Question

Factorize: 1) x3+x -3x² - 3

2) 2x^4- 7x²-13x²+63 x-45​

Answer 1

Step-by-step explanation:

$.$

We have,

f (1) = 2 (1)4 – 7 (1)3 – 13 (1)2 + 63 (1) – 45

= 2 – 7 – 13 + 63 – 45

= 0

And,

f (3) = 2 (3)4 – 7 (3)3 – 13 (3)2 + 63 (3) – 45

= 162 – 189 – 117 + 189 – 45

= 0

So, (x – 1) and (x + 3) are the factors of f (x)

(x – 1) (x + 3) is also a factor of f (x)

Let us now divide

f (x) = 2x4-7x3-13x2+63x-45 by (x2 – 4x + 3) to get the other factors of f (x)

Using long division method, we get

2x4-7x3-13x2+63x-45 = (x2 – 4x + 3) (2x2 + x – 15)

2x4-7x3-13x2+63x-45 = (x – 1) (x – 3) (2x2 + x – 15)

Now,

2x2 + x – 15 = 2x2 + 6x – 5x – 15

= 2x (x + 3) – 5 (x + 3)

= (2x – 5) (x + 3)

Hence, 2x4-7x3-13x2+63x-45 = (x – 1) (x – 3) (x + 3) (2x – 5)

Answer 2

Answer:

The questions posted on the site are solely user generated, Doubtnut has no ownership or control over the nature and content of those questions. Doubtnut is not responsible for any discrepancies concerning the duplicity of content over those questions.

Step-by-step explanation:

hope its help you....ʕ•ε•ʔ