Respuesta :

Wallind123

Polynomial 1 : x²-x²+4x -2+1 = 4x -1

Polynomial 2 : 3x-x-2x²-2+1 = -2x²+2x-1

Polynomial 3 : 4 -2x+x-x²+x²-x² = -x²-x+4

According to the question,

Polynomial 1+Polynomial2+Polynomial3 + Polynomial4 = 6x

=> 4x -1+ (-2x²+2x-1) +(-x²-x+4) + Polynomial4= 6x

=> -3x²-x+2+Polynomial4= 0

=> 3x²+x -2= Polynomial4

OPTION B

Answer:

B

Step-by-step explanation:

Objective: Advanced Algebra Thinking with Polynomials.

Convert the diagram into a polynomial using the Legend.

Then add the fourth polynomial to get 6x.

The first polynomial is

[tex]4x - 1[/tex]

The next is

[tex] - 2x {}^{2} + 2x - 1[/tex]

The third is

[tex] - {x}^{2} - x + 4[/tex]

Add all the expressions.

[tex] - 3 {x}^{2} + 5x + 2[/tex]

Set this equations equal 6x, let y represent the 4th polynomial.

[tex] - 3 {x}^{2} + 5x + 2 + y = 6x[/tex]

[tex] - 3 {x}^{2} + 2 + y = x[/tex]

[tex] - 3 {x}^{2} +y = x - 2[/tex]

[tex]y = 3 {x}^{2} + x - 2[/tex]