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) …

Question

asked Sep 19, 2019 67.5k views

2 Answers

Stigi · Answer 1 · 2019-09-24T21:07:47+0000

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.