Download P.4 Review

COLLEGE ALGEBRA
P.4 REVIEW HANDOUT
ANSWERS
1. For the following expressions, which are polynomials and which are not polynomials. If it is,
state its degree, leading term and leading coefficient. If not, state why.
a) 4x 3 − 7x 8 + 9 + x 5
Yes, degree = 8, Leading term = -7x 8 , and Leading coefficient = -7.
b) x 6 Yes, degree = 6, Leading term = x 6 , and Leading coefficient = 1.
x +1
No, x’s can’t be in the denominator, leads to negative exponents on x.
c)
x2
d) 1 + x + x 2 + x 3 + x 4 + ... No, infinite # of terms.
e) 1 + x + x 2 + x 3 + x 4 + ... + x100
Yes, degree = 100, Leading term = x100 , and Leading coefficient = 1.
f) 2x No, exponent isn't a constant.
g) 7 Yes, degree = 0, Leading term = 7, and Leading coefficient = 7.
i)
x No, exponent on x is ½ which isn’t a whole number.
4x -3 + 8x1.3 No, the exponents on x are -3 and 1.3 which aren’t whole numbers.
j)
2-2 x + 7x
h)
(
)
Yes, degree = 1, Leading term = 2-2 + 7 x, and
Leading coefficient = 2-2 + 7.
2. Multiply out.
a) x 3 y ( x 5 + 7y − 8 ) = x 8 y + 7x 3 y 2 − 8x 3 y
b)
c)
d)
( x + 3y )( x − 5y ) = x − 5x y + 3x y − 15y = x − 2x y − 15y
( 4x − y )( 4x + y ) = ( 4x ) − ( y ) = 16x − y
( x + 3) ( x − 3x + 9 ) = x − 3x + 9x + 3x − 9x + 27 = x + 27
2
2
3
4
2
2
3 2
2
3
2
3
4
2
2
2
2
2
2
6
3
e) ( 5x + 3z ) = ( 5x ) + 2 ( 5x )( 3z ) + ( 3z ) = 25x 2 + 30xz + 9z 2
3. Simplify.
a) 6x ( 3x 2 − 5x + 6 ) − 2 ( 9x − 1) + ( 3x + 2 )( x − 5 )
2
b)
(
2
2
= 18x 3 − 30x 2 + 36x − 18x + 2 + 3x 2 − 15x + 2x − 10 = 18x 3 − 27x 2 + 5x − 8
2
5x + 2 5x − 2 − 3 ( x − 7 )
)(
)
= 25x 2 − 2 − 3(x 2 − 14x + 49) = 25x 2 − 2 − 3x 2 + 42x − 147 = 22x 2 + 42x − 149