Question

Factorise: A) 2y3 - 4y2 - 2y + 4 B) 2x2 + 7x + 3 C) x3 + 13x2 + 32x + 20​

Answer 1

Answer:

A) 2 ( y - 2 ) ( y + 1 ) ( y - 1 )

B) ( x + 3 ) ( 2x + 1 )

C) ( x + 1 ) ( x + 10 ) ( x + 2 )

Step-by-step-explanation:

We have to factorize polynomial expressions.

A)

2y³ - 4y² - 2y + 4

Let this expression be A.

∴ A = 2y³ - 4y² - 2y + 4

⇒ A = 2y² ( y - 2 ) - 2 ( y - 2 )

⇒ A = ( y - 2 ) ( 2y² - 2 )

⇒ A = ( y - 2 ) [ 2 ( y² - 1 ) ]

⇒ A = 2 ( y - 2 ) ( y² - 1 )

We know that,

a² - b² = ( a + b ) ( a - b )

⇒ A = 2 ( y - 2 ) ( y + 1 ) ( y - 1 )

∴ The factorized form of 2y³ - 4y² - 2y + 4 is 2 ( y - 2 ) ( y + 1 ) ( y - 1 ).

─────────────────────

B)

2x² + 7x + 3

Let this expression be B.

∴ B = 2x² + 7x + 3

⇒ B = 2x² + ( 6 + 1 ) x + 3

⇒ B = 2x² + 6x + 1x + 3

⇒ B = 2x ( x + 3 ) + 1 ( x + 3 )

⇒ B = ( x + 3 ) ( 2x + 1 )

∴ The factorized form of 2x² + 7x + 3 is ( x + 3 ) ( 2x + 1 ).

─────────────────────

C)

x³ + 13x² + 32x + 20

Let this expression be C.

∴ C = x³ + 13x² + 32x + 20

⇒ C = x³ + x² + 12x² + 12x + 20x + 20

⇒ C = x² ( x + 1 ) + 12x ( x + 1 ) + 20 ( x + 1 )

⇒ C = ( x + 1 ) ( x² + 12x + 20 )

⇒ C = ( x + 1 ) ( x² + 10x + 2x + 20 )

⇒ C = ( x + 1 ) [ x ( x + 10 ) + 2 ( x + 10 ) ]

⇒ C = ( x + 1 ) ( x + 10 ) ( x + 2 )

∴ The factorized form of x³ + 13x² + 32x + 20 is ( x + 1 ) ( x + 10 ) ( x + 2 ).