2x = = x Activity 10 for and in each of the following equations, if x y x, y a) 2x + 3yi = b) (x + = 8 + x yi)(2 i) i – –6i – c) (3 + 2i)(x + yi) = i d) + = 4 2i x2 xi – – e) 2(x + = f) (x + + = 2x (y + 1)i yi) x yi yi)(2 i) – – g) + = 4 2i h) + + 3 = 4(–2 +5i) x yi x iy – –2i i) (2 + = j) + = + i)(3–2i) x + yi (3–5i)(4 i) x yi k) + = l) (2 = x yi x + yi –3i)2 POLYNOMIALS Outcomes for this section: By the end of this section, you should be able to: Define a polynomial Revise methods of factorization studied in earlier grades Apply the remainder and factor theorems to cubic polynomials Use long division and synthetic division to factorise polynomials Factorise cubic polynomials Polynomials You have studied polynomials in depth in earlier grades. Recall that a quadratic is a special form of a polynomial. Below are some examples of polynomials: 3x3–2x2+1 3 4–2x 1 x2 2x4 1–2x+3x5 x2 x17 x The number is called the degree of the polynomial; n The expressions ; which make up the polynomial are called terms. axn bxn–1,…,k The numbers are called coefficients; is called the leading coefficient. a, b, c,…..k; a The coefficient is called the constant term. k
2x = x = Activity 10 for x and y in each of the following equations, if x, y a) 2x + 3yi = – x –6i b) (x + yi)(2 – i) = 8 + i c) (3 + 2i)(x + yi) = – i d) x2 + xi = 4 – 2i e) 2(x + yi) = x – yi f) (x + yi)(2 + i) = 2x – (y + 1)i g) x + yi = 4 – 2i h) x + iy + 3 –2i = 4(–2 +5i) i) (2 + i)(3–2i) = x + yi j) (3–5i)(4 + i) = x + yi k) x + yi = l) (2 –3i)2 = x + yi POLYNOMIALS Outcomes for this section: By the end of this section, you should be able to: Define a polynomial Revise methods of factorization studied in earlier grades Apply the remainder and factor theorems to cubic polynomials Use long division and synthetic division to factorise polynomials Factorise cubic polynomials Polynomials You have studied polynomials in depth in earlier grades. Recall that a quadratic is a special form of a polynomial. Below are some examples of polynomials: 3x3–2x2+1 3 4–2x x2 1 2x4 1–2x+3x5 x2 x17 x The number n is called the degree of the polynomial; The expressions axn ; bxn–1,…,k which make up the polynomial are called terms. The numbers a, b, c,…..k; are called coefficients; a is called the leading coefficient. The coefficient k is called the constant term.
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