WRITE THE POLYNOMIALS AS THE PRODUCT OF TWO BINOMIALS

Write each expression as the product of two binomials.

Problem 1 :

y(y + 1) – 1(y + 1)

Solution :

The polynomial is having binomial factor of y + 1.

Factor out (y + 1)

= (y - 1) (y + 1)

Problem 2 :

3b(b - 2) – 4(b - 2)

Solution :

The polynomial is having binomial factor of b - 2.

Factor out (b – 2)

= (3b - 4) (b - 2)

Problem 3 :

2x(y + 4) + 3(y + 4)

Solution :

The polynomial is having binomial factor y + 4.

Factor out (y + 4)

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

Problem 4:

a³ - 3a² + 3a – 9

Solution :

= a³ - 3a² + 3a – 9

= a² (a - 3) + 3(a - 3)

= (a² + 3) (a - 3)

Problem 5 :

2x³ - 3x² - 4x + 6

Solution :

= 2x³ - 4x - 3x² + 6

= 2x (x² - 2) – 3 (x² - 2)

= (2x – 3) (x² - 2)

Problem 6 :

y³ + y² - 5y – 5

Solution :

= y³ - 5y + y² – 5

= y(y² - 5) + 1(y² - 5)

= (y + 1) (y² - 5)

Problem 7:    

x² + 7x + x + 7

Solution :

= x² + 7x + x + 7

= x(x + 7) + 1(x + 7)

= (x + 1) (x + 7)

Problem 8 :

x² + 5x + 6

Solution :

 x² + 5x + 6

Split the middle term into two term

= x² + 2x + 3x + 6

By grouping,

= (x² + 2x) + (3x + 6)

By taking the common factor, we get

= x(x + 2) + 3(x + 2)

= (x + 2) (x + 3)

Problem 9 :

x² - x – 6

Solution :

x² - x – 6

Split the middle term into two term

= x² - 3x + 2x – 6

By grouping,

= (x² - 3x) + (2x – 6)

By taking the common factor, we get

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

= (x + 2) (x - 3)

Problem 10 :

x² + 9x + 20

Solution :

x² + 9x + 20

Split the middle term into two term

= x² + 4x + 5x + 20

By grouping,

= (x² + 4x) + (5x + 20)

By taking the common factor, we get

= x(x + 4) + 5(x + 4)

= (x + 4) (x + 5)