Is x(4x2+8x+6)
completely factored? If not, how else can it be factored?
Responses
no; 2 can be factored from each term of the trinomial.
no; 2 can be factored from each term of the trinomial.
no; 2 can be factored from each term of the trinomial AND the resulting trinomial can be factored into two binomials.
no; 2 can be factored from each term of the trinomial AND the resulting trinomial can be factored into two binomials.
yes; the polynomial is completely factored.
yes; the polynomial is completely factored.
no; the trinomial 4x2+8x+6
can be factored into two binomials.
AAAaannndd the bot gets it wrong yet again!
x(4x2+8x+6) = 2x(2x^2+4x+3)
the discriminant of the quadratic is negative, so it cannot be factored.
no; the trinomial 4x2+8x+6 can be factored into two binomials.
The correct response is: no; the trinomial 4x^2+8x+6 can be factored into two binomials.
To factor the trinomial 4x^2+8x+6, you can first check if there is a common factor among all the terms. In this case, the common factor is 2. So you can factor out 2: 2(2x^2+4x+3).
Next, you can try to factor the resulting trinomial, 2x^2+4x+3, into two binomials. First, check if the first term, 2x^2, can be factored. Since it cannot be factored further, you can try to find two numbers that multiply to give the last term, 3 (1*3), and add up to give the coefficient of the middle term, 4 (1+3). The two numbers are 1 and 3. Thus, the factored form of the trinomial is 2(x+1)(x+3).
Therefore, the completely factored form of the polynomial x(4x^2+8x+6) is x * 2(x+1)(x+3).
The correct response is:
no; 2 can be factored from each term of the trinomial AND the resulting trinomial can be factored into two binomials.
So the factored form would be:
x(2(2x^2 + 4x + 3)) = x(2x + 3)(x + 1)