Question

Tyrone factored the polynomial completely. What is the value of b? 12x^4+30x^3+4x^2+10x

Ax(Bx^2+1)2x+5

Answer 1

The value of B = 2x (3x^2 + 1) (2x + 5)

Given: 12x^4 + 30x^3 + 4x^2 + 10x

Req'd: B = ?

Sol'n:

*use elimination

solving for B:

= 2x (6x^3 +15x^2 + 2x +5)
= 2x (3x^2(2x + 5 +2x +5)
= 2x (3x^2 + 1) (2x + 5)

Answer 2

`B=3`

Explanation:

We have been given an expression
`12x^4+30x^3+4x^2+10x`.

Let us factor our given expression to answer the given problem.

Factor out
`2x` from all terms:

`2x(6x^3+15x^2+2x+5)`

Now, we will make two groups of
`6x^3+15x^2+2x+5` as shown below:

`2x((6x^3+15x^2)+(2x+5))`

`2x((6x^3+15x^2)+(2x+5))`

Factor out
`3x^2` from 1st group:

`2x((3x^2(2x+5))+(2x+5))`

`2x(3x^2+1)(2x+5)`

Upon comparing
`2x(3x^2+1)(2x+5)` with
`Ax(Bx^2+1)(2x+5)`, we can see that
`A=2` and
`B=3`.

Therefore, the value of B is 3.