Questions: Jon is trying to factor (x^2+3 x-10) by looking for the factors of -10. Help Jon complete the table by dragging and dropping the correct values Positive Factor Negative Factor Sum of Factors --------- 1 -1 2 -2 Choices - i -10 - # 9 - # -5 - # -9 - # 3 - i -3 - i 10 - # 5

Jon is trying to factor (x^2+3 x-10) by looking for the factors of -10. Help Jon complete the table by dragging and dropping the correct values Positive Factor Negative Factor Sum of Factors --------- 1 -1 2 -2 Choices - i -10 - # 9 - # -5 - # -9 - # 3 - i -3 - i 10 - # 5
Transcript text: 6. Jon is trying to factor $x^{2}+3 x-10$ by looking for the factors of -10 . Help Jon complete the table by dragging and dropping the correct values \begin{tabular}{|c|c|c|} \hline Positive Factor & Negative Factor & Sum of Factors \\ \hline 1 & & \\ \hline & -1 & \\ \hline 2 & & \\ \hline & -2 & \\ \hline \end{tabular} \begin{tabular}{|l|} \hline Choices \\ \hline i -10 \\ \hline \# 9 \\ \hline \# -5 \\ \hline \# -9 \\ \hline \# 3 \\ \hline i -3 \\ \hline i 10 \\ \hline \# 5 \\ \hline \end{tabular}
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Solution

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Solution Steps

To factor the quadratic expression \(x^2 + 3x - 10\), we need to find two numbers whose product is \(-10\) (the constant term) and whose sum is \(3\) (the coefficient of the linear term). We will iterate through the possible factor pairs of \(-10\) and check their sums to find the correct pair.

Step 1: Identify the Problem

We need to factor the quadratic expression \(x^2 + 3x - 10\). This involves finding two numbers whose product is \(-10\) and whose sum is \(3\).

Step 2: Determine Factor Pairs

The factor pairs of \(-10\) that we need to consider are \((-2, 5)\) and \((5, -2)\). Both pairs satisfy the condition that their sum is \(3\).

Step 3: Verify the Correct Pair

For the quadratic expression \(x^2 + 3x - 10\), the correct factor pair is \((-2, 5)\) because:

  • The product of \(-2\) and \(5\) is \(-10\).
  • The sum of \(-2\) and \(5\) is \(3\).
Step 4: Write the Factored Form

Using the factor pair \((-2, 5)\), the quadratic expression can be factored as: \[ (x - 2)(x + 5) \]

Final Answer

The factored form of the quadratic expression \(x^2 + 3x - 10\) is \(\boxed{(x - 2)(x + 5)}\).

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