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Complex Numbers – Product of Linear Factors 1Complex Numbers – Product of Linear Factors 1
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Question 1 of 4
1. Question
Write out as a product of linear factors.
`x^2+16`
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Great Work!
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The products of linear factors can be found using the formulas `a^2b^2=(a+b)(ab)` and `a^2+b^2=(abi)(a+bi)`.To write out `x^2+16` as a product of linear factors, use the formula `a^2+b^2=(abi)(a+bi)` where `a=sqrt(x^2)=x` and `b=sqrt(16)=4`.`x^2+16` `=` `(x4i)(x+4i)` `(x4i)(x+4i)` 
Question 2 of 4
2. Question
Write out as a product of linear factors.
`x^2+3`
Correct
Great Work!
Incorrect
The products of linear factors can be found using the formulas `a^2b^2=(a+b)(ab)` and `a^2+b^2=(abi)(a+bi)`.To write out `x^2+3` as a product of linear factors, use the formula `a^2+b^2=(abi)(a+bi)` where `a=sqrt(x^2)=x` and `b=sqrt3`.`x^2+3` `=` `(xisqrt3)(x+isqrt3)` `(xisqrt3)(x+isqrt3)` 
Question 3 of 4
3. Question
Write out as a product of linear factors.
`4x^2+1`
Correct
Great Work!
Incorrect
The products of linear factors can be found using the formulas `a^2b^2=(a+b)(ab)` and `a^2+b^2=(abi)(a+bi)`.To write out `4x^2+1` as a product of linear factors, use the formula `a^2+b^2=(abi)(a+bi)` where `a=sqrt(4x^2)=2x` and `b=sqrt(1)=1`.`4x^2+1` `=` `(2xi)(2x+i)` `(2xi)(2x+i)` 
Question 4 of 4
4. Question
Write out as a product of linear factors.
`5x^2+9`
Correct
Great Work!
Incorrect
The products of linear factors can be found using the formulas `a^2b^2=(a+b)(ab)` and `a^2+b^2=(abi)(a+bi)`.To write out `5x^2+9` as a product of linear factors, use the formula `a^2+b^2=(abi)(a+bi)` where `a=sqrt(5x^2)=sqrt5x` and `b=sqrt(9)=3`.`5x^2+9` `=` `(sqrt5x3)(sqrt5x+3)` `(sqrt5x3)(sqrt5x+3)`
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