Question

) Find the value of b for which 50y +150 is a factor of y3 – by2 +by+3b. ​

Answer 1

`f(y) = y^3-by^2+by+3b\\\\\text{Since 50y+150 is a factor of f(y), }\\\\~~~~~f\left ( -(150)/(50)\right) = 0 \\\\\implies f(-3)=0 \\\\\implies (-3)^3 -b(-3)^2+b(-3)+3b =0\\\\\implies -27-9b-3b+3b=0\\\\\implies -27-9b =0\\\\\implies 9b = -27\\\\\implies b = -\frac{27}9\\\\\implies b = -3`