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Help To Solve This Polynomial! - Education - Nairaland

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Help To Solve This Polynomial! by debowale2015(m): 7:14am On Sep 28, 2016
please can anyone help to solve correctly this polynomial question.
It says that;
A polynomial f(x)= px^3+qx^2-x+3 has a factor of (x+1) and when divided by (x-4) leave a remainder of 15. Find f(x)?
I will appreciate your kindly contribution.
Re: Help To Solve This Polynomial! by SirBrightoc(m): 8:13am On Sep 28, 2016
Answer: f(x) = x^3 - 3x^2 - x + 3

Solution:
x + 1 is a factor means f(-1) = 0
: f(-1) = p(-1)^3 + q(-1)^2 - (-1) + 3 = 0

Therefore, -p + q + 4 = 0 . . . Equation 1

Also, x - 4 leaves a remainder of 15.
It means f(4) = 15.
ie f(4) = p(4)^3 + q(4)^2 - 4 + 3 = 15

That gives 4p + q - 1 = 0 . . . Equation 2

Solve the simultaneous equations to get
p = 1 and q = -3

1 Like

Re: Help To Solve This Polynomial! by debowale2015(m): 6:42pm On Sep 28, 2016
SirBrightoc:
Answer: f(x) = x^3 - 3x^2 - x + 3

Solution:
x + 1 is a factor means f(-1) = 0
: f(-1) = p(-1)^3 + q(-1)^2 - (-1) + 3 = 0

Therefore, -p + q + 4 = 0 . . . Equation 1

Also, x - 4 leaves a remainder of 15.
It means f(4) = 15.
ie f(4) = p(4)^3 + q(4)^2 - 4 + 3 = 15

That gives 4p + q - 1 = 0 . . . Equation 2

Solve the simultaneous equations to get
p = 1 and q = -3

Sir....I appreciate your effort! thats exactly what i had taught of (i mean your solution).
Thanks!

1 Like

Re: Help To Solve This Polynomial! by SirBrightoc(m): 4:12am On Sep 30, 2016
debowale2015:


Sir....I appreciate your effort! thats exactly what i had taught of (i mean your solution).
Thanks!
Welcome my brother.
Re: Help To Solve This Polynomial! by tosyne2much(m): 9:50am On Sep 30, 2016
SirBrightoc:
Answer: f(x) = x^3 - 3x^2 - x + 3
Solution: x + 1 is a factor means f(-1) = 0 : f(-1) = p(-1)^3 + q(-1)^2 - (-1) + 3 = 0
Therefore, -p + q + 4 = 0 . . . Equation 1
Also, x - 4 leaves a remainder of 15. It means f(4) = 15. ie f(4) = p(4)^3 + q(4)^2 - 4 + 3 = 15
That gives 4p + q - 1 = 0 . . . Equation 2
Solve the simultaneous equations to get p = 1 and q = -3
Kudos bro! Maths becomes a mystery to me till date cheesy

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