29-2%28x%2B1%29=0
%28x+%2B+1%29%2815x%5E2+-+x+-+2%29+=+0
%28x+%2B+1%29%2815x%5E2+%2B5x+-+6x+-+2%29+=+0
%28x+%2B+1%29%28%2815x%5E2+%2B5x%29+-+%286x+%2B+2%29%29+=+0
%28x+%2B+1%29%285x%283x+%2B1%29+-+2%283x+%2B+1%29%29+=+0

%28x+%2B+1%29%283x+%2B+1%29%285x-2%29+=+0

now, find solutions
if %28x+%2B+1%29+=+0=>x=-1
%283x+%2B+1%29=+0=>3x=-1=>x=-1%2F3
%285x-2%29+=+0=>5x=2=>x=2%2F5






Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the equation 15x^3+14x^2-3x-2=0given that -1 is a zero of f(x)15x^3+14x^2-3x-2=0
where does the (x+1) come from?

what is the best way to solve
15x^3+14x^2-3x-2=0
matrix%281%2C3%2C+15x%5E3+%2B+14x%5E2+-+3x+-+2%2C+%22=%22%2C+0%29

- 1 is a ROOT, which means that x = - 1.

Setting this equation equal to 0, we get: x + 1 = 0, which means that x + 1 is a FACTOR of this polynomial.

Do you now see where x + 1 came from?

An easy- maybe not the best - method to solve this is the method that Tutor ewatrrr posted, which is long-division of a polynomial.

Synthetic division is another easy method if you're familiar with that topic.

Pay no attention to the other person's, if you want to make live easier for yourself!.