Exam 5: Polynomials and Polynomial Functions

Solve. -An object is thrown upward from the top of a 160-foot building with an initial velocity of 48 feet per second. After $t$ seconds, the height $h ( t )$ of the object is given by the function $h ( t ) = - 16 t ^ { 2 } + 48 t + 160$ . Find how long it takes the object to hit the ground.

Factor the polynomial completely. - $2 x ^ { 2 } y - 18 y ^ { 3 }$

Multiply. - $( - 2 x - 10 ) ( 5 x - 9 )$

Factor the trinomial. - $35 x ^ { 3 } - 301 x ^ { 2 } + 392 x$

Solve. -If the area of a rectangle is $\left( 10 x ^ { 2 } + 33 x + 20 \right)$ square feet, and its length is $( 2 x + 5 )$ feet, find its width.

Factor the polynomial. - $x ^ { 2 } y ^ { 2 } - 15 x y ^ { 2 } + 54 y ^ { 2 }$

Multiply. - $( 9 x + 1 ) ^ { 2 }$

Solve the equation. - $\frac { n ^ { 2 } } { 672 } + \frac { 1 } { 14 } = \frac { n } { 48 }$

Multiply. - $( 9 x - y ) ^ { 2 }$

Simplify the polynomial by combining like terms. - $7 x ^ { 8 } + 9 x ^ { 6 } + 7 x ^ { 8 }$

Solve the equation. - $3 x ^ { 2 } - 4 x - 7 = 0$

Factor. - $216 y ^ { 3 } z - z$

Factor the polynomial by grouping. - $4 a + 32 + a b + 8 b$

Multiply. - $( x + 3 ) ^ { 3 }$

Find the area of the shaded region. -

Factor the trinomial. - $12 x ^ { 2 } y ^ { 2 } - 11 x y ^ { 2 } - 15 y ^ { 2 }$

Multiply. - $x ^ { 2 } - 3 x + 1$

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - $P ( x ) = x ^ { 2 } + 13 x + 29 ; - 4$

Divide. - $\left( 5 x ^ { 4 } - 7 x ^ { 2 } + 35 x ^ { 3 } - 49 x \right) \div ( 5 x + 35 )$

Multiply. - $2 a x ^ { 2 } \left( - 11 a x ^ { 6 } - 2 x ^ { 2 } + 4 a \right)$