Question

How do you write \[{x^2} + 13x + 12\] in factored form?

Answer 1

Hint:Above equation is quadratic expression of the form \[a{x^2} + bx + c\] in which a, b and c are numeric constants given, we need to factorize i.e., we must find two numbers that multiply to give a times c and that adding together must give value of b i.e., the first coefficient of \[x\].

Formula used:
\[a{x^2} + bx + c\] where a, b, and c values are given.

Complete step by step answer:
The equation \[{x^2} + 13x + 12\] is a quadratic expression of the form \[a{x^2} + bx + c\]in which here \[a = 1\], \[b = 13\] and \[c = 12\] which is rearranged in a standard form.Now let us simplify the expression by rewriting it as the given equation \[{x^2} + 13x + 12\]. Next simplifying the terms \[{x^2} + 13x + 12 = 0\]

Hence here to write the expression in factored form, so first we need to think of two numbers that sum up to \[b\] that is \[13\] and the product is \[c\] that is \[12\] which all together gives us the factors of the expression.Here we need to get the product of 12 which sums up to 13, hence by trial-and-error method let us find out the terms.

By multiplying two terms which gives a product as 12 is \[12 \times 1 = 12\] and sums up to 13 is \[12 + 1 = 13\], hence by solving this we got the values which satisfy the condition for the equation to be quadratic.Hence in factored form the equation is \[\left( {x + 12} \right)\left( {x + 1} \right) = 0\]. Therefore, the values are \[x = 12\]and \[x = 1\]

Hence the factors we got after solving are 12 and 1.

Note: The key point is, for any equation which is of the form \[a{x^2} + bx + c\] is considered as Quadratic Equation which can be factorized in which x is unknown term and a, b and c are known numeric constant terms in the expression, and if \[a = 0\] the equation is linear and not quadratic as there is no term.