Factor completely each polynomial, and indicate any that are not factorable using integers. 36a2−12a+1

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Tiefdruckot · Accepted Answer

Step 1  A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Factoring polynomials involves breaking up a polynomial into simpler terms (the factors) such that when the terms are multiplied together they equal the original polynomial.  Step 2  The given polynomial is 36a2−12a+1. Factor the polynomial completely by simplifying and taking the common terms out as follows;  36a2−12a+1=36a2−6a−6a+1  =6a(6a-1)-1(6a-1)...Take the common terms out.  =(6a−1)2....Factored form.  Hence, the given polynomial is factored completely and is equal to 36a2−12a+1=(6a−1)2.

Esta Hurtado · Accepted Answer

Given expression: 36a2−12a+1  Factor this expression completely.  View the expression 36a2−12a+1 as  36a2−12⏞∑a+1⏟∏uct 36−1=36  Find two integers such that whose product is 36 and whose sum is -12.  Since -6*-6=36, (-6)+(-6)=-12, the two integers are -6,-6.  So the middle term -12a can be written as -12a=-6a-6a.  Then, factor 36a2−6a−6a+1  =36a2−6a⏟group−6a+1⏟group  =6a(6a−1)⏟group−1(6a−1)⏟group(Fac→r out GCF om each group)  =(6a-1)(6a-1)   (Factor out (6a-1) from each group)  Therefore, 36a2−12a+1=(6a−1)(6a−1)  Check:  Considering,  (6a-1)(6a-1)=6a(6a-1)-1(6a-1)(using distributive property)  =36a2−6a−6a+1   (using distributive property)  =36a2−12a+1   (combine like terms)  Therefore, 36a2−12a+1=(6a−1)(6a−1) or =(6a−1)2

Factor completely each polynomial, and indicate any that are not

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