How do you write this in standard form? 6x^2-15tx+6t^2

Answer 1

You do not really write this in "standard" form, but it is an algebraic expression that can be written in factored form.

To factor a polynomial the first step is to factor out a GCF (greatest common factor), which in this case is 3 (every term is divisible by 3).

3(2x² - 5tx + 2t²).

Now the question is does the polynomial (trinomial) factor into the product of two binomials. Perhaps you have learned to factor trinomials using a technique called split-the-middle (or some call the "ac" method).

The product of ac is (2)(2) or 4. Looking for two numbers that multiply to give 4, have the same sign and combine to the value of b (-5). That would be -4 and -1 (because (-4)(-1) = 4 and (-4) + (-1) = -5.

Use those numbers to split-the-middle:

2x² - 5tx + 2t² = 2x² - 4tx -1tx +2t²

At this point use factoring by grouping to factor the GCF from the first two terms and the 2nd two terms.

2x(x -2t) - t(x - 2t) -- now factor out the common binomial factor (x - 2t):

(x - 2t)(2x - t).

Do not forget the 3 that was factored out in the first step:

3 (x - 2t) (2x - t) is the completely factored form for the original trinomial. Check your work by multiplying the binomial times the binomial using FOIL, and distributing the 3 over that result.