301 results for "polynomial".

Question in Content created by Newcastle University
Given two complex numbers, find by inspection the one that is a root of a given quartic real polynomial and hence find the other roots.

Question in Content created by Newcastle University
Find the first 3 terms in the Taylor series at $x=c$ for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.

Exam (13 questions) in Content created by Newcastle University
Questions about complex arithmetic; argument and modulus of complex numbers; complex roots of polynomials; de Moivre's theorem.

Question in Content created by Newcastle University
Finding the coordinates and determining the nature of the stationary points on a polynomial function

Question in Content created by Newcastle University
Complete the square for a quadratic polynomial $q(x)$ by writing it in the form $a(x+b)^2+c$. Find both roots of the equation $q(x)=0$.

Question in Content created by Newcastle University
Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.

Question in Content created by Newcastle University
$f(X)$ and $g(X)$ as polynomials over the rational numbers $\mathbb{Q}$.
Find their greatest common divisor (GCD) and enter as a normalized polynomial.

Question in Content created by Newcastle University
Expanding products of 3 linear polynomials over $\mathbb{Z}_3,\;\mathbb{Z}_5,\;\mathbb{Z}_7$

Question in Content created by Newcastle University
$f(X)$ and $g(X)$ are polynomials over $\mathbb{Z}_n$.
Find their greatest common divisor (GCD) and enter it as a monic polynomial.
Hence factorize $f(X)$ into irreducible factors.

Question in Content created by Newcastle University
Factorise 4 polynomials over $\mathbb{Z}_5$.

Question in Content created by Newcastle University
Given polynomial $f(X)$, $g(X)$ over $\mathbb{Q}$, find polynomials $q(X)$ and $r(X)$ over $\mathbb{Q}$ such that $f(X)=q(X)g(X)+r(X)$ and $\operatorname{deg}r(X) \lt \operatorname{deg}g(X)$.

Question in Transition to university
Apply the factor theorem to check which of a list of linear polynomials are factors of another polynomial.

Question in Transition to university
This question tests the student's knowledge of the remainder theorem and the ways in which it can be applied.

Question in Transition to university
Given a factor of a cubic polynomial, factorise it fully by first dividing by the given factor, then factorising the remaining quadratic.

Finding the full factorisation of a polynomial, using the Factor Theorem and long division Ready to useQuestion in Transition to university
Use a given factor of a polynomial to find the full factorisation of the polynomial through long division.

Question in Transition to university
Factorise polynomials by identifying common factors. The first expression has a constant common factor; the rest have common factors involving variables.

Question in Transition to university
Find the remainder when dividing two polynomials, by algebraic long division.

Question in Transition to university
This question tests the student's ability to find remainders using the remainder theorem.

Exam (5 questions) in Transition to university
Apply the factor and remainder theorems to manipulate polynomial expressions

Question in NC PreCalculus
No description given

Question in NC PreCalculus
No description given

Question in NC PreCalculus
Finding the coordinates and determining the nature of the stationary points on a polynomial function

Question in NC PreCalculus
No description given

Question in NC PreCalculus
No description given

Question in NC PreCalculus
No description given

Question in NC PreCalculus
No description given

Question in J. Richard's workspace
Factorise polynomials by identifying common factors. The first expression has a constant common factor; the rest have common factors involving variables.

Question in Kevin's workspace
Three graphs are given with areas underneath them shaded. The student is asked to calculate their areas, using integration. Q1 has a polynomial. Q2 has exponentials and fractional functions. Q3 requires solving a trig equation and integration by parts.

Exam (11 questions) in Andrew's workspace
Differentiation of polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.
From mathcentre.ac.uk

Exam (12 questions) in MATH7025
Differentiation of polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.
rebelmaths