1. Polynomial Practice Test Answer Key:
Answers are given first with explanations in the parenthesis behind the answers.
1. A. Trinomial (3 terms) & Quadratic (highest exponent is a 2)
B. Binonial (2 terms) & Cubic (highest exponent is a 3)
2. A. 3x2+4x+19 (make sure to combine like terms and then order from highest exponent to least
exponent)
B. x3-3x2-9x+10 (remember the minus changes the sign of every term in the parenthesis behind
it)
3. A. 10x3+10x (Distribute 2x to every term in the parenthesis)
B. 9x2-64 (Use rectangle method, FOIL, or third special case)
C. 18x3-27x2+583x+98 (Use rectangle method or distributive property)
D. 9x2+24x+16 (multiply 3x +4 by itself using either rectangle method, FOIL, or first special case)
4. A. 20 & -12 (This factors into (x – 20)(x +12), or use quadratic formula)
B. 10 & 20 ( This factors into (-x +20)(x -10), or use quadratic formula)
C. .3 and -10.3 (This DOES NOT factor, use quadratic formula)
D. No solution (The discriminant – the part under the square root in the quadratic formula – is
negative, so it is not possible to factor)
5. 2.98 seconds (The projectile formula filled in is: -16t2+44t+8 =h, Set this equal to 0, use the
quadratic formula to solve.)
6. w= 6.1 & l = 22.4 (The length expression is 4w – 2, multiply length times width and set equal to
the area of 135, that equation is w(4w-2)=135. Distribute w, set the equation equal to 0 and use
the quadratic formula to find w, use that number to find the length.
7. A. x + 2 (The numerator factors into (x +2)(x+1), the (x+1)’s cancel out and x + 2 is left)
B. 2(x-8) (The numerator factors into 2(x-8)(x+2), the (x+2)’s cancel out and 2(x-8) is left)
8. 410.1 ft2 (Divide 81 by 4, that gives the length of each side, 20.25, to find the area multiply 20.25
by 20.25)
9. A. x2 + 6.75x + 8.75 (Asquare – Atriangle = Ashaded part; Asquare= 2x2+13.5x +17.5; Atriangle= x2+6.75x +8.75;
2x2+13.5x +17.5– (x2+6.75x +8.75) gives the final answer.)

2. 10. A. Vertex: (0,-16); Y-intercept: (0,-16); No symmetrical point; X-intercepts: (-4,0) & (4,0); graph
opens up
B. Vertex: (1,-10); Y-intercept: (0,-11); Symmetrical point: (2,-11); X-intercepts: None; graph
opens down
11. 250 ft by 500 ft (The perimeter is 2w + l = 1000; solve for l to get l = 1000-2w. The area formula
is A = w (1000-2w); Distribute w and find the vertex to find the maximum w of 250, the length is
1000- 2w, which is 500)
12. 5.4 m by 13.1 m (the length = 3w -3; Arectangle= lw; 70 = w(3w-3). Distribute, set the equation
equal to 0 and use the quadratic formula to find the value of w. Plug w into 3w – 3 to find the
length.)
13. 280.5 in2 (DRAW A PICTURE! The length of the picture = 5w – 4. The length of the picture AND
frame is 5w – 4 + 4 + 4, which is 5w +4. The width of the picture is w. The width of the picture
AND frame is w +4 + 4, which is w + 8. The entire area is 689, so (5w +4)(w+8) = 689, multiply
the two binomials, set the equation equal to 0 and then use the quadratic formula to find the
value of w. Plug that value into 5w – 4 to find the length. Take the picture width multiplied by
the picture length to find the area of the picture.)