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Factor. 2x2−3x−5 (2x+5)(x−1) (x−5)(2x+1) (2x−5)(x−1) (2x−5)(x+1)

User Mariam
by
6.9k points

2 Answers

2 votes

Answer:


(2x -5)(x + 1)

Explanation:

Hello!

Standard form of a quadratic:
ax^2 + bx +c = 0

Given our equation:
2x^2 - 3x - 5

  • a = 2
  • b = -3
  • c = -5

We want to find two numbers that multiply to
a*c but add up to
b.

  • ac = 2 * -5 = -10
  • b = -3

The two numbers that work for this is -5 and 2.

Now, expand -3x to -5x + 2x, and factor by grouping.

Factor by Grouping


  • 2x^2 - 3x - 5

  • 2x^2 +2x - 5x - 5

  • 2x(x + 1) - 5(x + 1)

  • (2x -5)(x + 1)

The factored form is
(2x -5)(x + 1).

User Shubhendu Mahajan
by
6.9k points
6 votes

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Answer:
\textsf{Option D, (2x - 5)(x + 1)}

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Given:
\textsf{2x}^2\textsf{ - 3x - 5}

Find:
\textsf{Factor the expression}

Solution: In order to factor the expression we will have two parenthesis with an x variable and a constant.

Determine important information

  • The standard form for a quadratic equation is
    ax^2 + bx + c and looking at our equation we can see that a = 2, b = -3, and c = -5.
  • Now we need to determine two numbers that add up to b and multiply up to a * c. So, they must add up to -3 and multiply up to -10. The two numbers that fit the description is -5 and 2.

Determine the factors

We plug in -5x and 2x instead of -3x and factor the expression by grouping.


  • 2x^2-3x-5

  • 2x^2+2x-5x-5

  • 2x(x+1)-5(x+1)

  • (2x - 5)(x + 1)

Therefore, the final answer that fits our solve solution would be option D, (2x - 5)(x + 1).

User Jolean
by
6.9k points