Factor completely using the factor theorem. f(x)= x^4+8x^2+4x^2-48x
3 years ago
I think there is typo and f(x)=x4+8x3+4x2-48x
f(x)=x(x3+8x2+4x-48)
g(x)=x3+8x2+4x-48
Factors of 48: +-1, +-2, +-3, +-4, +-6, +-8, +-12, +-16, +-24
g(1)=1+8+4-48#0
g(-1)=-1+8-4-48#0
g(2)=8+32+8-48=0
Synthetic Division: g(x)÷(x-2)
1 8 4 -48
2 2 20 48
1 10 24 R=0
g(x)=(x-2)(x2+10x+24)
x2+10x+24=(x+4)(x+6)
f(x)=x(x-2)(x+4)(x+6)
3 years ago
Answered By Majid B
I think there is typo and f(x)=x4+8x3+4x2-48x
f(x)=x(x3+8x2+4x-48)
g(x)=x3+8x2+4x-48
Factors of 48: +-1, +-2, +-3, +-4, +-6, +-8, +-12, +-16, +-24
g(1)=1+8+4-48#0
g(-1)=-1+8-4-48#0
g(2)=8+32+8-48=0
Synthetic Division: g(x)÷(x-2)
1 8 4 -48
2 2 20 48
1 10 24 R=0
g(x)=(x-2)(x2+10x+24)
x2+10x+24=(x+4)(x+6)
f(x)=x(x-2)(x+4)(x+6)