calculuscan someone please help me with this ques
posted by Jennifer on .
I have two questions if someone can PLEASE help.
1.solve the equation in the real number system. x^4+11x^3+24x^223x+35=0
**Please show work**
2.Use the remainder theorem to find the remainder. When f(x)is divided by x3. Then use the factor theorem to determine whether x3 is a factor of f(x)
f(x)=2x^48x^3+14x+12
the remainder is ?
is x3 a factor of f(x)=2x^48x^3+14x+12
**please show work here as well. Thanks**

1.
you know that any rational roots will be factors of 35
a little synthetic division shows that
f(x) = (x+5)(x+7)(x^2x+1)
the quadratic has no real roots
2.
the remainder is f(3). Naturally, if the remainder is zero, (x3) is a factor.
f(3) = 2*818*27+14*3+12=0