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Factorise x^3+3x^2-x-3

Test factors of -3 to find a root for the equation. For example, try 1, 1^3+3*1^2-1-3=0, so 1 is a root, and (x-1) is a factor. Now it's known that: (ax^2+bx+c)(x-1)=x^3+3x^2-x-3. By comparing coefficients f...
SC
Answered by Sian C. • Maths tutor
7815 Views

Draw the curve for x^2-5x+6

In order to find the intercepts of this curve, we first need to factorise the quadratic equation. We need to find 2 numbers that add together to equal -5 and those two same numbers multiply together to equal...
NS
Answered by Nilja S. • Maths tutor
4585 Views

why is sin(x) squared plus cos(x) squared 1?

Thinking of sine and cosine as ratios of side lengths in a right angled triangle, sin(x) = o/h and cos(x) = a/h, so the sin(x)^2 + cos(x)^2 becomes (o^2 + a^2)/h^2. By Pyhtagoras, o^2 + a^2 = h^2, so we get ...
MS
Answered by Matthew S. • Maths tutor
23502 Views

How can I calculate the maximum value of the compound angle formulae Rsin(x+a) and Rcos(x+a)?

Often, the compound angle formulae can seem quite offputting, especially since exam pressures can mean the random "R" at the front of an angle addition formulae appears confusing. However, finding ...
LB
Answered by Luke B. • Maths tutor
15937 Views

using the substitution u=6-x^2 integrate (x^3)/(6-x^2)^1/2 with respect to x, between 1 and 2

First we calculate du/dx = -2x and rearrange to get dx as the subject, dx=du/(-2x). Now we change the limits of integration because we are now integrating with respect to u. So the bottom limit will be u(1) ...
DB
Answered by Daniel B. • Maths tutor
5522 Views