Question

Factorize: x³-6x² + 3x + 10 urgent faaaaaaaaaaaaaaaaaaaaaast​

Answer 1

To Factorise:

${\green{ {x}^{3} - {6x}^{2} + 3x + 10}}$

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SOLUTION:

$==> {x}^{3} + {x}^{2} - {7x}^{2} - 7x + 10x + 10$

$==> {x}^{2} (x + 1) - 7x(x + 1) + 10(x + 1)$

$==>(x + 1)( {x}^{2} - 7x + 10)$

$==>(x + 1)( {x}^{2} - 5x - 2x + 10)$

$==>(x + 1)[x(x- 5) - 2(x - 5)]$

$= = > {\blue{(x + 1)(x - 5)(x - 2)}}$

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Answer 2

Question

Factorize: x³-6x²+3x+10

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Answer

We'll use the factor theorem for this question since it's a cubic polynomial and cannot be factorized in the usual method of splitting the middle term.

Step 1 -: Trial and Error

Here we will take (x + 1) as the factor of the given polynomial p(x) and see if the remainder obtained is 0.

x + 1 = 0

x = -1

→ p(x) = x³- 6x² + 3x + 10

→ p(-1) = (-1)³ - 6(-1)² + 3(-1) + 10

→ p(-1) = -1 - 6(1) - 3 + 10

→ p(-1) = -1 - 6 - 3 + 10

→ p(-1) = -10 + 10

→ p(-1) = 0

∴ (x + 1) is a factor of x³- 6x² + 3x + 10.

Step 2 -: Long Division

Now we will perform the long division method with the one obtained factor and find the quotient.

[Attached below]

Step 3 -: Factorization by Splitting Middle Term

Now we will factorize the obtained quotient by the method of splitting the middle term.

→ x² - 7x + 10

S = 7

P = 10

2, 5 ✔

→ x² - 5x - 2x + 10

→ x (x - 5) - 2 (x - 5)

→ (x - 2) (x - 5)

∴ Upon factorizing x³ - 6x² + 3x + 10 we obtain (x + 1)(x - 2)(x - 5)

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