tive of -1/40*q**5 - b*q**2 + 2*q + 0 + 1/24*q**4 + 1/12*q**3. Factor c(x).
-(x - 1)**2*(x + 1)/2
Suppose 5*k - 6 - 19 = 0. Factor -33 - 4*l**2 - 2*l + 0*l**2 + 33 + 2*l**k + 4*l**4.
2*l*(l - 1)*(l + 1)**3
Let g(h) = h**3 - 16*h**2 - 3*h + 50. Let u be g(16). Find p, given that 1/4*p**u - 1/4*p**3 + 1/4*p - 1/4 = 0.
-1, 1
Let k = -53 + 91. Suppose 5*z + n + 0*n = 15, -2*z + 5*n = -6. Let -162*o**4 - 2*o - 5*o**5 + 6*o + 59*o**5 + 118*o**z + 8*o**3 - k*o**2 = 0. What is o?
0, 1/3, 2
Let v(q) be the third derivative of q**8/672 + q**7/210 - q**6/80 - q**5/30 + q**4/12 + 9*q**2. Factor v(f).
f*(f - 1)**2*(f + 2)**2/2
Let o be 3/1 - (-5)/(-2). Let s be 14/(-8)*(-16)/56. Find y such that -1/2*y**3 + o*y + 1/2 - s*y**2 = 0.
-1, 1
Suppose -k + 2*i + 33 = 0, -4*k + 220 = k + i. Suppose -3*l**2 - l - k + 43 + 4*l**2 = 0. What is l?
0, 1
Let c(n) be the third derivative of 1/150*n**5 + 0*n - 1/20*n**4 - 3*n**2 + 0 + 2/15*n**3. Factor c(x).
2*(x - 2)*(x - 1)/5
Solve -5/2*k - 5/4*k**4 + 0*k**3 + 0 + 15/4*k**2 = 0 for k.
-2, 0, 1
Factor -28*x**4 - 93*x**3 - 64*x + 13*x**3 - 21*x**3 + 25*x**3 - 100*x**2 - 16 - 4*x**5.
-4*(x + 1)**3*(x + 2)**2
Let u(r) be the third derivative of -r**6/60 + r**4/12 + 2*r**2 - 1. Factor u(v).
-2*v*(v - 1)*(v + 1)
Let y(p) = p**3 - 8*p**2 + 7*p + 8. Let a be y(7). Suppose -3*j = 2 - a. Determine f, given that -5*f**3 + 0*f + 7*f**5 - 2*f + 2*f**2 + 9*f**4 - 11*f**j = 0.
-1, -2/7, 0, 1
Factor 0 + 3/4*i - 3/8*i**2.
-3*i*(i - 2)/8
Suppose -3*x + 5*i - 6*i + 3 = 0, -2*i = -3*x - 6. What is p in 6/5*p**3 - 2/5*p**4 - 4/5*p**2 + 0*p + x = 0?
0, 1, 2
Suppose 0 = a + a + 4. Let g be ((-3)/1 - a)*-2. Factor 2*l - 2 - 3*l + 2*l**2 + l**g.
(l - 1)*(3*l + 2)
Let y = 151/34 + -50/17. Determine a so that -9/8*a + 1/4*a**4 + 11/8*a**3 + y*a**2 + 0 = 0.
-3, 0, 1/2
Find g such that 0*g**3 + 6*g + g**3 - g - 4*g**2 - 2 + 0*g**2 = 0.
1, 2
Let g(a) be the third derivative of a**7/2520 + a**4/12 - 2*a**2. Let b(f) be the second derivative of g(f). Solve b(s) = 0.
0
Let r(q) be the second derivative of 0 - 1/3*q**3 - 3/10*q**6 + 0*q**2 + 3/10*q**5 + 5/12*q**4 - 2*q. Suppose r(p) = 0. Calculate p.
-2/3, 0, 1/3, 1
Let p(m) be the second derivative of 0 + 1/147*m**7 - 1/35*m**5 - 1/7*m**2 + 1/21*m**4 + 1/21*m**3 - 1/105*m**6 - m. Suppose p(s) = 0. Calculate s.
-1, 1
Let z(n) be the first derivative of 0*n**3 + 1 - n + 1/60*n**5 + 0*n**4 + 0*n**2 + 1/30*n**6 + 1/63*n**7. Let q(u) be the first derivative of z(u). Factor q(y).
y**3*(y + 1)*(2*y + 1)/3
Let y(w) be the third derivative of 1/126*w**8 + 0*w - 1/35*w**7 - 1/6*w**4 + 4/45*w**5 + 1/9*w**3 + 1/90*w**6 - 3*w**2 + 0. Find m, given that y(m) = 0.
-1, 1/4, 1
Determine y, given that 0 + 3/5*y**5 - 39/5*y**2 + 3/5*y**4 - 18/5*y - 21/5*y**3 = 0.
-2, -1, 0, 3
Suppose 1 = 2*s - 3. Let o = 30 + -27. Factor 0*z**s + 0 - 2/11*z**o + 2/11*z.
-2*z*(z - 1)*(z + 1)/11
Let t be 28/36 - 1 - 114/(-27). Factor -2/3*c**2 + 2/3*c**t + 0 + 0*c + 2/3*c**3 - 2/3*c**5.
-2*c**2*(c - 1)**2*(c + 1)/3
Let u(j) be the first derivative of 0*j + 1 + 2/3*j**3 + 1/3*j**2. Factor u(b).
2*b*(3*b + 1)/3
Let v(w) = 9*w - 3. Let a be v(2). Determine x, given that -a*x**3 + 1 - 6*x**2 - 1 = 0.
-2/5, 0
Let g(c) be the first derivative of 9 - 2/15*c**5 + 0*c**2 + 0*c + 1/6*c**4 + 0*c**3. Factor g(w).
-2*w**3*(w - 1)/3
Let q(d) be the first derivative of -2*d - 6 + 2/3*d**2 - 2/27*d**3. Factor q(r).
-2*(r - 3)**2/9
Let r(t) = -t**3 - t**2 - 2*t - 2. Let s be r(-2). Suppose 2*m = 0, -4*l - 2*m = -14 + s. Factor -3*z**4 - 3*z**l + 3*z**4 - 2*z**4 - 2 + 7*z**2.
-2*(z - 1)**2*(z + 1)**2
Suppose 7*f = -0*f. Determine l, given that 3*l**4 + f*l**3 + 0*l**3 - 4*l**5 + l**5 = 0.
0, 1
Let g be 45/18*8/10. Determine q so that 4/3*q - 2*q**g + 0 + 2/3*q**3 = 0.
0, 1, 2
Let u be 3 + 2/(-4)*0. Factor 3*w**u + 0*w**3 - 9*w**4 + 6*w**4.
-3*w**3*(w - 1)
Factor -36/5*n**2 - 192/5 + 144/5*n + 3/5*n**3.
3*(n - 4)**3/5
Suppose -12*l + 14*l = 0. Let i be l - 8/(-84)*3. Suppose i*n**2 + 0 + 0*n = 0. Calculate n.
0
Let f = 139/99 + -11/9. Suppose 2/11*a**2 + 0 - f*a**4 + 0*a**3 + 0*a = 0. What is a?
-1, 0, 1
Let f(h) be the second derivative of 0*h**6 - 1/105*h**7 + 1/50*h**5 + 0 + 0*h**2 + 0*h**3 + 3*h + 0*h**4. Factor f(s).
-2*s**3*(s - 1)*(s + 1)/5
Let j(o) be the second derivative of -o**6/360 + o**5/60 + 5*o**3/6 + 4*o. Let f(i) be the second derivative of j(i). Determine a, given that f(a) = 0.
0, 2
Let q = -129/10 + 67/5. Factor -1/2*u + 1 - q*u**2.
-(u - 1)*(u + 2)/2
Let c(i) be the third derivative of i**5/540 + 5*i**4/216 - 59*i**2. Factor c(p).
p*(p + 5)/9
Let j(o) = -o**2 - o + 1. Let r be j(-2). Let s be 1/(r/(-8 - -2)). Factor -4*b**2 - b**4 + s*b**2 - b**2.
-b**2*(b - 1)*(b + 1)
Suppose d = 5*t + 17, -3*d - d - 4*t - 4 = 0. Let a = -9 + 18. Determine m, given that -m**d + 9*m - a*m = 0.
0
Let q(b) be the third derivative of -b**11/166320 + b**9/15120 - b**7/2520 - b**5/60 + 2*b**2. Let s(p) be the third derivative of q(p). Solve s(n) = 0.
-1, 0, 1
Let s = 10 - 6. Let x(v) be the third derivative of 1/6*v**s + 0 - v**2 + 0*v + 0*v**3 - 1/10*v**5. Determine c so that x(c) = 0.
0, 2/3
Let f(z) be the first derivative of -z**6/10 + 3*z**5/5 - 27*z**4/20 + 7*z**3/5 - 3*z**2/5 + 10. Suppose f(d) = 0. What is d?
0, 1, 2
Let k(n) be the third derivative of 0*n**3 - 3*n**2 + 0*n**4 + 0 + 0*n**5 - 1/720*n**6 + 0*n. Factor k(o).
-o**3/6
Let w(x) be the second derivative of 3*x - 1/5*x**2 - 2/15*x**3 - 1/30*x**4 + 0. Suppose w(t) = 0. What is t?
-1
Suppose -2*w = -6*w + 8. Let v(q) be the first derivative of 4/15*q**3 - w + 0*q + 1/5*q**2 + 1/10*q**4. Factor v(o).
2*o*(o + 1)**2/5
Let i(j) be the third derivative of j**6/90 - j**5/20 + j**4/12 - j**3/2 + 2*j**2. Let d(w) be the first derivative of i(w). Find o such that d(o) = 0.
1/2, 1
Let 0*p - 3/4*p**2 + 0 + 1/4*p**3 = 0. What is p?
0, 3
Suppose 2*a = -3*a. Factor a + 2/3*q - 1/3*q**2.
-q*(q - 2)/3
Let a be 4*1*14/8. Let b be a - 2 - (2 - 0). Solve -30*q**2 + 234*q**b + 8*q - 32*q**2 + 9*q**2 - 19*q**2 + 150*q**5 - 320*q**4 = 0.
0, 1/3, 2/5, 1
Let s(v) be the first derivative of 7*v**4/6 + 3*v**3 + 2*v**2 - 4*v - 6. Let r(l) be the first derivative of s(l). Find x, given that r(x) = 0.
-1, -2/7
Let x(n) = 2*n**3 - 13*n**2 + 13*n + 5. Let u(c) = c**3 - 6*c**2 + 6*c + 2. Let s be 4/(-14) - (-102)/14. Let t(w) = s*u(w) - 3*x(w). Factor t(y).
(y - 1)**3
Let u(c) = 20*c**3 + 28*c**2 + 8*c - 6. Let g(f) = -20*f**3 - 28*f**2 - 8*f + 5. Let a(s) = 6*g(s) + 5*u(s). Factor a(r).
-4*r*(r + 1)*(5*r + 2)
Suppose -z - 6 = 2*z, 2*g = -z + 16. Suppose 3*k = -5*a, -g + 3 = 2*a. Find j, given that 2/7*j**k - 2/7 - 2/7*j**4 + 2/7*j + 4/7*j**2 - 4/7*j**3 = 0.
-1, 1
Let b(k) = -2*k**2 + 13*k + 47. Let f be b(9). Factor 5/2*i - 1 + 1/2*i**3 - f*i**2.
(i - 2)*(i - 1)**2/2
Let n be -1 + 1 + (-4)/2. Let i(p) = 2*p**3 - 4*p**3 + 6*p**3 - 2*p**2. Let v(y) = 13*y**3 - 5*y**2 - y. Let g(l) = n*v(l) + 7*i(l). Factor g(k).
2*k*(k - 1)**2
Let r(v) be the first derivative of 25*v**6/21 - 16*v**5/7 + 3*v**4/7 + 16*v**3/21 + v**2/7 + 8. Factor r(h).
2*h*(h - 1)**2*(5*h + 1)**2/7
Let n(y) be the first derivative of y**5/60 + y**4/18 - y**3/18 - y**2/3 - 4*y + 1. Let t(r) be the first derivative of n(r). Let t(x) = 0. Calculate x.
-2, -1, 1
Let o be ((-2)/(-9))/((-1)/(-21)). Suppose -3*z - 24 = -7*z. Factor o*a**3 - 4/3*a**4 + 10/3*a - z*a**2 - 2/3.
-2*(a - 1)**3*(2*a - 1)/3
Let g(q) = 3*q**2. Suppose 0 = 8*j - 4*j + 4. Let u be g(j). Factor c**5 + 2*c**2 - 3*c**3 + 2 + c**4 + c - 4*c**2 + c**u - 1.
(c - 1)**2*(c + 1)**3
Let j be 5 + (-16)/(-36) - 5. Factor -2/9*a - j + 2/9*a**2.
2*(a - 2)*(a + 1)/9
Let a be 50/126 + (-2)/7. Let v(l) be the second derivative of a*l**2 - 1/54*l**4 - l + 0*l**3 + 0. Suppose v(d) = 0. Calculate d.
-1, 1
Find k such that -1/4*k**3 + 1/4*k**5 + 1/4*k**2 + 0*k + 0 - 1/4*k**4 = 0.
-1, 0, 1
Let c(w) be the second derivative of 0*w**2 + 0*w**4 + 1/126*w**7 + 0*w**5 + 0 + 1/90*w**6 + 0*w**3 - w. Factor c(u).
u**4*(u + 1)/3
Suppose t = -5*a - 0*a - 15, 2*t - 9 = 3*a. Let h be (-6)/(-3) - -3 - 2. Factor t*u**2 + 2*u**2 - h + 1 + 2*u - 2*u**3.
-2*(u - 1)**2*(u + 1)
Find n such that -15*n - 3/2*n**2 - 75/2 = 0.
-5
Suppose 0 = m + 2*a + 2 - 10, 0 = -2*m - 5*a + 18. Let o(d) be the second derivative of 1/7*d**2 + d + 0*