Question

Factor the expression. $$45 x^{2}-60 x+20$$

Short answer

The factored form of the expression \(45x^{2}-60x+20\) is \(5 * (3x - 2)^2\).

Step-by-step solution

Identify common factors

Examine the coefficients of the given quadratic polynomial \(45x^{2}-60x+20\). Here, we can see that 5 is a common factor.

Factor out

We factor out this common factor from each term which results in \(5(9x^{2} - 12x + 4)\). Now, our expression is easier to manage.

Factor the quadratic polynomial

We now need to factor the quadratic polynomial \(9x^{2} - 12x + 4\). This can be represented as \((3x - 2)^2\) since \((3x)^2 = 9x^{2}\), \(- 2 * (3x) * 2 = -12x\) and \(2^2 = 4\).

Combine the factored expressions

Combine the common factor we factored out in step 2 with the quadratic polynomial we factored in step 3. So, \(45x^{2}-60x+20\) can be factored as \(5 * (3x - 2)^2\).