Answer: The correct options are :
(4). (A) [tex](5b+3y)(a+1).[/tex]
(5). (C) [tex] (x+7)(4x^2+7).[/tex]
(6). (D) [tex] (3x+5)(7x^2+3).[/tex]
(7). (C) [tex] (10x+3)(y+2a).[/tex]
Step-by-step explanation: We are given to completely factor the following expressions :
Expression 4 :
The given expression is
[tex]E_1=5ab+3ay+5b+3y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
The factorization of expression (i) is as follows :
[tex]E_1\\\\=5ab+3ay+5b+3y\\\\=a(5b+3y)+1(5b+3y)\\\\=(5b+3y)(a+1).[/tex]
So, option (A) is CORRECT.
Expression 5 :
The given expression is
[tex]E_2=4x^3+28x^2+7x+49~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
The factorization of expression (ii) is as follows :
[tex]E_2\\\\=4x^3+28x^2+7x+49\\\\=4x^2(x+7)+7(x+7)\\\\=(x+7)(4x^2+7).[/tex]
So, option (C) is CORRECT.
Expression 6 :
The given expression is
[tex]E_3=21x^3+35x^2+9x+15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
The factorization of expression (iii) is as follows :
[tex]E_3\\\\=21x^3+35x^2+9x+15\\\\=7x^2(3x+5)+3(3x+5)\\\\=(3x+5)(7x^2+3).[/tex]
So, option (D) is CORRECT.
Expression 7 :
The given expression is
[tex]E_4=10xy+3y+20ax+6a~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)[/tex]
The factorization of expression (iv) is as follows :
[tex]E_4\\\\=10xy+3y+20ax+6a\\\\=y(10x+3)+2a(10x+3)\\\\=(10x+3)(y+2a).[/tex]
So, option (C) is CORRECT.
