3. the function f(x) is given in factored form. convert f(x) to standard/general form,

f(x) = (x - 3)(x - 5)(3x + 1)

standard form: s(x) = ax3 + bx2 + cx + d
factored form: f(x) = (x - 1)(x-2)(x - 1)

  f(x) = 3x^3 -23x^2 +37x +15

Step-by-step explanation:

Perform the multiplication. The distributive property is useful for this.

  f(x) = (x - 3)(x - 5)(3x + 1)

  = (x -3)(x(3x +1) -5(3x +1)) . . . . distribute the second factor to the third

  = (x -3)(3x^2 +x -15x -5) . . . . . finish the distribution

  = (x -3)(3x^2 -14x -5) . . . . . . . .collect terms

  = x(3x^2 -14x -5) -3(3x^2 -14x -5) . . . distribute the first factor

  = 3x^3 -14x^2 -5x -9x^2 +42x +15 . . . finish the distribution

  f(x) = 3x^3 -23x^2 +37x +15 . . . . . . . . collect terms

let's solve your equation step-by-step.

4x+2=2x+12

step 1: subtract 2x from both sides.

4x+2−2x=2x+12−2x

2x+2=12

step 2: subtract 2 from both sides.

2x+2−2=12−2

2x=10

step 3: divide both sides by 2.

2x

2

=

10

2

x=5

step-by-step explanation: