3. (a) Square is already completed; irreducible (b) Square is already completed; factors as (x – /5)(x + /5) (c) x² + 4x + 6 = (x + 2)² + 2; irreducible (d) x² +4x +2 = (x + 2)² – 2; factors as (x + 2 – /2)(x + 2 + /2)
In algebra, a quadratic equation is a polynomial whose degree is equal to 2. Every quadratic equation can be expressed in terms of a complete square and a constant. Sum of two squares are irreducible while difference of two squares can be rewritten as product of their sum and difference.
To do: Prove given statements.
(a) Square is already completed; irreducible
Lets assume a polynomial:
We can see in this example if a polynomial is already complete it can't be reduced further.
(b) Square is already complete: Lets assume an polynomial according to question
As we know difference of two squares can be reduced according to formula:
So we can write our polynomial as:
We can see difference of squares factors as shown in question.
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