Multiply \( (x^{2} - 3x + 1) \) by \( (x - a) \)

  • A \(x^{3} - (3 + a) x^{2} + (1 + 3a)x - a \)
  • B \(x^{3} - (3 - a)x^{2} + 3ax - a \)
  • C \(x^{3} - (3 - a)x^{2} - (1 + 3a) - a \)
  • D \(x^{3} + (3 - a)x^{2} + (1 + 3a) - a \)
jamb 1991mathematics

The correct answer is A. \(x^{3} - (3 + a) x^{2} + (1 + 3a)x - a \)

Let's solve this problem step by step. We are given the expressions \( (x^{2} - 3x + 1) \) and \( (x - a) \) and asked to find their product.

First, let's expand the product of these two expressions:

\( (x^{2} - 3x + 1)(x - a) \)

= \( x^{3} - ax^{2} - 3x^{2} + 3ax + x - a \)

= \( x^{3} - (a + 3)x^{2} + (3a + 1)x - a \)

So, the product of these two expressions is \( x^{3} - (a + 3)x^{2} + (3a + 1)x - a \).

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