Question

Factorize the following polynomials/using synthetic division method
a) 2x3- 7x2 - 10x + 24
b) 2x3 -x2-15.x+18​

Answer 1

Answer:

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2". 1 more similar replacement(s).

(((2 • (x3)) - 7x2) - 10x) + 24

3.1 2x3-7x2-10x+24 is not a perfect cube

Factoring: 2x3-7x2-10x+24

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: -10x+24

Group 2: 2x3-7x2

Pull out from each group separately :

Group 1: (5x-12) • (-2)

Group 2: (2x-7) • (x2)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Step-by-step explanation:

Polynomial Long Division

Dividing : 2x3-7x2-10x+24

("Dividend")

By : x-4 ("Divisor")

dividend 2x3 - 7x2 - 10x + 24

- divisor * 2x2 2x3 - 8x2

remainder x2 - 10x + 24

- divisor * x1 x2 - 4x

remainder - 6x + 24

- divisor * -6x0 - 6x + 24

remainder 0

Quotient : 2x2+x-6 Remainder: 0

$\boxed{f} \red{o} \boxed{l} \pink{l}\boxed{o} \green{w} \: \: \boxed{m} \purple{e}$

Answer 2

Answer:

a)( x + 2 )( 2 x - 3 )( x - 4 )

b)( x - 2 )( 2 x - 3 )( x + 6)

Step-by-step explanation:

a) 2 x³ - 7 x² - 10 x + 24

First, we will put it equal to 0:

2 x³ - 7 x² - 10 x + 24 = 0

We can see that this equation is satisfied by x = -2.

So, we get one factor as x + 2.

Dividing 2 x³ - 7 x² - 10 x + 24 by x + 2, we get:

( x + 2 )( 2 x² - 11 x + 12 )

= ( x + 2 )( 2 x² - 8 x - 3 x + 12 )

= ( x + 2 )( 2 x( x - 4) - 3( x - 4 ))

= ( x + 2 )( 2 x - 3 )( x - 4 )

b) 2 x³ - x² - 15 x + 18

First, we will put it equal to 0:

2 x³ - x² - 15 x + 18 = 0

It is divisible by: x + 1

Diving it we get,

( x - 2 )( 2 x² + 3 x - 9)

= ( x - 2 )( 2 x² + 6 x - 3 x - 9)

= ( x - 2 )( 2 x ( x + 3) - 3 ( x + 6)

= ( x - 2 )( 2 x - 3 )( x + 6)

Therefore, we get ( x + 2 )( 2 x - 3 )( x - 4 ) and ( x - 2 )( 2 x - 3 )( x + 6) by factorizing.

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