Question

Factorise:

1. 4x2+4x-15

2. x2-14x+45

3. x7y+xy7

4.x3+8y3-z3+6xyz

Answer 1

1. To factorise quadratic polynomial you need firstly to find its roots
& 4x2+4x-15=0
D/4=4+60=64
x1=(-2+8)/4=3/2
x2=(-2-8)/4=-3
So we obtain
& 4x2+4x-15=4(x-3/2)(x+3)


2.& x2-14x+45
Find roots: x=5, x=9
Therefore
x2-14x+45=(x-5)(x-9)

3. x7y+xy7=xy(x6+y6)

4. x3+8y3-z3+6xyz=xyz(x2/(yz)+8y2/(xz)-z2/(xy)+6)