Tyrone factored the polynomial completely. what is the value of b?

12x4 + 30x3 + 4x2 + 10x

ax(bx2 + 1) (2x + 5)

b =

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12x4 + 30x3 + 4x2 + 10x

ax(bx2 + 1) (2x + 5)

b =

B=3,A=2

Step-by-step explanation:

We are given that a polynomial

[tex]12x^4+30x^3+4x^2+10x[/tex]

We have to find the value of B.

Taking common 2x from the given polynomial

[tex]2x(6x^3+15x^2+2x+5)[/tex]

[tex]2x(3x^2(2x+5)+1(2x+5))[/tex]

Taking common factor [tex](2x+5)[/tex] then we get

[tex]2x(2x+5)(3x^2+1)[/tex]

After factorization compare with

[tex]Ax (Bx^2+1)(2x+5)[/tex]

Then, we get

A=2,B=3

Comparing both sides of the equation:

12x⁴ + 30x³ + 4x² + 10x = Ax(Bx² + 1)(2x + 5)

The first term on the left hand side of the equation = 12x⁴

The first term on the right hand side of the equation = (Ax)*(Bx²)*(2x)

= 2ABx⁴

Therefore 12x⁴ = 2ABx⁴

12 = 2AB (a)

Comparing the last terms:

The last term on the left hand side of the equation = 10x

The last term on the right hand side of the equation = Ax*(1)*(5)

= 5Ax

5Ax = 10x Comparing and cancelling out x from both sides.

5A = 10

A = 10/5

A = 2

From (a)

12 = 2AB Recall A = 2.

12 = 2*2*B

12 = 4B

12 / 4 = B

3 = B

Therefore B = 3.

I hope this helps.

b

Step-by-step explanation: