nature of factors of trinomials?
6x2t5-6
check your tying.
did you mean: 6x^2 + 5x - 6 ?
which would be (2x+3)(3x - 2)
the nature of factors??
never heard that term before, but I think they are rather good-natured.
Did you mean the nature of the roots of
6x^2 + 5x - 6 = 0 ?
6x^2 + 5x - 6 = 0 ?
is that
please help me
6x^2 + 5x - 6 = 0
(2x+3)(3x-2)=0
so 2x+3 = 0
x = -3/2
or
3x-2 = 0
x = 2/3
x = -3/2 or x = 2/3
thank you
To determine the nature of the factors of a trinomial, we first need to factorize it. Let's use your trinomial, 6x^2t^5 - 6, as an example.
Step 1: Look for the greatest common factor (GCF) among the terms. In this case, both terms have a common factor of 6. So, we can factor out a 6 from both terms:
6(x^2t^5 - 1)
Step 2: Now, let's focus on the expression inside the parentheses: x^2t^5 - 1
Since this is a difference of squares, we can use the formula (a^2 - b^2) = (a - b)(a + b) to factorize it further. In this case, a = x^2t^5 and b = 1.
(x^2t^5 - 1) can be factored as (xt^2 - 1)(xt^2 + 1).
Therefore, the fully factored form of the trinomial 6x^2t^5 - 6 is:
6(xt^2 - 1)(xt^2 + 1).
Now that we have factored the trinomial, let's discuss the nature of its factors.
The factors of the trinomial are (xt^2 - 1) and (xt^2 + 1). Since both factors have a subtraction and an addition respectively, neither of them is a perfect square. Therefore, the factors of the trinomial are not perfect squares.
Additionally, both factors are binomials, representing a quadratic expression. The first factor (xt^2 - 1) can be further factored as the difference of squares, resulting in (xt - 1)(xt + 1). The second factor (xt^2 + 1) cannot be factored further using real numbers.
So, the nature of the factors of the given trinomial 6x^2t^5 - 6 are:
- They are not perfect squares.
- The first factor, (xt - 1)(xt + 1), is factored as the difference of squares.
- The second factor, xt^2 + 1, cannot be factored using real numbers.