Is 9x^2 - 12x + 4 a perfect square? Why?

Because it is equal to (3x - 2)^2.

Step-by-step explanation:

If we factor we'll see why:

9x^2 - 12x + 4

To factor we can use the 'ac' method:

Multiplying the leading coefficient by the constant term: 9 * 4 = 36.

We need 2 numbers whose product is 36 and whose sum is -12:

These are -6 and -6 so we write:

9x^2 - 6x - 6x + 4  

Factor by grouping:

= 3x(3x - 2)  - 2(3x - 2)

= (3x - 2)(3x - 2)

= (3x - 2)^2  which is a perfect square.

a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. because no real number satisfies this equation, i is called an imaginary number. has no real solution, since the square of a real number cannot be negative.

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step-by-step explanation: