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The curve's equation is presented as an implicit function. Therefore we must use implicit differentiation to solve this problem. To do this, we differentiate both sides of the equation with respect to x, ...

A prime number is a number only divisible by itself and 1. To write 36 as a product of its prime factors we use a factor tree. The key thing to remember is to always circle the prime numbers. So we start ...

a) To show (x+2) is a factor, we want to show f(-2)=0. So (-2)^3-2(-2)^2 -29(-2)-42=-8-8+58-42=0
b) Divide  x^3 -2x^2-29x-42 by x+2 to get x^2-4x-21 which we factorise to get (x+3)(x-7). Hence f(x)=(...

This question is suited to A2 maths students, particularly those who are doing further maths and may be looking for a challenge. In one question it tests the students ability to use implicit differentiati...

Firstly we need to understand what the question is asking us to do. Factorise means we need to take out the Highest Common Factor (HCF) that each term can be divided by.The two terms in this question is 3...