Question #10519

Factorise:
1. 4x2+4x-15
2. x2-14x+45
3. x7y+xy7
4.x3+8y3-z3+6xyz

Expert's answer

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)

& 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)

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