Question

If -1 is the remainder when 3x^3 - 4mx + 8 is divided by x + 3, find m.​

Answer 1

Answer :

m = -3

Note :

★ Remainder theorem : If a polynomial p(x) is divided by (x - c) , then the remainder obtained is given as R = p(c) .

★ Factor theorem :

• If the remainder obtained on dividing a polynomial p(x) by (x - c) is zero , ie. if R = p(c) = 0 , then (x - c) is a factor of the polynomial p(x) .

• If (x - c) is a factor of the polynomial p(x) , then the remainder obtained on dividing the polynomial p(x) by (x - c) is zero , ie. R = p(c) = 0 .

Solution :

Here ,

The given quadratic polynomial is ;

3x² - 4mx + 8 .

Let the given quadratic polynomial be p(x) .

Thus ,

p(x) = 3x² - 4mx + 8

Here ,

The given quadratic polynomial p(x) is divided by (x + 3) .

Thus ,

If x + 3 = 0 , then x = -3

Also ,

It is given that , if the given quadratic polynomial p(x) is divided by (x + 3) , then the remainder R is -1 .

Thus ,

=> R = -1

=> p(-3) = -1

=> 3•(-3)² - 4m•(-3) + 8 = -1

=> 27 + 12m + 8 = -1

=> 12m = -1 - 8 - 27

=> 12m = -36

=> m = -36/12

=> m = -3

Hence , m = -3 .

Answer 2

Answer:

Value of m is 6

Hope it will help you.