I have two questions if someone can PLEASE help.

Question

1.solve the equation in the real number system. x^4+11x^3+24x^2-23x+35=0
**Please show work**

2.Use the remainder theorem to find the remainder. When f(x)is divided by x-3. Then use the factor theorem to determine whether x-3 is a factor of f(x)
f(x)=2x^4-8x^3+14x+12

the remainder is ?
is x-3 a factor of f(x)=2x^4-8x^3+14x+12
**please show work here as well. Thanks**

Answer 1

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^2-x+1)
the quadratic has no real roots

2.
the remainder is f(3). Naturally, if the remainder is zero, (x-3) is a factor.
f(3) = 2*81-8*27+14*3+12=0