Factor Polynomials
Example about factoring polynomials
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Example 1
$3x^2-5x+2=$
- $3x(x-1)$
- $(3x-1)(x-2)$
- $(3x+2)(x+1)$
- $(3x-2)(x-1)$
- $x(3x-2)$
Solution
This example is about factoring polynomials.
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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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