x + 6 is a factor of the polynomial mx3 + 13x2 - 69x - 18. The polynomials 3x2 - ax + 6m and x 3 + ax2 - 2 leave the same remainder when divided by (x - 2). Find the values of a and m. how to solve these type of questions

Asked by rajivjoshigoldtech | 9th Sep, 2016, 12:12: PM

Expert Answer:

begin mathsize 12px style straight x plus space 6 space is space straight a space factor space of space mx cubed plus 13 straight x squared minus 69 straight x minus 18
So comma space minus 6 space is space straight a space zero space of space the space given space polynomial.
rightwards double arrow straight m left parenthesis negative 6 right parenthesis cubed plus 13 left parenthesis negative 6 right parenthesis squared minus 69 left parenthesis negative 6 right parenthesis minus 18 equals 0
rightwards double arrow negative 216 straight m plus 468 plus 414 minus 18 equals 0
rightwards double arrow negative 216 straight m equals negative 864
rightwards double arrow straight m equals 4
By space the space Remainder space theorem comma space
we space know space that space since space straight x minus 2 space divides space the space polynomials space 3 straight x squared minus ax plus 6 straight m comma space that space is space 3 straight x squared minus ax plus 24 space and space the space polynomial
straight x cubed plus ax squared minus 2 comma space
So comma space 3 left parenthesis 2 right parenthesis squared minus straight a left parenthesis 2 right parenthesis plus 24 equals left parenthesis 2 right parenthesis cubed plus straight a left parenthesis 2 right parenthesis squared minus 2
rightwards double arrow 12 minus 2 straight a plus 24 equals 8 plus 4 straight a minus 2
rightwards double arrow negative 6 straight a equals negative 30
rightwards double arrow straight a equals 5
So comma space straight a equals 5 space and space straight m equals 4.
end style

Answered by Rebecca Fernandes | 9th Sep, 2016, 12:48: PM