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#6. Factor completely.

Type your answers to each problem in the table below. The order of the factors doesn't matter, but use parentheses around each one! 2x^2 + x - 10

1 answer

To factor the quadratic expression \(2x^2 + x - 10\), we can follow these steps:

  1. Multiply the leading coefficient (2) by the constant term (-10): \[ 2 \times -10 = -20. \]

  2. We need to find two numbers that multiply to -20 and add up to the middle coefficient (1). The numbers that satisfy this are: \[ 5 \text{ and } -4. \]

  3. Rewrite the middle term (x) using these two numbers: \[ 2x^2 + 5x - 4x - 10. \]

  4. Now, group the terms: \[ (2x^2 + 5x) + (-4x - 10). \]

  5. Factor out the common factors in each group: \[ x(2x + 5) - 2(2x + 5). \]

  6. Now, factor out the common binomial factor \((2x + 5)\): \[ (2x + 5)(x - 2). \]

So, the completely factored form of the expression \(2x^2 + x - 10\) is: \[ (2x + 5)(x - 2). \]

Final Answer

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