Question

Which statements are true about the polynomial 4x3 – 6x2 + 8x – 12? Check all that apply. The terms 4x3 and 8x have a common factor. The terms 4x3 and – 6x2 have a common factor. The polynomial is prime. The factored polynomial is (2x2 – 3)(2x + 4). The polynomial can be grouped in different ways to factor by grouping.

Answer 1

Answer:

Option 1,2 and 5 are true.

Step-by-step explanation:

Given : The polynomial  $4x^3- 6x^2 + 8x- 12$

To find : Which statements are true about the polynomial? Check all that apply.

Solution :

First we find the factor of the given polynomial.

$4x^3- 6x^2 + 8x- 12=2(x^2+2)(2x-3)$

Now, We check one by one.      

1) The terms $4x^3 \text{ and } 8x$ have a common factor.

Yes, it is true they have common factor i.e, 4x.

2) The terms  $4x^3 \text{ and } -6x^2$ have a common factor.

Yes, it is true they have common factor i.e, $2x^2$.

3) The polynomial is prime.  

No, It is not prime, and the factored polynomial is 4(2x-3)

4) The factored polynomial is $(2x^2-3)(2x + 4)$.

No, It is not correct. As factored of polynomial is $2(x^2+2)(2x-3)$

5) The polynomial can be grouped in different ways to factor by grouping.  

Yes, it is true.

Therefore, Option 1,2 and 5 are true.

Answer 2

hi

1 The terms 4x3 and 8x have a common factor.

2 The terms 4x3 and – 6x2 have a common factor.

5 The polynomial can be grouped in different ways to factor by grouping.

are right!

:)