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Describe the steps you would use to factor
2x3 + 5x2 - 8x - 20 completely. Then state the
factored form.
I

Sagot :

Nifer5126idn

Answer:

Factor by Grouping

2[tex]x^{3}[/tex] + 5[tex]x^{2}[/tex]  - 8x - 20

2[tex]x^{3}[/tex] + 5[tex]x^{2}[/tex]

[tex]x^{2}[/tex] (2x + 5)

-8x - 20

-4 (2x + 5)

(2x + 5) ([tex]x^{2}[/tex] - 4)

(2x + 5) (x - 2) (x + 2)

Solution:

  • 2x³ + 5x² - 8x - 20

Putting the terms, which have something in common, in brackets:

  • (2x³ + 5x²) - (8x - 20)

Factor them by taking the common terms outside the bracket.

  • => x²(2x + 5) - 4(2x + 5)

Factor by taking the common expression out of the brackets:

  • => (2x + 5)(x² - 4)

The multiplier (x² - 4) is in squared form.

Square root the multiplier of (2x + 5)(x² - 4), aka (x² - 4):

  • => (2x + 5)(x - 2)(x + 2)

The factorized form is (2x + 5)(x - 2)(x + 2).

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