Math CentralQuandaries & Queries


Question from ma., a student:

hi this is sophia, 10th grade from the philippines. im really having a hard time in factor theorem im just asking if you could help me solve these problems because i really dont have an idea on how to do solve these.. please

find the values of A and B so that (x+3) (x-2) are both factors of x^3+Ax^2+Bx-12
find the values of A, B, and C so that (x-3) (x+1)and (x-2) factors of P(x)=x^4+Ax^3+Bx^2+Cx+12

please help me.. i really do not understand these problems

Hi Ma,

Since (x + 3) is a factor of x3 + Ax2 + Bx + 12 there is a polynomial g(x) so that

x3 + Ax2 + Bx + 12 = (x + 3) g(x)

Notice that when x = -3 the right side is zero so

(-3)3 + A(-3)2 + B(-3) + 12 = 0 or 9A -3B = 15

This is a linear equation in the variables A and B.

Use the fact that (x - 2) is a factor of x3 + Ax2 + Bx + 12 to find a second linear equation is A ab\nd B and then solve these two equation for A and B.

I hope this helps,

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