Factor Polynomials

Example about factoring polynomials

Example 1


$3x^2-5x+2=$

  1. $3x(x-1)$
  2. $(3x-1)(x-2)$
  3. $(3x+2)(x+1)$
  4. $(3x-2)(x-1)$
  5. $x(3x-2)$

Solution

This example is about factoring polynomials.

  1. Note that all the 5 possible answers are the product of polynomial which means that we need to factor the given polynomial. We first need to find terms that when multiplied would give $3x^2$. Our factoring starts as follows

    $(3x + ?)(x + ?)$ or $(3x - ?)(x - ?)$

    $(3x + ?)(x + ?)$ is rejected because when we expanded, we cannot get $-5x$. We now need to find 2 numbers that when put in place of the question marks and multiplied gives 2, taking into account the term $-5x$. Hence it will either

    $(3x - 1)(x - 2)$ or $(3x - 2)(x - 1)$

    When expanded, $(3x - 2)(x - 1)$ gives the original polynomial $3x^2-5x+2=$. Hence

    $3x^2-5x+2=(3x - 2)(x - 1)$

    Answer D
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