301 results for "polynomial".

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• Question

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

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)

Questions about complex arithmetic; argument and modulus of complex numbers; complex roots of polynomials; de Moivre's theorem.

• Question

Finding the coordinates and determining the nature of the stationary points on a polynomial function

• Question

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 $q(x)=0$.

• Divide Polynomials
Question

Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.

• Question

$f(X)$ and $g(X)$ as polynomials over the rational numbers $\mathbb{Q}$.

Find their greatest common divisor (GCD) and enter as a normalized polynomial.

• Question

Expanding products of 3 linear  polynomials over $\mathbb{Z}_3,\;\mathbb{Z}_5,\;\mathbb{Z}_7$

• Question

$f(X)$ 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.

• Factorise 4 polynomials over $\mathbb{Z}_5$.

• Question

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

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

• Question

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

• Question

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

• Question

Use a given factor of a polynomial to find the full factorisation of the polynomial through long division.

• Question

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

• Question

Find the remainder when dividing two polynomials, by algebraic long division.

• Question

This question tests the student's ability to find remainders using the remainder theorem.

• Exam (5 questions)

Apply the factor and remainder theorems to manipulate polynomial expressions

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Finding the coordinates and determining the nature of the stationary points on a polynomial function

• Question

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• Question

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

• Question

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)

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.

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