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# Solve this maths problem on Factor Theorem? watch

1. Given that f(x) = x^3 = 2x^2 - 5x - 6 use the Factor Theorem to factorise f(x) completely, hence solve the inequality x^3 + 2x^2 - 5x - 6 > 0
2. (Original post by Sniper21)
Given that f(x) = x^3 = 2x^2 - 5x - 6 use the Factor Theorem to factorise f(x) completely, hence solve the inequality x^3 + 2x^2 - 5x - 6 > 0
Guess a root and factorise. A good start is to plug in factors of the constant term.
3. Factor theorem says that if f(a)=0 then (x-a) is a factor and since this is a cubic f(x)=(x-a)(bx^2+cx+d)=x^3+2x^2-5x-6.Find a suitable a(try factors of -6) and then equate coefficients to find b,c and d and then factorise the quadratic.
4. (Original post by Sniper21)
Given that f(x) = x^3 = 2x^2 - 5x - 6 use the Factor Theorem to factorise f(x) completely, hence solve the inequality x^3 + 2x^2 - 5x - 6 > 0
Is that all the information that is given?
5. (Original post by Sniper21)
Given that f(x) = x^3 = 2x^2 - 5x - 6 use the Factor Theorem to factorise f(x) completely, hence solve the inequality x^3 + 2x^2 - 5x - 6 > 0
I'm doing additional maths gcse this year and have self taught this so I'm gonna give it a go, no guarantees that it will be correct.

By substituting values in for x I can see that f(2) = 0
So (x-2) is one of the three brackets
Then we divide f(x) by (x-2)
x^3+2x^2-5x-6 = (x-2) + x^2+4x+4
f(x) = (x-2)(x+1)(x+3)
6. (Original post by RDKGames)
Guess a root and factorise. A good start is to plug in factors of the constant term.
This is the first part of the question
Use the Remainder Theorem to find the remainder when f(x) = 8x^3 - 4x^2 + 6x +7 is divided by x-1

Please show me the step by step solution.
Is that all the information that is given?
No, this is the original question:
Use the remainder theorem to find the remainder when f9x) = 8x^3 - 4x^2 +6x+7 is divided by x-1
8. (Original post by Sniper21)
This is the first part of the question
Use the Remainder Theorem to find the remainder when f(x) = 8x^3 - 4x^2 + 6x +7 is divided by x-1

Please show me the step by step solution.
The remainder of a polynomial f(x) when divided by (x-a) is f(a), so you would replace any x in f(x) with an a. Step by step solutions are not allowed.
9. (Original post by Sniper21)
This is the first part of the question
Use the Remainder Theorem to find the remainder when f(x) = 8x^3 - 4x^2 + 6x +7 is divided by x-1

Please show me the step by step solution.
These basics should be covered in the C1 book shouldn't they?

Just plug in x=1 and your output is the remainder.
10. (Original post by Sniper21)
No, this is the original question:
Use the remainder theorem to find the remainder when f9x) = 8x^3 - 4x^2 +6x+7 is divided by x-1
8x^2+4x+10

x-1 | 8x^3 - 4x^2 +6x+7
-(8x^3-8x^2)
4x^2+6x+7
-(4x^2-4x)
10x+7
-(10x-10)
17

Remainder = 17

I think it's right, i find these questions easier written down haha
11. (Original post by RDKGames)
These basics should be covered in the C1 book shouldn't they?

Just plug in x=1 and your output is the remainder.
This is what I got for part a) Remainder theorem:
polynomial f(x) has remainder r when divided by (x-a) if f(a) = r
f(x) = 8x^3 - 4x^2 + 6x + 7
f(x) = 8 - 4 + 6 + 7 = 17
It is very straightforward, thanks a lot for your help!
12. (Original post by Sniper21)
This is what I got for part a) Remainder theorem:
polynomial f(x) has remainder r when divided by (x-a) if f(a) = r
f(x) = 8x^3 - 4x^2 + 6x + 7
f(x) = 8 - 4 + 6 + 7 = 17
It is very straightforward, thanks a lot for your help!
No worries Don't forget to give us all the information in future though!

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