hoow wto use remainder theorem to factoriseee

### Asked by rajatpullinacd | 15th May, 2019, 04:35: PM

Expert Answer:

### We can't use remainder theorem to find the the factors it is used to find the remainder only.
Example:

**Remainder Therorem:**
If x^{3} + 3x^{2} - x + 5 is divided by x + 3, find the remainder.

Let p(x) =x^{3} + 3x^{2} - x + 5
By using remainder theorem,
x + 3 = 0 → x = -3
→ p(-3) =(-3)^{3} + 3(-3)^{2} - (-3) + 5
= -27 + 27 + 3 + 5
= 8
→ Remainder = 8

**Factor theorem: **It is used to find the factors of the given polynomial
Let p(x) =2x^{3} - 13x^{2} + 26x - 15
Put x = 1 in p(x), we get
p(1) =2(1)^{3} - 13(1)^{2} + 26(1) - 15
= 2 - 13 + 26 - 15
= 0
→ (x - 1) is a factor of p(x)
Divide p(x) by (x - 1), we get the quotient (2x^{2} - 11x + 15).
→2x^{3} - 13x^{2} + 26x - 15 = (x - 1)(2x^{2} - 11x + 15)
= (x - 1)(x - 3)(2x - 5)

**Remainder Therorem:**

^{3}+ 3x

^{2}- x + 5 is divided by x + 3, find the remainder.

^{3}+ 3x

^{2}- x + 5

^{3}+ 3(-3)

^{2}- (-3) + 5

**Factor theorem:**It is used to find the factors of the given polynomial

^{3}- 13x

^{2}+ 26x - 15

^{3}- 13(1)

^{2}+ 26(1) - 15

^{2}- 11x + 15).

^{3}- 13x

^{2}+ 26x - 15 = (x - 1)(2x

^{2}- 11x + 15)

### Answered by Yasmeen Khan | 16th May, 2019, 09:34: AM

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