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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 Ch 1 Class 10 Maths Icse 01 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. Enter the OTP sent to your number Change. Resend OTP. Starting early can help you score better! Avail Offer. Question 2. Question 3. Question 4. Question 5. Question 6. Question 7. Question 8. Question 9.
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