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Take the polynomial p(x)=x^4+x^3+2x^2+4x-8, use the factor theorem to write p(x) as two linear factors and an irreducible quadratic. An irreducible quadratic is a quadratic that can not be factorised.

We must use the factor theorem since that is what the question asks. So we take p(x) and think about the factors of 8 we then evaluate it at x=1 to start, then move onto x=-1,2,-2 and so on. We see that it h...
JC
Answered by Jordan C. • Maths tutor
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How would the integral ∫x^2sin2xdx be solved using integration by parts?

The general formula for integration by parts is given as ∫u(dv/dx)dx = uv - ∫v(du/dx)dx given that the equation to be solved is ∫x 2 sin2xdx, the values for u, v, du/dx and dv/dx can be assigned as u = x 2 d...
SN
Answered by Samuel N. • Maths tutor
11573 Views

A stone is thrown from a bridge 10m above water at 30ms^-1 30 degrees above the horizontal. How long does the stone take to strike the water? What is its horizontal displacement at this time?

The first thing to do for part a) is work out the vertical component of the velocity. By drawing a triangle where 30m/s is the hypotenuse with angles of 30 degrees, 90 degrees, and 60 degrees, and by applyin...
SU
Answered by Sarah U. • Maths tutor
6424 Views

What is the derivative of f(x)=sqrt(3x+2)=(3x+2)^(1/2)?

By the power rule, the derivative of x^(n) is nx(n^1) and by the chain rule, the derivative of g(h(x)) is g'(h(x))h'(x). Let g(x)=x^(1/2) and h(x)=3x+2 so that f(x)=g(h(x)). Then by the power rule, g'(x)=(1/...
LP
Answered by Luke P. • Maths tutor
5610 Views

A circle C with centre at the point (2, –1) passes through the point A at (4, –5). Find an equation for the circle C.

You would start with this equation (x – a) 2 + (y – b) 2 = r 2 , with the center being at the point (a, b) and the radius being "r". Therefore you would have (x-2) 2 +(y+1) 2 =r 2 , in order to det...
IN
Answered by Ishan N. • Maths tutor
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