Question

Factor completely: 5ab + 3ay + 5b + 3y (1 point)

(5b + 3y)(a + 1)
(5b - 3y)(a + 1)
(5b + 3y)(a - 1)
Prime
5. Factor completely: 4x3 + 28x2 + 7x + 49 (2 points)
(x - 7)(4x2 + 7)
(x - 7)(4x2 - 7)
(x + 7)(4x2 + 7)
(x + 7)(4x2 - 7)
6. Factor completely: 21x3 + 35x2 + 9x + 15 (2 points)
(3x - 5)(7x2 - 3)
(3x - 5)(7x2 + 3)
(3x + 5)(7x2 - 3)
(3x + 5)(7x2 + 3)
7. Factor completely: 10xy + 3y + 20ax + 6a (2 points)
(10x - 3)(y - 2a)
(10x - 3)(y + 2a)
(10x + 3)(y + 2a)
(10x + 3)(y - 2a)

Answer 1

4. ( 5b + 3y ) ( a + 1 )

5. ( x + 7 ) ( 4x² +7 )

6. ( 3x + 5 ) ( 7x² +3 )

7. ( 10x + 3 ) ( y + 2a )

Answer 2

Answer: The correct options are :

(4). (A)
`(5b+3y)(a+1).`

(5). (C)
`(x+7)(4x^2+7).`

(6). (D)
`(3x+5)(7x^2+3).`

(7). (C)
`(10x+3)(y+2a).`

Step-by-step explanation: We are given to completely factor the following expressions :

Expression 4 :

The given expression is

`E_1=5ab+3ay+5b+3y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

The factorization of expression (i) is as follows :

`E_1\\\\=5ab+3ay+5b+3y\\\\=a(5b+3y)+1(5b+3y)\\\\=(5b+3y)(a+1).`

So, option (A) is CORRECT.

Expression 5 :

The given expression is

`E_2=4x^3+28x^2+7x+49~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

The factorization of expression (ii) is as follows :

`E_2\\\\=4x^3+28x^2+7x+49\\\\=4x^2(x+7)+7(x+7)\\\\=(x+7)(4x^2+7).`

So, option (C) is CORRECT.

Expression 6 :

The given expression is

`E_3=21x^3+35x^2+9x+15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)`

The factorization of expression (iii) is as follows :

`E_3\\\\=21x^3+35x^2+9x+15\\\\=7x^2(3x+5)+3(3x+5)\\\\=(3x+5)(7x^2+3).`

So, option (D) is CORRECT.

Expression 7 :

The given expression is

`E_4=10xy+3y+20ax+6a~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)`

The factorization of expression (iv) is as follows :

`E_4\\\\=10xy+3y+20ax+6a\\\\=y(10x+3)+2a(10x+3)\\\\=(10x+3)(y+2a).`

So, option (C) is CORRECT.