write the expression in a completely factored form (p+6) - p(p+6)=

Accepted Solution

Answer:The expression in a completely factored form (p+6) - p(p+6) is not factorizableSolution:Factorisation is basically splitting a two degree polynomial in such a way as to find two roots of the equation that satisfy it. The given equation is (p+6)-p(p+6)=0 For factorisation we have to convert the given equation into the form [tex]a x^{2}+b x+c=0[/tex]To do that the given equation has to be simplified. [tex]\begin{array}{c}{p+6-p^{2}+6 p=0} \\\\ {-p^{2}+7 p+6=0}\end{array}[/tex]There are two ways to solve this equation. We can either factorise it or use the quadratic equation formula. For factorising it, it has to satisfy certain conditions. The condition is [tex]b^2 - 4ac[/tex] should be a perfect square otherwise the equation is not factorable. a = -1,b = 7,c = 6[tex]7^2-4(-1)(6)[/tex]= 73 On substituting the values of a,b and c in the quadratic equation the answer is 73. 73 is not a perfect square. Therefore it is not factorizable.