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igoroleshko156

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

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Given:  [tex]\textsf{2x}^2\textsf{ - 3x - 5}[/tex]

Find:  [tex]\textsf{Factor the expression}[/tex]

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 [tex]ax^2 + bx + c[/tex] 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.

  • [tex]2x^2-3x-5[/tex]
  • [tex]2x^2+2x-5x-5[/tex]
  • [tex]2x(x+1)-5(x+1)[/tex]
  • [tex](2x - 5)(x + 1)[/tex]

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

chetankachana

Answer:

[tex](2x -5)(x + 1)[/tex]

Step-by-step explanation:

Hello!

Standard form of a quadratic: [tex]ax^2 + bx +c = 0[/tex]

Given our equation: [tex]2x^2 - 3x - 5[/tex]

  • a = 2
  • b = -3
  • c = -5

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

  • 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

  • [tex]2x^2 - 3x - 5[/tex]
  • [tex]2x^2 +2x - 5x - 5[/tex]
  • [tex]2x(x + 1) - 5(x + 1)[/tex]
  • [tex](2x -5)(x + 1)[/tex]

The factored form is [tex](2x -5)(x + 1)[/tex].

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