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Factorise the expression: 2x^2 + 17x + 21

There are several ways to factorise this quadratic expression, but the best way in my opinon is: Take the constant in front of the x^2 and multiply it by the standalone constant (i.e. multiply 2 by 21, which...
TM
Answered by Tushar M. • Maths tutor
9828 Views

Solve the simultaneous equations: 4x+y=25 and x-3y=16

Lets first give the equations names. 4x+y=25 (A) x-3y=16 (B) We want to get the equations so that they have either the same number of x's or same number of y's. So let's multiply equation (A) by three so tha...
MD
Answered by Michael D. • Maths tutor
10155 Views

You are given the function f(x)=x^3-x^2-7x+3, and that x=3 is a root of f(x)=0. Find the exact values of the other 2 roots. (6 marks)

First step is to realise that as x=3 is a root of f(x)=0, then we can use (x-3) as a factor of f(x). A really good method to use to find what (fx)/(x-3) gives is Synthetic Division. Using this method we then...
DH
Answered by David H. • Maths tutor
3884 Views

How do you find the point or points of intersection of a straight line and a circle?

Given the equation of the straight line is: x+y=9 and the equation of the circle is: (x-2) 2 +(y-3) 2 =16 , find the point or points of intersection? The equation x+y=9 can be rearranged to make x=9-y. This ...
EC
Answered by Edward C. • Maths tutor
6182 Views

Integrate | x^7 (ln x)^2 dx ( | used in place of sigma throughout question)

Start the integration by parts process |udv = uv - |vdu u = (ln x) 2 dv = x 7 dx du = 2(ln x)/x dx v = 1/8 x 8 = 1/8 x 8 (ln x) 2 - | 1/4(ln x)x 7 dx = 1/8 x 8 (ln x) 2 -1/4 | x 7 (ln x) dx Repeat the integr...
RD
Answered by Rowan D. • Maths tutor
8692 Views