Question

polynomial
${x}^{4} + {7x}^{3} + {7x}^{2} + px + q$
is exactly divisible by
${x}^{2} + 7x + 12$ then find the value of p & q.

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Answer 1

now x*2+7x+12

x*2+4x+3x+12

x(x+4)+3(x+4)

x=-4,-3

now substitute -3,-4

now -3

(-3)*4+7(-3)*3+7(-3)*2+p(-3)+q

81-189+63-3p+q=0

-3p+q=45

now substitute -4

-4*4+7(-4*3)+7(-4*2)-4p+q

256-448+112-4p+q

-4p+q=80

add -3p+q-(-4p+q)=45-80

p=35

now p=35

so q =45+3(35)

q=150

p=35:q=150