If mx3 +nx2 +x-6 has (x+2)as a factor and leaves a remainder 4 when divided by (x-2) find the value - Maths - Polynomials

Question

If mx3 +nx2 +x-6 has (x+2)as a factor and
leaves a remainder 4 when divided by (x-2) find the value of m and
n

Neha Sethi · Accepted Answer

Dear student
If has as a factor and leaves a remainder 4 when divided by  find the value of m and nLet the given polynomial be  px= mx3 +nx2 +x-6Given (x+2) is a factor of px⇒p-2=0   factor theorem⇒m-23 +n-22 +-2-6=0⇒-8m+4n-2-6=0⇒4n-8m=8⇒n-2m=2  
1Given: px leaves a  reamainder 4 when divided by (x-2)So, p2=4  remainder theorem⇒ m23 +n22 +2-6=4⇒8m+4n-4=4⇒8m+4n=8⇒2m+n=2  
2Adding  1 and 2 we getn-2m+2m+n=2+2⇒2n=4⇒n=2⇒2-2m=2⇒2-2=2m⇒m=0
Regards

If mx3 +nx2 +x-6 has (x+2)as a factor and leaves a remainder 4 when divided by (x-2) find the value of m and n

If mx³ +nx² +x-6 has (x+2)as a factor and leaves a remainder 4 when divided by (x-2) find the value of m and n