Question

factorize 2x³‐3x²‐17x+30​

Answer 1

Step-by-step explanation:

2x^3 - 3x^2 - 17x + 30

2x^3 - 4x^2 + x^2 - 2x - 15x + 30

2x^2 (x - 2 ) + x ( x - 2 ) - 15 ( x - 2 )

(x - 2 )( 2x^2 + x - 15 )

(x - 2 )( 2x^2 + 6x - 5x - 15 )

( x - 2 )[ 2x ( x + 3 ) - 5 ( x + 3 )]

(x - 2 )( x + 3 )( 2x - 5 )

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Answer 2

Answer: (x + 3)(2x - 5)(x - 2)

Step-by-step explanation:

Let $p(x)=2x^{3} -3x^{2} -17x+30$

First, we will found the factors of the constant 30. These are ±1, ±2, ±3, ±5, ±6, ±10, ±15, ±30.

By trial and error method, we find that when x is (-3), p(x) = 0.

Therefore, one of the factors is (x + 3).

Now by long division method, we will divide p(x) by (x + 3). See in attachment. We get the quotient as $(2x^{2} -9x+10)$. Now we will factorise this by splitting the middle term.

$=2x^{2} -9x+10\\=2x^{2} -4x-5x+10\\=2x(x-2)-5(x-2)\\=(2x-5)(x-2)$

Therefore, the factors of p(x) are $(x+3)(2x-5)(x-2)$

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