Question

Suppose the profit is given by the equation
$p = 8{x}^{2} + 12x$
where x is the amount of item that was sold (in thousands).
a. What is the greatest common monomial factor of
$18 {x}^{2} + 12x$

b. Write P in factored form.
c. find the profit if x=2 and if x=3​

Answer 1

$Given \: P = 8x^{2} + 12x$

8x² = 2 × 2 × 2 × x × x

12x = 2 × 2 × 3 × x

$Common \: factor \: 8x^{2} \:and \: 12x = 4x$

$\red{ a ) The \: greatest \: common }\\\red{ monomial\: factor \: of \: 8x^{2} + 12x}\\\green { =4x}$

$\red{b ) Factored \: form \: of \: P }\\= (4x) \times 2x + (4x) \times 3 \\\green { = 4x(2x+3) }$

$\red{c )If \: x = 2 } \: then \: the \: profit P = 8 \times 2^{2} + 12 \times 2 \\= 8\times 4 + 24 \\= 32 + 24 \\\green {= 56}$

$\red{c )If \: x = 3 } \: then \: the \: profit P = 8 \times 3^{2} + 12 \times 3 \\= 8\times 9 + 36 \\= 72 + 36 \\\green {= 108}$

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