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Write the degree of each of the following polynomials:
(i) 2x³ + 5x2- 7
(ii) 5x2 - 35x + 2
(iii) 2x + x2 - 8
(iv) (1/2)y7 -12y6 + 48y5 − 10
(v) 3x3 + 1
(vii) 20x3 + 12x2y2 - 10y2 + 20
Which of the following expressions are not polynomials:
(i) x2 + 2x-2
(v) 3x-2 + 2x-1 + 4x + 5
Write each of the following polynomials in the standard form. Also, write their degree:
(i) (x2 + 3 + 6x + 5x4)
(ii) a2 + 4 + 5a6
(iii) (x3 - 1)(x3- 4)
(iv) (y3 - 2)(y3 + 11)
The standard form of the given polynomial can be expressed as:
(5x4 + x2 + 6x + 3) or (3 + 6x + x2 + 5x4)
The degree of the polynomial is 4
(5a6 + a2 + 4) or (4 + a2 + 5a6)
The degree of the polynomial is 6
(iii) (x3 - 1)(x3 - 4)
(x3 - 1)(x3 - 4) = x6 - 5x3 + 4
(x6 - 5x3 + 4) or (4 - 5x3 + x6)
(y3 - 2)(y3 + 11) = y6 + 9y3 - 22
(y6 + 9y3 - 22) or (- 22 + 9y3 + y6)
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Chapter 8: Division of Algebraic Expressions...