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How do you show that (x+2) is a factor of f(x) = x^3 - 19x - 30, and then factorise f(x) completely?

A1) Showing that (x+2) is a factor of f(x). General Method: If A is a number, then (x- A) is a factor of f(x) if when x=A, f(x=A)=0 <-- This is what we want to show ...

Answered by Rebecca W. • Maths tutor

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f(x) = 2x^3 – 7x^2 + 4x + 4 (a) Use the factor theorem to show that (x – 2) is a factor of f(x). (2) (b) Factorise f(x) completely.

We are presented with a third order polynomial with 4 terms, so we expect 3 solutions for f(x)=0. To prove that (x-2) is a factor we must insert the value of x=2 into the function and if f(2)=0 then we ha...

Answered by Nazar A. • Maths tutor

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Consider a cone of vertical height H (in metres) and base radius R (in metres) which is full with water. The cone, at time t=0, starts to leak such that it loses water at a rate of k m^3 per second. Give an expression for the rate of change of H.

L = (H²+R²)^1/2 V = (1/3)πR²(H²+R²)^1/2

dV/dt = -k

dH/dt = dH/dV × dv/dt

dV/dH = (1/3)πR²H(H^...

Answered by Callum E. • Maths tutor

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Integrate the following function: f(x) = ln(x)

∫ln(x)dx = xln(x) - ∫x/x dx = xln(x) - x + C

Answered by Callum E. • Maths tutor

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Why is the differential of a constant zero?

Any constant (say k) can be rewritten as kx⁰ since x⁰=1. When you differentiate this, the 0 which is the power of the x term gets dragged to the front and is multiplied with the rest...

Answered by Jawad C. • Maths tutor

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