Learn how to solve problems using the remainder theorem. Revise the right steps to factorise a given expression by practising with our Selina solutions.
Get the necessary self-study materials to score high marks in your Maths exam at TopperLearning. Find, in each case, the remainder when:.
By remainder theorem we know that when a polynomial f x is divided by x - a, then the remainder is f a. Show that:. Thus, 2x - 1 is not a factor of the polynomial f x. Adding 1 and 2 , we get,. Putting the value of a in 1 , we get,. Putting the value of m in 1 , we get,. Find the value of constant k. On dividing f x by x - 2, it leaves a remainder k. On dividing f x by x - 3, it leaves a remainder 3. Subtracting i from ii , we get,. Substituting the value of a in i , we get,. Calculate the values of a and b.
On dividing f x by 2x - 3, it leaves a remainder 7. Adding i and ii , we get,. Let the number k be added and the resulting polynomial be f x. It is given that when f x is divided by x - 3 , the remainder is 8. Thus, the required number is Let the number to be subtracted be k and the resulting polynomial be f x. It is given that when f x is divided by x - 2 , the remainder is Thus, the required number is 8. Find the value of 'a'. By the given condition, we have:. Thus, the value of a is Using the Factor Theorem, show that:.
Hence, x - 2 is a factor of f x. Now, we have:. Using the Remainder Theorem, factorise each of the following completely. Hence, find all the factors of f x. Subtracting ii from i , we get,. Substituting the value of a in ii , we get,. Calculate the values of b and c. Hence, factorise the expression completely.
It is given that when f x is divided by 2x - 3 , the remainder is Multiplying i by 4 and subtracting it from ii , we get,. Substituting the value of b in i , we get,. From i and ii , we get,. Hence, proved. Find the value of a. It is given that x - a is a factor of f x. Let the number to be subtracted from the given polynomial be k. Hence, completely factorise the given expression.
Hence, x - 1 is a factor of f x. Using Remainder Theorem, factorise :. Find the value of m. According to the given information,. Let the required number be k. And then, factorise the given expression completely. Since, x - 2 is a factor of f x. It is given that:. It is given that f x and g x leave the same remainder when divided by x - 2. Therefore, we have:. Also, for these values of p and q factorize the given polynomial completely.
Substituting the value of q in i , we get,. Given that f x is completely divisible by x 2 - 1. Using i and ii , we get,. Find the value of 'a', factorise the given polynomial completely. Find the value of 'p'. Use the Remainder Theorem to factorise the following expression:. Factors of constant term 6 are 1, 2, 3, 6. Hence x - 2 is a factor of f x. Using Remainder Theorem, we have. Let the number subtracted be k from the given polynomial f x.
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