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Complex Numbers - Product of Linear Factors>
Complex Numbers – Product of Linear Factors 2Complex Numbers – Product of Linear Factors 2
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Question 1 of 4
1. Question
Write out as a product of linear factors.
`x^3+x`
Correct
Great Work!
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The products of linear factors can be found using the formulas `a^2-b^2=(a+b)(a-b)` and `a^2+b^2=(a-bi)(a+bi)`.To write out `x^3+x` as a product of linear factors, first factor out an `x` and then use the formula `a^2+b^2=(a-bi)(a+bi)` on `x^2+1` where `a=sqrt(x^2)=x` and `b=sqrt(1)=1`.`x^3+x` Factor out an `x`. `=` `x(x^2+1)` Substitute into the formula `a^2+b^2=(a-bi)(a+bi)` where `a=sqrt(x^2)=x` and `b=sqrt(1)=1`. `=` `x(x-i)(x+i)` `x(x-i)(x+i)` -
Question 2 of 4
2. Question
Write out as a product of linear factors.
`x^2+25`
Correct
Great Work!
Incorrect
The products of linear factors can be found using the formulas `a^2-b^2=(a+b)(a-b)` and `a^2+b^2=(a-bi)(a+bi)`.To write out `x^2+25` as a product of linear factors, use the formula `a^2+b^2=(a-bi)(a+bi)` where `a=sqrt(x^2)=x` and `b=sqrt(25)=5`.`x^2+25` `=` `(x-5i)(x+5i)` `(x-5i)(x+5i)` -
Question 3 of 4
3. Question
Write out as a product of linear factors.
`x^2+13`
Correct
Great Work!
Incorrect
The products of linear factors can be found using the formulas `a^2-b^2=(a+b)(a-b)` and `a^2+b^2=(a-bi)(a+bi)`.To write out `x^2+13` as a product of linear factors, use the formula `a^2+b^2=(a-bi)(a+bi)` where `a=sqrt(x^2)=x` and `b=sqrt(13)`.`x^2+13` `=` `(x-isqrt13)(x+isqrt13)` `(x-isqrt13)(x+isqrt13)` -
Question 4 of 4
4. Question
Write out as a product of linear factors.
`9x^2+49`
Correct
Great Work!
Incorrect
The products of linear factors can be found using the formulas `a^2-b^2=(a+b)(a-b)` and `a^2+b^2=(a-bi)(a+bi)`.To write out `9x^2+49` as a product of linear factors, use the formula `a^2+b^2=(a-bi)(a+bi)` where `a=sqrt(9x^2)=3x` and `b=sqrt(49)=7`.`9x^2+49` `=` `(3x-7i)(3x+7i)` `(3x-7i)(3x+7i)`
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