3.7 Finding Zeros of Polynomials by Division

​3.7 Finding Zeros of the Polynomials by Division

​

Unit 3: Polynomials​

Don't forget to title and date your notes!​

Draw

Use long division to find each quotient.

Draw

Use long division to find each quotient.

​1. Long Division

​Long division can be applied to dividing polynomials! If there is no remainder, then the divisor is a factor, and can be used to find the zero.

• Divide

• Multiply

• Subtract

• Bring Down

• REPEAT

​Is (x+6) a factor of the polynomial?

Multiple Choice

Is x=-4 a zero of the polynomial? $$x^3-7x^2+14x-8$$  

• Yes

• No

​2. Synthetic Division

​Easier way of division when the divisor is x+c.

Doesn't work if x is multiplied by anything but 1.

​Is (x+6) a factor of the polynomial?

• flip the divisors sign

• bring down first term

• multiply

• add

• repeat

Multiple Choice

Is (x+4) a zero of the polynomial? $$3x^3-22x^2+37x-10$$  

• Yes

• No

Multiple Choice

Is (x+5) a factor of the polynomial function? $$x^3+x^2-22x-1$$  

• Yes

• No

Multiple Choice

Is (x+8) a factor of the polynomials function? $$x^3-49x+120$$  

• Yes

• No

Multiple Choice

Divide $$x^4-9x^3-1$$   by x-9.

• $$x^2-1$$  

• $$x^4-\frac{1}{x-9}$$  

• $$x^3-\frac{1}{x-9}$$