# algebra factor

• Feb 16th 2007, 04:04 AM
nbukhari
algebra factor
Hi i am having difficulty in solving the following questions i would appreciate if you can provide me with the help of solving the following pleeeeese

The question are:

Factorise the following
1. a2 + 6x + 5

2. 3x2 - 2x -5

3. 10x2 + 19x + 7

4. 15a2 - 14a -8

Solve the following simultaneous equation
1. 5x +3y = 52 7x + 11y = 100

2. 15x -19y = 22 20x -23y = 34

i would appreciate all your help thank you
• Feb 16th 2007, 04:29 AM
chogo
1. x2 + 6x + 5

(x+1)(x+5)

2. 3x2 - 2x -5

(3x +5)(x-1)

3. 10x2 + 19x + 7

(2x+1)(5x+7)

4. 15a2 - 14a -8

(5x+2)(3x - 4)
• Feb 16th 2007, 04:37 AM
chogo
1. 5x +3y = 52
7x + 11y = 100

make x the subject in eqn 1

x = (52 - 3y)/5

substitute this value of x in eqn 2

7*[ (52 - 3y)/5 ] +11y = 100

multiply through by 5 and expand

364 - 21y + 55y = 500
y=4

substutute this value of y into our definition of x

x = (52 - 3y)/5
x = (52 - 3*4)/5
x=8
• Feb 16th 2007, 04:41 AM
chogo
2. 15x -19y = 22
20x -23y = 34

same method as above

15x -19y = 22
x = (22 + 19y) / 15

resubstitute in eqn 2

20*[ (22 + 19y) / 15 ] -23y = 34

multiply by 15 and expand

440 + 380y - 345y = 510

y = 2

resubstitute into x

x = (22 + 19*2) / 15
x = 4

p.s these can be hard, so work through them slowly. if u dont understand still then please dont hesitate to ask
• Feb 16th 2007, 04:44 AM
chogo
oh also check carefully that i have not made any obvious mistakes. A good way to do this is check the values of x and y give you the answers you want. E.g for simultaneous equation 1

15x -19y = 22

x=4, y = 2

15*4 - 19*2 = 22