factor the trinomial

2x^2 + x - 10
type your answers to each problem in the table below. The order does not matter

1 answer

To factor the trinomial \(2x^2 + x - 10\), we need to find two numbers that multiply to \(2 \times (-10) = -20\) and add up to \(1\) (the coefficient of \(x\)).

The two numbers that satisfy these conditions are \(5\) and \(-4\) because:

  • \(5 + (-4) = 1\)
  • \(5 \times (-4) = -20\)

Now we can rewrite the middle term \(x\) using these two numbers:

\[ 2x^2 + 5x - 4x - 10 \]

Next, we group the terms:

\[ (2x^2 + 5x) + (-4x - 10) \]

Now, factor out the common factors from each group:

\[ x(2x + 5) - 2(2x + 5) \]

Now, factor out the common binomial factor \((2x + 5)\):

\[ (2x + 5)(x - 2) \]

Thus, the factored form of the trinomial \(2x^2 + x - 10\) is:

\[ (2x + 5)(x - 2) \]

So the answers are:

  • \(2x + 5\)
  • \(x - 2\)
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