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The factor theorem states that a polynomial f(x) has a factor (x-k) if and only if f(k)=0. 
f(2) = 3(2)^3 - 8(2)^2 + 3(2) + 2 = 3(8) - 8(4) + 6 + 2 = 24 - 32 + 8 = 0.
==> (x-2) is a fac...

Step 1 - Label y = x²  + 4x – 8 as equation 1 and y = - 2x – 17 as equation 2.Step 2 - In this particular question it is easier to eliminate the y variable from both equations, as they are both...

LHS: Factorise numerator and denominator, which gives:((2x - 7)(x + 2))/((x + 2)(x + 4))Cancel out (x + 2), gives:(2x - 7)/(x + 4)Multiply both sides by (x + 4)(x + 3) to cancel the denominators, gives:(2...

Let's start by assuming that the squared root of 2 is a rational number and will prove it is irrational by contradiction.If srqt(2) is rational then it can be represented by an irreducible fraction. Let t...

Let n be any whole number. Any odd number can be written as 2n+1. Any odd number squared is therefore (2n+2)²=2n2n+22n+1=4n²+4n+1=4(n²+n)+1. n²+n is a ...