Factoring cubic polynomial

[scottjohnston]

my teacher gave me this problem as a homework assignment and I am struggling to factor and find the roots of the following polynomial.

f(x)=2x³+42x+40 given that f(4)=0. I can factor out a 2 of course but that really does not help me find additional roots. So I tried used synthetic division. I wrote the coefficients of the terms in the polynomial: 2 for x³, 0 for x², 42 for x and 40. I divide them by the given root, 4 and I find that there is a remainder of 80 so it seems 4 is not a root after all. Am I correct? What am I missing?

Thanks very much.

 

[Deleted member 4993]

my teacher gave me this problem as a homework assignment and I am struggling to factor and find the roots of the following polynomial.

f(x)=2x³+42x+40 given that f(4)=0. I can factor out a 2 of course but that really does not help me find additional roots. So I tried used synthetic division. I wrote the coefficients of the terms in the polynomial: 2 for x³, 0 for x², 42 for x and 40. I divide them by the given root, 4 and I find that there is a remainder of 80 so it seems 4 is not a root after all. Am I correct? What am I missing?

Thanks very much.

You must have made some mistake in your division.

f(x) = 2x³+42x+40 = 2(x-4)(x² + 4x - 5)

 

[scottjohnston]

Thanks for the prompt response but I am still confused. When I multiply 2(x-4)(x²+4x-5) I get 2(x³-21x+20) or 2x³-42x+40. The original function was 2x³+42+40=f(x)

Sorry to be so dense.

 

[scottjohnston]

Denis:
Thanks. There is no typo in the original function. That has been what is so confusing to me in trying to factor and find the roots. Given that I have written the function correctly would you agree that 4 is not a root? I think the homework question has an error in it but I needed to make sure I was not missing something here.

Scott

 

[Deleted member 4993]

Denis:
Thanks. There is no typo in the original function. That has been what is so confusing to me in trying to factor and find the roots. Given that I have written the function correctly would you agree that 4 is not a root? I think the homework question has an error in it but I needed to make sure I was not missing something here.

Scott

To check whether f(4) = 0 or not → evaluate f(x) at x = 4

if f(x) = 2x³+42x+40 → f(4) = 336

 

[HallsofIvy]

f(x)=2x³+42x+40 given that f(4)=0.

The sum of positive numbers cannot be 0.