Answers>Maths>IB>Article

Let (x + 3) be a factor of the polynomial P(x) = x^3 + ax^2 - 7x + 6. Find a and the other two factors.

Firstly, (x - c) is a factor of a polynomial P(x) if and only if there exists a polynomial Q(x) such that P(x) = (x - c)Q(x), where c is a real or complex constant.
Therefore, we can write: P(x) = x^3 + ax^2 - 7x + 6 = (x + 3)(ux^2 + vx + w), where u, v, and w are constants. Now, u = 1 and w = 2, which we find by equating coefficients when we expand the brackets on the R.H.S.
To find v, we expand the brackets to give:
x^3 + ax^2 - 7x + 6 = x^3 + 3x^2 + vx^2 + 3vx + 2x + 6 = x^3 + (3 + v)x^2 + (3v + 2)x + 6.
By equating coefficients we find that v = -3, and that a = 0. Hence, P(x) = x^3 - 7x + 6 = (x + 3)(x - 1)(x - 2).
Therefore: a = 0, and the other two factors of P(x) are (x - 1) and (x - 2).

Answered by Maths tutor

1443 Views

See similar Maths IB tutors

Related Maths IB answers

All answers ▸

Let f (x) = sin(x-1) , 0 ≤ x ≤ 2 π + 1 , Find the volume of the solid formed when the region bounded by y =ƒ( x) , and the lines x = 0 , y = 0 and y = 1 is rotated by 2π about the y-axis.


The function f has a local extreme at point (1,4). If f''(x)=3x^2+2x, then find f(0)?


Solve for x in the following equation: e^x + 10e^(-x) = 7


When the polynomial 3x^3 +ax+ b is divided by x−2 , the remainder is 2, and when divided by x +1 , it is 5. Find the value of a and the value of b.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences