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What is the completely factored form of the expression 16x^2+8x+32?
First, note that 8 is a common factor of all coefficients. Thus, factorize 8 first, as it is easier to work with smaller numbers.
#16x^2 + 8x + 32 = 8 (2x^2 + x + 4)#
Note that for a quadratic expression
#ax^2 + bx + c#
cannot be factorized into linear factors if the discriminant #b^2 – 4ac < 0#.
For this quadratic #2x^2 + x + 4#,
#a = 2#
#b = 1#
#c = 4#
#b^2 – 4ac = (1)^2 – 4(2)(4) = -31 < 0#
Thus, #2x^2 + x + 4# cannot be factorized into linear factors.
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