\nThe following is by my understanding.<\/p>\n
\nIn high school math, the conjugate refers to a binomial construction that, when multiplied by its own conjugate, yields no “middle terms.”<\/p>\n
\nExample: What is the conjugate of x-5?<\/p>\n
\nSolution: x+5 is the conjugate of x-5. <\/p>\n
\nTo see why x+5 is the conjugate of x-5, we multiply the two together using the FOIL method (see my post from November 26, 2012.<\/a>)<\/p>\n \n(x-5)(x+5) = x^2-25<\/p>\n \nNote, in the product, the absence of an “x” term, which confirms that x+5 is the conjugate of x-5. Conversely, x-5 is the conjugate of x+5.<\/p>\n \nAs a non-example, x-4 is not the conjugate of x-5, as follows:<\/p>\n \n(x-5)(x-4) = x^2-9x+20<\/p>\n \nIn this product, the presence of the “x” term, -9x, aka the middle term, shows that x-4 isn’t the conjugate of x-5.<\/p>\n \nConjugates are used for dividing and other purposes. Not only polynomials have them.<\/p>\n \nSource:<\/p>\n \nTravers, K.J., Dalton, L.C., Brunner, V.F., Taylor, A.R. (1977). Using Advanced Algebra.<\/em> Doubleday Canada Limited.<\/p>\nJack of Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.\n \n","protected":false},"excerpt":{"rendered":" Tutoring math, the idea of a conjugate arises. The tutor mentions it. The following is by my understanding. In high school math, the conjugate refers to a binomial construction that, when multiplied by its own conjugate, yields no “middle terms.” …<\/p>\n