Answers>Maths>IB>Article

Given f(x)=(x^3-7)*(x+4)^5, find the term x^3 of f(x).

Before starting to solve this problem, student should acknowledge that there are more than a variable, which satisfies the condition x^3. There are two ways to obtain this answer: (1) x^3 in the first multiple is multiplied by the constant in the second multiple; (2) -7 multiplied by the term x^3 with some coefficient, which should be obtained after expanding and simplifying the binomial theorem. The correct answer would be (1)+(2). 

Bearing this in mind, the first step should be using binomial theorem to expand and simplify the equation.Since we are looking for the constant (x^0) and x^3 terms, even without simplifying the whole expression, the correct answer can be found. The constant is the last term in the expression with x^0, nCr(5,0)=1, hence 41=4; and the term with x^3 is the 3rd term, nCr(5,3)=10, 10x^34^2=160x^3

(1) => 4x^3 and (2) => -7160x^3=-112x^3 

Hence, the correct answer is (4-112)x^3= -108x^3.

Answered by Amina H. Maths tutor

1145 Views

See similar Maths IB tutors

Related Maths IB answers

All answers ▸

The velocity, v, of a moving body at time t is given by v = 50 - 10t. A) Find its acceleration. B) The initial displacement, s, is 40 meters. Find an expression for s in terms of t.


Solve (sec (x))^2 + 2tan(x) = 0


The normal to the curve x*(e^-y) + e^y = 1 + x, at the point (c,lnc), has a y-intercept c^2 + 1. Determine the value of c.


Solve: 1/3 x = 1/2 x + (− 4)


We're here to help

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