Factor as the product of two binomials. 36+12 x+x^(2)=

Question

Factor as the product of two binomials.  36+12 x+x^(2)=

Bytelearn · Accepted Answer

Recognize the structure: Recognize the structure of the expression. The given expression is a quadratic trinomial, which can often be factored into the product of two binomials. 36 + 12x + x^2 can be written as (ax + b)(cx + d), where a, b, c, and d are numbers we need to find.Look for a pattern: Look for a pattern in the coefficients. The expression is in the form of x^2 + bx + c, where b is the coefficient of x and c is the constant term. In this case, b = 12 and c = 36. We need to find two numbers that multiply to give c (36) and add up to give b (12).Find the two numbers: Find the two numbers that fit the pattern. The numbers that multiply to 36 and add up to 12 are 6 and 6, since 6 * 6 = 36 and 6 + 6 = 12.Write the expression: Write the expression as the product of two binomials. Using the numbers found in Step 3, we can write the expression as (x + 6)(x + 6).Check the factored form: Check the factored form by expanding it. (x + 6)(x + 6) = x^2 + 6x + 6x + 36 = x^2 + 12x + 36 This matches the original expression, so the factoring is correct.

Factor as the product of two binomials. $\newline$ $36+12x+x^{2}=$

Full solution

More problems from Factor quadratics: special cases

Related topics

Factor as the product of two binomials.\newline36+12x+x2=36+12x+x^{2}=36+12x+x2=

Factor as the product of two binomials. $\newline$ $36+12x+x^{2}=$