Use factor method to evaluate:
(a2 - 14a - 32) ÷ (a + 2)
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(a2−14a−32)(a+2)=(a2−(16−2)a−32)(a+2)=(a2−16a+2a−32)(a+2)=((a2−16a)+(2a−32))(a+2)=(a(a−16)+2(a−16))(a+2)=((a−16)(a+2))(a+2)=(a−16)(a+2)(a+2)=(a−16)\dfrac{(a^2 - 14a - 32)}{(a + 2)}\\[1em] = \dfrac{(a^2 - (16 - 2)a - 32)}{(a + 2)}\\[1em] = \dfrac{(a^2 - 16a + 2a - 32)}{(a + 2)}\\[1em] = \dfrac{((a^2 - 16a) + (2a - 32))}{(a + 2)}\\[1em] = \dfrac{(a(a - 16) + 2(a - 16))}{(a + 2)}\\[1em] = \dfrac{((a - 16)(a + 2))}{(a + 2)}\\[1em] = \dfrac{(a - 16)\cancel{(a + 2)}}{\cancel{(a + 2)}}\\[1em] = (a - 16)(a+2)(a2−14a−32)=(a+2)(a2−(16−2)a−32)=(a+2)(a2−16a+2a−32)=(a+2)((a2−16a)+(2a−32))=(a+2)(a(a−16)+2(a−16))=(a+2)((a−16)(a+2))=(a+2)(a−16)(a+2)=(a−16)
Hence, (a2 - 14a - 32) ÷ (a + 2) = (a - 16)
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