Question

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)

Answer 1

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

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