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Question 3: Check whether 7 + 3x is a factor of 3×3 + 7x. Question 2 Ex: 2.4 | Question 1 Prerequisite X is a factor of Y if X divides Y completely. This means, dividing Y by X should…
Read MoreQuestion 2: Find the remainder when x3 – ax2 + 6x – a is divided by x – a. Question 1 Question 3 Prerequisite It is a direct application of remainder theorem. Remainder theorem
Read MoreExample 10: Check whether the polynomial q(t) = 4t3 + 4t2 – t – 1 is a multiple of 2t + 1. Example 9 Example 11 Prerequisite Factor theorem
Read MoreExample 9: Find the remainder when x4 + x3 – 2×2 + x + 1 is divided by x – 1. Example 8 Example 10 Prerequisite Remainder theorem
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Remainder theorem: Let p(x) be any polynomial of degree greater than or equal to one and let a be any real number. If p(x) is divided by the linear polynomial x – a, then the remainder is p(a). Basics of polynomials…
Read MoreExample 8: Find the remainder obtained on dividing p(x) = x3 + 1 by x + 1. Example 7 Example 9 Prerequisite Read the prerequisite section of example 6. Basics of polynomials / Introduction to polynomials
Read MoreExample 7: Divide the polynomial 3×4 – 4×3 – 3x –1 by x – 1. Example 6 Example 8 Prerequisite Read the prerequisite section of example 6. Basics of polynomials / Introduction to polynomials
Read MoreExample 6: Divide p(x) by g(x), where p(x) = x + 3×2 – 1 and g(x) = 1 + x. Example 5 Example 7 Prerequisite Dividing a polynomial with another polynomial is not a difficult task but could be bit confusing…
Read MoreQuestion 4: Find the zero of the polynomial in each of the following cases: (i) p(x) = x + 5 (ii) p(x) = x – 5 (iii) p(x) = 2x + 5 (iv) p(x) = 3x – 2 (v) p(x)…
Read MoreQuestion 3: Verify whether the following are zeroes of the polynomial, indicated against them. (i) p(x) = 3x + 1, x = -1/3 (ii) p(x) = 5x – π, x = 4/5 (iii) p(x) = x2 – 1, x = 1,…
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