Question

the expression 2x^3+ax^3+bx+6 is divisible by x-2 and gives a remainder of -12 when divided by x+1. find the values of a and b and factorize the expression completely the expression 2x^3+ax^3+bx+6 is divisible by x-2 and gives a remainder of -12 when divided by x+1. find the values of a and b and factorize the expression completely @Mathematics

Answer 1

replace x by 2, set expression = 0 and get an equation in a and b
replace x by -1, set equal to -12 and get another equation in a and b
solve the system for a and b

Answer 2

what do u get when u do the simultaneous equation

Answer 3

is there a typo here because you have
\[2x^3+ax^3+bx+6\] and i am thinking it should be
\[2x^3+ax^2+bx+6\]

Answer 4

clarify this and i will work it out for you

Answer 5

yes typo sorry

Answer 6

the second one u wrote is the right one

Answer 7

ok so replace x by 2 and get
\[2\times 2^3+a\times 2^2+b\times 2+6=0\] or
\[16+4a+2b+6=0\] or
\[4a+2b=-22\]

Answer 8

then replace x by -1 and get
\[2\times (-1)^3+a\times (-1)^2+b\times (-1)+6=-12\]
\[-2+a-b+6=-12\]
\[a-b=-16\]

Answer 9

so your two equations are
\[4a+2b=-22\]
\[a-b=-16\] multiply the second by 2 to get
\[4a+2b=-22\]
\[2a-2b=-32\]
\[6a=-54\]
\[a=-9\]

Answer 10

then
\[-9-b=-16\]
\[-b=-7\]
\[b=7\]

Answer 11

check my arithmetic, because i just typed it and didn't do it with pencil and paper, but it looks right

Answer 12

ok im checking i have more questions to post hoping u can help me along the way