Question

Completely factor the expression. $$4 x^{2}-28 x+49$$

Short answer

The completely factored form of \(4x^{2} - 28x + 49\) is \((2x - 7)^{2}\).

Step-by-step solution

Identify the coefficients

First identify the coefficients in the quadratic equation \(4x^{2} - 28x + 49\). The coefficient a is attached to \(x^{2}\) which is 4, the coefficient b is attached to x which is -28 and the constant c is 49.

Factor

Then factor the quadratic equation. This can be done by observing the pattern and making use of the identity \((a-b)^{2} = a^{2} - 2ab + b^{2}\). So the given expression can be rewritten as: \((2x - 7)^{2}\) as \(2^{2} = 4\) and \(2*2*7 = 28\) and \(7^{2} = 49\)

Write the final factored form

The completely factored form of the given quadratic expression \(4x^{2} - 28x + 49\) is \((2x - 7)^{2}\).