Binomial (x - 6) and trinomial (-2x2 + x + 9) are the factors of which of the following polynomials?
2x^3+12x-3x+54
-2x^2+15
-2x^3+13x^2+3x-54
O 2x^2-3

Option (3)

Step-by-step explanation:

If binomial (x - 6) and trinomial (-2x² + x + 9) are the factors of a polynomial then their multiplication will be equal to the polynomial.

(x - 6)(-2x² + x + 9) = x(-2x² + x + 9) - 6(-2x² + x + 9)

                              = -2x³ + x² + 9x + 12x² - 6x - 54

                              = -2x³ + 13x² + 3x - 54

Therefore, Option (3) will be the correct option.

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3