Answered

Find expert answers and community support for all your questions on IDNLearn.com. Our experts provide accurate and detailed responses to help you navigate any topic or issue with confidence.

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).

Thank you for participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.