FACTORING POLYNOMIALS AND POLYNOMIAL EQUATIONS
Factor the following polynomials using synthetic division. And show your complete solution..
1. x
³ – 10x² – x + 10?
2. x
³ – 3x² – 10x + 24?
3. 2x³ – 3x² – 3x + 2?
4. 4x³ – 7x + 3?
5. x
³ + x² – 14x - 24?
I need Genius please.. don't answer if you don't know the answer, don't play my question..
Answers
EXPLANATION.
(1) x³ - 10x² - x + 10.
As we know that,
We can write equation as,
⇒ x³ - x - 10x² + 10.
⇒ x(x² - 1) - 10(x² - 1).
⇒ (x - 10)(x² - 1).
⇒ (x - 10)(x + 1)(x - 1).
(2) x³ - 3x² - 10x + 24.
As we know that,
We can write equation as,
⇒ x³ - 4x² + x² - 6x - 4x + 24.
⇒ x³ + x² - 6x - 4x² - 4x + 24.
⇒ x(x² + x - 6) - 4(x² + x - 6).
⇒ (x - 4)(x² + x - 6).
(3) 2x³ - 3x² - 3x + 2.
As we know that,
We can write equation as,
⇒ 2x³ - 4x² + x² - 2x - x + 2.
⇒ 2x³ + x² - x - 4x² - 2x + 2.
⇒ x(2x² + x - 1) - 2(2x² + x - 1).
⇒ (x - 2)(2x² + x - 1).
(4) 4x³ - 7x + 3.
As we know that,
We can write equation as,
⇒ 4x³ + 4x² - 4x² - 4x - 3x + 3.
⇒ 4x³ + 4x² - 3x - 4x² - 4x + 3.
⇒ x(4x² + 4x - 3) - 1(4x² + 4x - 3).
⇒ (x - 1)(4x² + 4x - 3).
(5) x³ + x² - 14x - 24.
As we know that,
We can write equation as,
⇒ x³ + 5x² - 4x² - 20x + 6x - 24.
⇒ x³ + 5x² + 6x - 4x² - 20x - 24.
⇒ x(x² + 5x + 6) - 4(x² + 5x + 6).
⇒ (x - 4)(x² + 5x + 6).
Step-by-step explanation:
solution :
- please check the attached file
