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.

AH
Answered by Amina H. Maths tutor

1347 Views

See similar Maths IB tutors

Related Maths IB answers

All answers ▸

In the arthmetic sequence, the first term is 3 and the fourth term is 12. Find the common difference (d) and the sum of the first 10 terms.


What method of series convergence test is the correct test?


Solve the equation log2(x + 3) + log2(x - 3) = 4


integrate arcsin(x)


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning