use factoring to solve the polynomial equation:
(x−2)(x+4)=7
Answers
Rewrite x4x4 as (x2)2(x2)2.
(x2)2+7x2−18=0(x2)2+7x2-18=0
Let u=x2u=x2. Substitute uu for all occurrences of x2x2.
u2+7u−18=0u2+7u-18=0
Factor u2+7u−18u2+7u-18 using the AC method.
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(u−2)(u+9)=0(u-2)(u+9)=0
Replace all occurrences of uu with x2x2.
(x2−2)(x2+9)=0(x2-2)(x2+9)=0
If any individual factor on the left side of the equation is equal to 00, the entire expression will be equal to 00.
x2−2=0x2-2=0
x2+9=0x2+9=0
Set the first factor equal to 00 and solve.
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x=√2,−√2x=2,-2
Set the next factor equal to 00 and solve.
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x=3i,−3ix=3i,-3i
The final solution is all the values that make (x2−2)(x2+9)=0(x2-2)(x2+9)=0 true.
x=√2,−√2,3i,−3ix=2,-2,3i,-3i
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