Question

1. If x-1 is a factor of p(x)=x^3-7x^2+15x-9, which of the following represents the complete factorization for p(x)?
A. (x-3)(x+4)(x+1)
B. (x-3)(x-3)(x-1)
C. (x-3)(x+3)(x-1)
D. (x-3)(x+3)(x+1)

2. The point (1,0) lies on the graph of p(x)=x^4-2x^3-x+2
True or false

Answer 1

1.divide P(x) by (x-1) to get the quadratic equation... from which can be solve using any method in finding the roots of quadratic equation.... 
2 true

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Answer 2

Answer:

1. Option B is the correct answer.

2. The point (1,0) lies on the graph of p(x)=x⁴-2x³-x+2.

Step-by-step explanation:

1. Dividing x³-7x²+15x-9 with (x-1).

      $\frac{x^3-7x^2+15x-9}{x-1}=x^2-6x+9$

  Factorizing x²-6x+9 we will get

       x²-6x+9 = (x - 3)(x-3)

  x³-7x²+15x-9 = (x-1)(x - 3)(x-3)

  Option B is the correct answer.

2. We have p(x)=x⁴-2x³-x+2

   That is y = x⁴-2x³-x+2

   We have coordinates (1,0), substituting

   y = 1⁴-2 x 1³-1+2 = 0

   So when we are substituting x value as 1 we are getting y as zero, so the point lies in curve.