OP Malhotra Factor Theorem-Factorization S.Chand Class-10 ICSE Maths Solutions Ch-7

OP Malhotra Factor Theorem-Factorization S.Chand Class-10 ICSE Maths Solutions Ch-7.  We Provide Step by Step Answer of Exe-7 with Self Evaluation and Revision of S Chand OP Malhotra Maths . Visit official Website CISCE  for detail information about ICSE Board Class-10.

OP Malhotra Factor Theorem-Factorization S.Chand Class-10 ICSE Maths Solutions Ch-7

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Exercise-7

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Exercise-7

OP Malhotra Factor Theorem-Factorization S.Chand Class-10 ICSE Maths Solutions Ch-7

Factor Theorem:

Factor theorem is commonly used for factoring a polynomial and finding the roots of the polynomial. It is a special case of a polynomial remainder theorem.

Use of Factor Theorem :

The steps are given below to find the factors of a polynomial using factor theorem:

Step 1 : If f(-c)=0, then (x+ c) is a factor of the polynomial f(x).

Step 2 : If p(d/c)= 0, then (cx-d) is a factor of the polynomial f(x).

Step 3 : If p(-d/c)= 0, then (cx+d) is a factor of the polynomial f(x).

Step 4 : If p(c)=0 and p(d) =0, then (x-c) and (x-d) are factors of the polynomial p(x).

Rather than finding the factors by using polynomial long division method, the best way to find the factors are factor theorem and synthetic division method. This theorem is used primarily to remove the known zeros from polynomials leaving all unknown zeros unimpaired, thus by finding the zeros easily to produce the lower degree polynomial.

There is another way to define the factor theorem. Usually, when a polynomial is divided by a binomial, we will get a reminder. The quotient obtained is called as depressed polynomial when the polynomial is divided by one of its binomial factors. If you get the remainder as zero, the factor theorem is illustrated as follows:

The polynomial, say f(x) has a factor (x-c) if f(c)= 0, where f(x) is a polynomial of degree n, where n is greater than or equal to 1 for any real number, c.

Division of Polynomial:

The division is the process of splitting a quantity into equal amounts. In terms of mathematics, the process of repeated subtraction or the reverse operation of multiplication is termed as division. For example, when 20 is divided by 4 we get 5 as the result since 4 is subtracted 5 times from 20.

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Exercise-7

OP Malhotra Factor Theorem-Factorization S.Chand Class-10 ICSE Maths Solutions Ch-7

Question 1:

Find the reminder when the expression

(i)………….

…………………

Question 2:

When x³ + 3x² – kx + 4 is divide by x – 2 the reminder is k. Find the value of the constant k.

Question 3:

……………………….

……………………….

………………………..

Question 17:

(i) What number must be subtracted from ………….. by x + 4

(ii) What number must be added to …………… divisible by x – 2.

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OP Malhotra Factor Theorem-Factorization S.Chand Class-10 ICSE Maths Solutions Ch-7

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