document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203028>Question 203028</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am so confused! \r<BR>\n" );
document.write( "\n" );
document.write( "From the given polynomials, identify the polynomials of degree one.\r<BR>\n" );
document.write( "\n" );
document.write( "a.	11y2 – 5 – 4y <BR>\n" );
document.write( "b.	(3x2)1/2 + 12<BR>\n" );
document.write( "c.	7 – (12)1/2x <BR>\n" );
document.write( "d.	2x + 13x2 <BR>\n" );
document.write( "e.	5x + 7y + 8<BR>\n" );
document.write( "f.	(12)1x1 <BR>\n" );
document.write( "g.	x3 + 2x - 10<BR>\n" );
document.write( "h.	3x + 4x - 4\r<BR>\n" );
document.write( "\n" );
document.write( "Solve the following:<BR>\n" );
document.write( "i.	2x = -3x + 9 <BR>\n" );
document.write( "ii.	3x/5 = -6 <BR>\n" );
document.write( "iii.	y/4 + 2 = 7 <BR>\n" );
document.write( "iv.	16 = -2x/3 <BR>\n" );
document.write( "v.	Find f(1) for f(x) = 2x3 - 3x2 + x – 21  <BR>\n" );
document.write( "vi.	A function gives the value of C as 2 × (22/7) × r. Find C when r = 7 cm and r = 91 cm.<BR>\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153163 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=153163\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a. 11y2 – 5 – 4y <BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this would be a polynomial of degree 2 because the highest exponent is 2.<BR>\n" );
document.write( "by the way, y squared is usually shown as y^2 rather than y2.  I think you mean y squared.<BR>\n" );
document.write( "^ is shift 6 on your keyboard.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "b. (3x2)1/2 + 12<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "degree of 2 because highest exponent is 2<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "c. 7 – (12)1/2x <BR>\n" );
document.write( "-----<BR>\n" );
document.write( "not a polynomial because the x variable is in the denominator.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "d. 2x + 13x2 <BR>\n" );
document.write( "-----<BR>\n" );
document.write( "degree of 2 because the highest exponent is 2<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "e. 5x + 7y + 8<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this is a mixed polynomial.  each term is looked at separately (5x is a term, 7y is a term).  this would be degree 1 because the highest exponent is 1.  any variable shown by itself is a degree 1 polynomial.  x = x^1, etc.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "f. (12)1x1 <BR>\n" );
document.write( "-----<BR>\n" );
document.write( "degree of 1 because highest exponent is 1.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "g. x3 + 2x - 10<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "degree of 3 because the highest exponent is 3.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "h. 3x + 4x - 4 <BR>\n" );
document.write( "-----<BR>\n" );
document.write( "degree of 1 because the highest exponent is 1.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "to be a polynomial, all exponents has to be a positive integer.  0 is a positive integer.<BR>\n" );
document.write( "the degree of the polynomial is the highest exponent used in the polynomial.<BR>\n" );
document.write( "mixed polynomials have the degree equal to the highest sum of exponents in each term.<BR>\n" );
document.write( "example:<BR>\n" );
document.write( "x^5 + x^4 = degree 5<BR>\n" );
document.write( "x^5*y^2 + x^4*y^4 would be degree 8 because the sum of the exponents in the second term is greater than the sum of the exponents in the first term. <BR>\n" );
document.write( "-----<BR>\n" );
document.write( "variable that are multiplied together are called a term.<BR>\n" );
document.write( "variables that are added together form separate terms.<BR>\n" );
document.write( "x^2*x^3 = one term = degree of 5 because the exponents add up to 5.<BR>\n" );
document.write( "x^2 + x^3 = 2 terms = degree of 3 because 3 is the highest exponent.<BR>\n" );
document.write( "x^2*y^3*z^3 = one term = degree of 8 because the exponents add up to 8.<BR>\n" );
document.write( "x^2 + y^3 + z^3 = 3 terms = degree of 3 because the highest exponent in any one term is 3.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Solve the following:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "i. 2x = -3x + 9 <BR>\n" );
document.write( "-----<BR>\n" );
document.write( "add 3x to both sides of the equation to get:<BR>\n" );
document.write( "2x + 3x = 9 which becomes 5x = 9<BR>\n" );
document.write( "divide both sides of equation by 5 to get:<BR>\n" );
document.write( "x = 9/5<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "ii. 3x/5 = -6 <BR>\n" );
document.write( "-----<BR>\n" );
document.write( "multiply both sides of the equation by 5 to get:<BR>\n" );
document.write( "3x = (-6)*5 which becomes 3x = -30<BR>\n" );
document.write( "divide both sides of the equation by 3 to get:<BR>\n" );
document.write( "x = (-30)/3 which becomes x = -10<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "iii. y/4 + 2 = 7 <BR>\n" );
document.write( "-----<BR>\n" );
document.write( "subtract 2 from both sides to get:<BR>\n" );
document.write( "y/4 = 7 - 2 which becomes y/4 = 5<BR>\n" );
document.write( "multiply both sides by 4 to get:<BR>\n" );
document.write( "y = 4*5 which becomes y = 20<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "iv. 16 = -2x/3 <BR>\n" );
document.write( "-----<BR>\n" );
document.write( "multiply both sides of the equation by 3 to get:<BR>\n" );
document.write( "3*16 = -2x which becomes 48 = -2x<BR>\n" );
document.write( "divide both sides of the equation by (-2) to get:<BR>\n" );
document.write( "48 / (-2) = x which becomes -24 = x<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "v. Find f(1) for f(x) = 2x3 - 3x2 + x – 21 <BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you substitute 1 for x and solve:<BR>\n" );
document.write( "f(1) = 2*(1^3) - 3*(1^2) + 1 - 21<BR>\n" );
document.write( "since 1 to any power = 1, this becomes:<BR>\n" );
document.write( "f(1) = 2*1 - 3*1 + 1 - 21 which becomes:<BR>\n" );
document.write( "f(1) = 2 - 3 + 1 - 21 which becomes:<BR>\n" );
document.write( "f = (-12)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "vi. A function gives the value of C as 2 × (22/7) × r. Find C when r = 7 cm and r = 91 cm.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your formula is:<BR>\n" );
document.write( "C = f(r) = 2*(22/7)*r<BR>\n" );
document.write( "This means that the value of C is a function of r and can be found by the formula 2*(22/7)*r.<BR>\n" );
document.write( "C if a function of r means that the value of C depends on what the value of r is.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "When r = 7, then f(r) becomes f(7).<BR>\n" );
document.write( "You have C = f(7) = 2*(22/7)*7 = 44 cm.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "When r = 91, then f(r) becomes (f(91).<BR>\n" );
document.write( "You have C = f(91) = 2*(22/7)*91 = 572 cm.<BR>\n" );
document.write( "-----\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );