Question

P(x) = 3x^3-7x^2-22x+8


True or false: the intercept form of the polynomial function above is P(x) = (x+2)(3x-1)(x-4)

Answer 1

Answer:

  true

Step-by-step explanation:

There are some quick checks you can make:

• is the product of the x-terms equal to the leading term (yes, 3x^3)
• is the product of the constants equal to the constant (yes, 8)
• is the sum of coefficients of x^2 correct (yes, 2(3)-1(1)-4(3)=-7)
• is the sum of coefficients of x correct (yes, (-1)(-4)+3(2)(-4)+(2)(-1)=-22)

So, the factored form multiplies out to give the standard form shown. The proposition is TRUE.

__

I find it much easier to identify the factored form from the graph. We know the leading coefficient is 3, so the factor 3(x-1/3) becomes (3x -1).