Question

If the polynomial y³-5y²+7y+m is divided by y+2 and the remainder is 50 then find the value of m.

Answer 1

Answer:

m = 92

Step-by-step explanation:

the polynomial y³-5y²+7y+m is divided by y+2 and the remainder is 50

using Remainder theorem  

putting y = - 2 should give remainder

=> (-2)³ - 5(-2)² + 7(-2) + m  = 50

=> -8 - 20 - 14 + m = 50

=> m = 92

Value of m = 92

Verification

                        y² - 7y  + 21

    y + 2    _|     y³-5y²+7y+92

                        y³ + 2y²

                 ___________________

                                -7y²  + 7y + 92

                                -7y²  - 14y

                  _____________________

                                         21y + 92

                                          21y + 42

                                    _____________

                                                     50

Answer 2

Answer:

the value of m = 92

Step-by-step explanation:

according to remainder theorem , when we divide a polynomial f(y) by (y−a) the remainder is f(a).

now given f(y) =$y^{3}-5y^{2}+7y+m$ which is divided by y+2.

y+2=0

⇒ y = -2

f(-2) = $\left ( -2 \right )^{3}-5\left ( -2 \right )^{2}+7\left ( -2 \right )+m$=50

      ⇒ -8-5(4)+7(-2)+m =50

      ⇒ -42+m = 50

      ⇒ m = 50+42

      ⇒ m = 92