Question

guys please help me with this question and whoever will give me the answer I will mark them as brainliest but I don't want useless answers please help me it's urgent​

Answer 1

Step-by-step explanation:

I think this answer is helpful for you

Answer 2

GiveN:-

2x³ + 3x² - 9x - 10

To FinD:-

Using remainder theorem have to factorize.

SolutioN:-

Analysis :

First we have find out the factor of 2x³ + 3x² - 9x - 10. After getting the factor we have to divide this 2x³ + 3x² - 9x - 10 by the factor we get. Then factorising the resultant expression we will get all factors of 2x³ + 3x² - 9x - 10.

Solution :

Let f(x) = 2x³ + 3x² - 9x - 10 -------------- (eq.(i))

Putting x = 2 in (eq.(i)), we get

⇒ f(2) = 2(2)³ + 3(2)² - 9(2) - 10

= 2 × 8 + 3 × 4 - 9 × 2 - 10

= 16 + 12 - 18 - 10

= 28 - 28

= 0

∴ f(2) = 0.

∴ By remainder theorem, (x - 2) is a factor of f(x).

On dividing 2x³ + 3x² - 9x - 10 by x - 2, we get 2x² + 7x + 5 as quotient and remainder = 0.

(refer to the attachment for the division)

∴ The other factors of f(x) are the factors of 2x² + 7x + 5.

Now we have to factorize 2x² + 7x + 5 :

⇒ 2x² + 7x + 5

Splitting the middle term,

⇒ 2x² + 2x + 5x + 5

⇒ 2x(x + 1) + 5(x + 1)

⇒ (2x + 5)(x + 1)

∴ (2x + 5)(x + 1)

Hence, 2x³ + 3x² - 9x - 10 = (x - 2) (2x + 5) (x + 1).