# Synthetic Division

1) (381:3)

Solve graphically.

x^{2} + 2y^{2} = 8

x − 2y = 4

2) (381:11)

Solve graphically.

x^{2} − 4y^{2} = 16

x^{2} + y^{2} = 1

3) (385:5)

Solve algebraically.

x + y = 1

x^{2}− y^{2} = 1

4) (385:29)

A roof truss is in the shape of a right triangle.

If there are 4.60 m of lumber in the truss,

and the longest side (the hypotenuse) is

2.20m long, what are the lengths of the

other two sides of the truss?

5) (388:9)

Solve algebraically.

6) (388:27)

A rectangular TV screen has an area of 347 in^{2}

and a diagonal of 27.0 in.

Find the dimensions of the screen.

7) (391:9)

Solve.

8) (391:23)

Solve.

9) (391:37)

A freighter is 5.2 km farther from a Coast Guard

station on a straight coast than from the closest

point, A, on the coast. If the station is 8.3 km

from point A, how far is it from the freighter?

10) (397:15)

Find the remainder using the remainder theorem.

( x^{5} − 3x^{3} + 5x^{2} − 10x + 6 ) ÷ ( x − 2 )

11) (397:23)

Use the factor theorem to determine whether or

not the second expression is a factor of the first

expression.

x^{6} + 1, x + 1

12) (401:17)

Perform the indicated divisions by synthetic

division.

( x^{6} + 2x^{2} − 6 ) ÷ ( x − 2 )

13) (401:29)

Use the factor theorem and synthetic division

to determine whether or not the second

expression is a factor of the first.

2x^{4} − x^{3} + 2x^{2} − 3x + 1 ; 2x − 1

14) (405:5)

Solve using synthetic division, given the

root indicated.

2x^{3} + 11x^{2} + 20x + 12 = 0 ( r_{1} = −3/2 )

15) (405:21)

Solve using synthetic division, given the

root indicated.

x^{5} − 3x^{4} − x + 3 = 0 ( r_{1} = 3, r_{2} = j )

16) (411:15)

Solve **without using a graphing calculator.**

12x^{4} + 44x^{3} + 21x^{2} − 11x − 6 = 0

17) (411:31)

The deflection y of a beam at a horizontal

distance x from one end is given by

y = k( x^{4} − 2Lx^{3} + L^{3}x ),

where L is the length of the beam and k is a constant.

For what values of x is the deflection zero?

18) (411:35)

For electrical resistors connected in parallel,

the reciprocal of the combined resistance equals

the sum of the reciprocals of the individual

resistances. If three resistors are connected in

parallel such that the second resistance is 1 ohm

more than the first and the third is 4 ohm more

than the first, find the resistance for a combined

resistance of 1 ohm.

19) (411:37)

A rectangular tray is made from a square piece

of sheet metal 10.0 cm on a side by cutting equal

squares from each corner, bending up the sides,

and then welding them together. How long is the

side of the square that must be cut if the volume

of the tray is 70.0 cm^{3}?

20) (411:39)

The pressure difference p ( in kPa ) at a

distance x ( in km ) from one end of an oil

pipeline is given by

p = x^{5} − 3x^{4} − x^{2} + 7x .

If the pipeline is 4 km long, where is p = 0?

ANSWERS

3) x = 1, y = 0

4) 2.19 m, 0.21 m

5) 1, 25/4

6) 15.9 in, 21.8 in

7) x = −1

8) x = 7, −1

9) 9.2 km

10) 14

11) no

12) x^{5} + 2x^{4} + 4x^{3} + 8x^{2} + 18x + 36, R = 66

13) yes

14) x = −2, −2

15) x = −j, −1, 1

16) x = 1/2, −2/3, −3, −1/2

17) x = 0, L

18) 2 Ω, 3 Ω, 6 Ω

19) 1.23 cm or 2.14 cm

20) x = 0.0 km, 1.6 km, 2.8 km