Practice Test

487.

For the polynomial $8 y^{4} - 3 y^{2} + 1$

ⓐ Is it a monomial, binomial, or trinomial? ⓑ What is its degree?

488.

$(5 a^{2} + 2 a - 12) (9 a^{2} + 8 a - 4)$

489.

$(10 x^{2} - 3 x + 5) - (4 x^{2} - 6)$

490.

${(- \frac{3}{4})}^{3}$

491.

$x^{−3} x^{4}$

492.

$\frac{5^{6}}{5^{8}}$

493.

${(47 a^{18} b^{23} c^{5})}^{0}$

494.

$4^{−1}$

495.

${(2 y)}^{−3}$

496.

$p^{−3} \cdot p^{−8}$

497.

$\frac{x^{4}}{x^{−5}}$

498.

${(3 x^{−3})}^{2}$

499.

$\frac{24 r^{3} s}{6 r^{2} s^{7}}$

500.

${(\frac{x^{4} y^{9}}{x^{−3}})}^{2}$

501.

$(8 x y^{3}) (−6 x^{4} y^{6})$

502.

$4 u (u^{2} - 9 u + 1)$

503.

$(m + 3) (7 m - 2)$

504.

$(n - 8) (n^{2} - 4 n + 11)$

505.

${(4 x - 3)}^{2}$

506.

$(5 x + 2 y) (5 x - 2 y)$

507.

$(15 x y^{3} - 35 x^{2} y) \div 5 x y$

508.

$(3 x^{3} - 10 x^{2} + 7 x + 10) \div (3 x + 2)$

509.

Use the Factor Theorem to determine if $x + 3$ a factor of $x^{3} + 8 x^{2} + 21 x + 18 .$

510.

ⓐ Convert 112,000 to scientific notation. ⓑ Convert $5.25 \times 10^{−4}$ to decimal form.

In the following exercises, simplify and write your answer in exponential notation.

511.

$(2.4 \times 10^{8}) (2 \times 10^{−5})$

512.

$\frac{9 \times 10^{4}}{3 \times 10^{−1}}$

513.

514.

For $f (x) = 2 x^{2} - 3 x - 5$ and $g (x) = 3 x^{2} - 4 x + 1,$ find
ⓐ $(f + g) (x)$ ⓑ $(f + g) (1)$
ⓒ $(f - g) (x)$ ⓓ $(f - g) (−2)$

515.

For functions
$f (x) = 3 x^{2} - 23 x - 36$ and
$g (x) = x - 9,$ find
ⓐ $(\frac{f}{g}) (x)$ ⓑ $(\frac{f}{g}) (3)$

516.

A hiker drops a pebble from a bridge 240 feet above a canyon. The function $h (t) = −16 t^{2} + 240$ gives the height of the pebble $t$ seconds after it was dropped. Find the height when $t = 3 .$