Question

factorise x
${x}^{3 } + 3x ^{2} - 16x + 12$
pls find it
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Answer 1

$\huge\boxed{\mathbb\green{Answer✒}}$

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Put x-a=0 i.e x=a into the given expression

Example : As per given question put x+1=0 i.e x=-1 into the given expression

i.e x^3 -3* x^2 - 16 * x -12

= (-1)^3 -3 * (-1)^2–16* (-1)-12

= -1 - 3 + 16 -12

= -4+4

=0…………………………………………………………..(1)

2. Check whether the expression yields resultant value ZERO.

If ‘YES’ then (x-a) is a factor of the given expression

else (x-a) is not a factor of given expression

Example : As per given question after putting x+1=0 i.e x=-1 into the given expression, the resultant value is ZERO [From Equation (1)]

Thus , (x+1) is a factor of given expression.

Normal process:

Try to take (x-a) factor from each term.

If you can then (x-a) is a factor of given expression else not.

Example :

Is (x+1) a factor of x^3 -3* x^2 - 16 * x -12 ??

$\small\purple{\fbox{\bf{Solution}}}$

x^3 -3* x^2 - 16 * x -12

= x^3 + x^2 - 4* x^2 - 4*x -12 *x -12

= x^2 (x+1) -4 * x (x+1) -12 (x+1)

= (x^2 - 4*x -12)(x+1)………………………………….(2)

Here a factor (x+1) is clearly seen as from equation (2)

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ɪ ʀᴇǫᴜᴇsᴛ ᴜ ɢᴜʏs ɴᴏᴛ ᴛᴏ❌sᴘᴀᴍ☹☹☹

@Vaishnavi Sah_❤:)

Answer 2

Step-by-step explanation:

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Polynomial Long Division

Dividing : x3-3x2-16x-12

("Dividend")

By : x-6 ("Divisor")

dividend x3 - 3x2 - 16x - 12

- divisor * x2 x3 - 6x2

remainder 3x2 - 16x - 12

- divisor * 3x1 3x2 - 18x

remainder 2x - 12

- divisor * 2x0 2x - 12

remainder 0

Quotient : x2+3x+2 Remainder: 0

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Trying to factor by splitting the middle term

2.5 Factoring x2+3x+2

The first term is, x2 its coefficient is 1 .

The middle term is, +3x its coefficient is 3 .

The last term, "the constant", is

Step-1 :

Multiply the coefficient of the first term by the constant 1 • 2 = 2

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Step-2 :

Find two factors of 2 whose sum equals the coefficient of the middle term, which is 3 .

-2 + -1 = -3

-1 + -2 = -3

1 + 2 = 3 That's it

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Step-3 :

Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 1 and 2

x2 + 1x + 2x + 2

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Step-4 :

Add up the first 2 terms, pulling out like factors :

x • (x+1)

Add up the last 2 terms, pulling out common factors :

2 • (x+1)

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Step 5:

Add up the four terms of step 4 :

(x+2) • (x+1)

Which is the desired factorization

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Final result :

(x + 2) • (x + 1) • (x - 6)