. Find the coefficient of x3 in the expansion of (3+2x+x2)6

9180

Step-by-step explanation:

(3 + 2x + x^2)^6 = x^12 + 12x^11 + 78x^10 + 340x^9 + 1095x^8 + 2712x^7 + 5284x^6 + 8136x^5 + 9855x^4 + 9180x^3 + 6318x^2 + 2916x + 729

This can be found using Pascal's Triangle.

The coefficient of x^3 is 9180.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.