The greatest power (exponent) of the terms of a polynomial is called degree of the polynomial. Example 1: \u00a0 \u00a0<\/strong>Find which of the following algebraic expression is a polynomial. Example 2: \u00a0 \u00a0<\/strong>Find the degree of the polynomial : Degree Of A Polynomial The greatest power (exponent) of the terms of a polynomial is called degree of the polynomial. For example : In polynomial 5×2 \u2013 8×7\u00a0+ 3x: (i) The power of term 5×2 = 2 (ii) The power of term \u20138×7 = 7 (iii) The power of 3x = 1 Since, the greatest […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[5],"tags":[28,24,25],"yoast_head":"\n
\nFor example :
\nIn polynomial 5x2<\/sup> \u2013 8x7<\/sup>\u00a0+ 3x:
\n(i) The power of term 5x2<\/sup> = 2
\n(ii) The power of term \u20138x7<\/sup> = 7
\n(iii) The power of 3x = 1
\nSince, the greatest power is 7, therefore degree of the polynomial 5x2<\/sup> \u2013 8x7<\/sup> + 3x is 7
\nThe degree of polynomial :
\n(i) 4y3<\/sup> \u2013 3y + 8 is 3
\n(ii) 7p + 2 is 1(p = p1<\/sup>)
\n(iii) 2m \u2013 7m8<\/sup> + m13<\/sup> is 13 and so on.<\/p>\nDegree Of A Polynomial With\u00a0Example Problems With Solutions<\/h2>\n
\n(i) 3x2<\/sup> \u2013 5x \u00a0 \u00a0 \u00a0 \u00a0(ii) \\(\\text{x + }\\frac{1}{\\text{x}}\\)\u00a0 \u00a0 \u00a0(iii) \u221ay\u2013 8\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (iv) z5<\/sup> \u2013 \u221bz + 8
\nSol.<\/strong>
\n(i) 3x2<\/sup> \u2013 5x = 3x2<\/sup> \u2013 5x1<\/sup>
\nIt is a polynomial.
\n(ii) \\(\\text{x + }\\frac{1}{\\text{x}}\\) = x1<\/sup>\u00a0+\u00a0x-1<\/sup>
\nIt is not a polynomial.
\n(iii)\u00a0\u221ay\u2013 8 = y1\/2<\/sup>\u2013 8
\nSince, the power of the first term (\u221ay) is \\(\\frac{1}{2}\\), which is not a whole number.
\n(iv) z5<\/sup> \u2013 \u221bz + 8\u00a0= z5<\/sup>\u00a0\u2013 z1\/3<\/sup>\u00a0+ 8
\nSince, the exponent of the second term is\u00a01\/3, which in not a whole number. Therefore, the given expression is not a polynomial.<\/p>\n
\n(i) 5x \u2013 6x3<\/sup> + 8x7<\/sup> + 6x2<\/sup> \u00a0 \u00a0(ii) 2y12<\/sup> + 3y10<\/sup>\u00a0\u2013 y15<\/sup>\u00a0+ y + 3 \u00a0\u00a0(iii) x \u00a0 \u00a0(iv) 8
\nSol.<\/strong>
\n(i)\u00a0\u00a0<\/strong>Since the term with highest exponent (power) is 8x7<\/sup> and its power is 7.
\n\u2234 The degree of given polynomial is 7.
\n(ii)\u00a0 The highest power of the variable is 15
\n\u2234 degree = 15
\n(iii) \u00a0x = x1<\/sup>\u00a0 \u00a0\u21d2\u00a0 \u00a0degree is 1.
\n(iv) \u00a08 = 8x0<\/sup> \u00a0\u00a0\u21d2\u00a0 \u00a0degree = 0<\/p>\n","protected":false},"excerpt":{"rendered":"