Question

rewrite each expression in factored or standard form.
factored form | standard form
--- | ---
| $x^2 + 9x + 18$
$(2x - 3)(2x - 7)$ |
| $3x^2 + 10x - 8$

Explanation:

Step1: Factor $x^2+9x+18$

Find two numbers that multiply to 18 and add to 9: 3 and 6.
$x^2+9x+18=(x+3)(x+6)$

Step2: Expand $(2x-3)(2x-7)$

Use FOIL method: multiply first, outer, inner, last terms.
$(2x)(2x) + (2x)(-7) + (-3)(2x) + (-3)(-7) = 4x^2-14x-6x+21$
Combine like terms: $4x^2-20x+21$

Step3: Factor $3x^2+10x-8$

Find two numbers that multiply to $3\times(-8)=-24$ and add to 10: 12 and -2. Split the middle term and factor by grouping.
$3x^2+12x-2x-8 = 3x(x+4)-2(x+4)=(3x-2)(x+4)$

Answer:

Factored Form	Standard Form
$(2x-3)(2x-7)$	$4x^2-20x+21$
$(3x-2)(x+4)$	$3x^2+10x-8$