Question

Find the value of m if (m-2) is a factor of x^3+2x^2-mx+10.Hence determine whether (m+5) is a factor of the polynomial given.

Answer 1

since (x-2) is factor of polynomial,, therefore x=2 will satisfy the eqn
${x}^{3} + 2 {x}^{2} - mx + 10 \\ at \:x = 2 \\ 8 + 8 - 2m + 10 = 0 \\ m = 13$
Now the polynomial become i
${x}^{3} + 2 {x}^{2} - 2x + 10 = 0$
to check whether (x+5) is factor of not... we have to find the value of polynomial at x=-5,,it should be zero
${ - 5}^{3} + 2(25) + 10 + 10 \\ = - 125 + 50 + 20 \\ not \: equal \: to \: zero \: \\ hence \: it \: is \: not \: factor$
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