Adding and Subtracting Polynomials

Example 6.13

Evaluate \(5 x^{2}-8 x+4\) when

1. \(x=4\)
2. \(x=−2\)
3. \(x=0\)

Solution

\(x=4\)
	\(5 x^{2}-8 x+4\)
Substitute \(4\) for \(x\).	\(5(4)^{2}-8(4)+4\)
Simplify the exponents.	\(5 \cdot 16-8(4)+4\)
Multiply.	\(80-32+4\)
Simplify.	\(52\)

 

\(x=−2\)
	\(5 x^{2}-8 x+4\)
Substitute \(-2\) for \(x\).	\(5(-2)^{2}-8(-2)+4\)
Simplify the exponents.	\(5 \cdot 4-8(-2)+4\)
Multiply.	\(20+16+4\)
Simplify.	\(40\)

\(x=0\)
	\(5 x^{2}-8 x+4\)
Substitute \(0\) for \(x\).	\(5(0)^{2}-8(0)+4\)
Simplify the exponents.	\(5 \cdot 0-8(0)+4\)
Multiply.	\(0+0+4\)
Simplify.	\(4\)

Try It 6.25

Evaluate: \(3 x^{2}+2 x-15\) when

1. \(x=3\)
2. \(x=−5\)
3. \(x=0\)

Try It 6.26

Evaluate: \(5 z^{2}-z-4\) when

1. \(z=−2\)
2. \(z=0\)
3. \(z=2\)

Example 6.14

The polynomial \(-16 t^{2}+250\) gives the height of a ball \(t\) seconds after it is dropped from a 250 foot tall building. Find the height after \(t=2\) seconds.

Solution

	\(-16 t^{2}+250\)
Substitute \(t=2\).	\(-16(2)^{2}+250\)
Simplify.	\(-16 \cdot 4+250\)
Simplify.	\(-64+250\)
Simplify.	\(186\)
	After 2 seconds the height of the ball is 186 feet.

Try It 6.27

The polynomial \(-16 t^{2}+250\) gives the height of a ball \(t\) seconds after it is dropped from a 250-foot tall building. Find the height after \(t=0\) seconds.

Try It 6.28

The polynomial \(−16t2+250\) gives the height of a ball \(t\) seconds after it is dropped from a 250-foot tall building. Find the height after \(t=3\) seconds.

Example 6.15

The polynomial \(6 x^{2}+15 x y\) gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side \(x\) feet and sides of height \(y\) feet. Find the cost of producing a box with \(x=4\) feet and \(y=6\) feet.

Solution

	\(6 x^{2}+15 x y\)
Substitute \(x=4, y=6\)	\(6(4)^{2}+15(4)(6)\)
Simplify.	\(6 \cdot 16+15(4)(6)\)
Simplify.	\(96+360\)
Simplify.	\(456\)
	The cost of producing the box is $456.

Try It 6.29

The polynomial \(6 x^{2}+15 x y\) gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side \(x\) feet and sides of height \(y\) feet. Find the cost of producing a box with \(x=6\) feet and \(y=4\) feet.

Try It 6.30

The polynomial \(6 x^{2}+15 x y\) gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side \(x\) feet and sides of height \(y\) feet. Find the cost of producing a box with \(x=5\) feet and \(y=8\) feet.