### Home > PC3 > Chapter 4 > Lesson 4.1.2 > Problem 4-29

Consider the polynomial .

If you want to determine the factors of

, isa reasonable guess for one of the factors? Explain.Is

a factor of the last term ( )? How can you determine if

is a factor? Can you think of more than one way?Is

a factor of?Set up the area model with the divisor on the left of the box. Input only the first term of the dividend.

Generic rectangle, 2 rows, 4 columns, left edge labeled, x minus 5, interior top left, labeled x cubed.

Since

divides into,times, write theon top and multiplywith theand fill in the area model with the product. Labels added, top edge left, x squared, interior bottom left, negative 5, x squared.

Add an expression to

in order to get the needed . Add it to the right of .Label added, interior top, second from left, 9 x squared.

Dividing

intogives . Add the at the top. Then multiply and and fill the answer in the area model. Labels added: top edge, second from left, + 9 x, interior bottom, second from left, negative 45 x.

Add an expression to

in order to get the needed . Add it to the right of . Label added: interior top, second from right, 34 x.

Dividing

intogives . Add the at the top. Then multiply and and fill the answer in the area model. Labels added: top edge, second from right, + 34, interior bottom, second from right, negative 170.

Add an expression to

in order to get the needed . Add it to the right of . This is the remainder. Labels added: top edge, right, 140 divided by quantity x minus 5. Interior top right, 140.