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Question 2: Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases: (i) p(x) = 2×3 + x2 – 2x – 1, g(x) = x + 1 (ii) p(x) = x3 +…
Read MoreQuestion 1: Determine which of the following polynomials has (x + 1) a factor : (i) x3 + x2 + x + 1 (ii) x4 + x3 + x2 + x + 1 (iii) x4 + 3×3 + 3×2 + x + 1…
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Factor theorem: If p(x) is a polynomial of degree n > 1 and a is any real number, then (i) x – a is a factor of p(x), if p(a) = 0, and (ii) p(a) = 0, if x –…
Read MoreQuestion 1: Find the remainder when x3 + 3×2 + 3x + 1 is divided by (i) x + 1 (ii) x – 1/2 (iii) x (iv) x + π (v) 5 + 2x Ex: 2.2 | Question 4 Question…
Read MoreQuestion 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: In Fig. 6.38, the sides AB and AC of ∆ABC are produced to points E and D respectively. If bisectors BO and CO of ∠ CBE and ∠ BCD respectively meet at point O, then prove that ∠…
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