What is the quotient (6x4 + 15x3 − 2x2 + 10x − 4) ÷ (3x2 + 2)? a.2x2 − 5x + 2 b.2x2 + 5x − 2 c.2x2 − 5x − 2 d.2x2 + 5x + 2

The given problem is :

(6x^4 + 15x^3 − 2x^2 + 10x − 4) ÷ (3x^2 + 2)?

now we can write expression (6x^4 + 15x^3 − 2x^2 + 10x − 4) as

(6x^4 + 4x^2 + 15x^3 + 10x - 6x^2 -4)

we have somehow arrange the expression in a way that 3x^2 + 2 is common

now the expression comes out to be

2x^2(3x^2 + 2) + 5x(3x^2+2) -2(3x + 2) / (3x^2+2)

After dividing final result comes out to be (2x^2 + 5x -2)

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.