Question

x + 3 is a factor of x4 + 4x3 - 7x2 - 22x + m. Check whether x + 4 is also a factor of this polynomial.

Answer 1

Answer:

x+3=0

=>x= -3

=>f(x)=x^4+4x^3-7x^2-22x+m

=>f(-3)=(-3)^4+4(-3)^3-7(-3)^2-22(-3)+m=0

=>81-108-63+66+m=0

=>-24+m=0

=>m=24

now the polynomial become

p(x)=x^4+4x^3-7x^2-22x+24

since,we have to check weather x+4 is the factor of p(x) or not

=>x+4=0

=>x= -4

=> p(-4)=(-4)^4+4(-4)^3-7(-4)^2-22(-4)+24

=>p(-4)=256-256-112+88+24

=>p(-4)=0

hence x+4 is the factor of given polynomial