When Given Two Zeros That are Complex Use Long Division to Find the Remaining Zeros

The video tutorial explains the concept of imaginary units and their complex conjugates, emphasizing the zero product property for factorization. It demonstrates polynomial division using long division, highlighting the steps involved and the importance of ensuring the divisor is in descending order. The tutorial concludes by showing how to complete the division process and identify factors, ensuring the remainder is zero.

What is the relationship between an imaginary unit and its complex conjugate?

• They are conjugates of each other.

• They are multiplicative inverses.

• They are additive inverses.

• They are equal.

Why can't synthetic division be used for dividing by X^2 + 1?

• Because it is a quadratic, not a linear binomial.

• Because it is not a polynomial.

• Because it is not factorable.

• Because it has imaginary coefficients.

In the long division process, what is the first step after writing the divisor and dividend?

• Multiply the divisor by the dividend.

• Divide the first term of the dividend by the first term of the divisor.

• Subtract the divisor from the dividend.

• Add the divisor to the dividend.

What is the result when the remainder is zero in polynomial division?

• The dividend is zero.

• The division process is incorrect.

• The divisor is a factor of the dividend.

• The divisor is not a factor of the dividend.

What does it mean if X - 12 is a factor of the polynomial?

• 12 is a root of the polynomial.

• The polynomial is not factorable.

• The polynomial has no real roots.

• The polynomial is linear.