0, 1
Let b = 13 + -9. Suppose -20 = 5*v + b*a, -v - 2 - 8 = 2*a. Factor 5/4*p**5 + 1/4*p**3 + v + 0*p + 2*p**4 - 1/2*p**2.
p**2*(p + 1)**2*(5*p - 2)/4
Let o(y) be the first derivative of -y**6/585 + y**5/260 + y**4/156 + 2*y**3/3 - 3. Let h(v) be the third derivative of o(v). Let h(j) = 0. What is j?
-1/4, 1
Let f(w) = 7*w**2 - 3*w + 3. Let c(b) = -22*b**2 + 8*b - 8. Let v(l) = -5*c(l) - 16*f(l). Suppose v(n) = 0. What is n?
2
Let h(n) = -3*n + 3. Let a be h(-9). Let b be ((-5)/30)/((-4)/a). Factor -1 - 3*s - b*s**2.
-(s + 2)*(5*s + 2)/4
Let f(g) be the first derivative of -2*g**3/15 - 4*g**2/5 + 2*g + 48. Factor f(a).
-2*(a - 1)*(a + 5)/5
Let k(s) be the first derivative of -1/5*s**2 - 6 + 2/25*s**5 - 1/15*s**6 - 4/15*s**3 + 2/5*s + 1/5*s**4. Factor k(y).
-2*(y - 1)**3*(y + 1)**2/5
Find o such that -2*o + 5*o**5 + 2*o**3 - 6*o**5 + o = 0.
-1, 0, 1
Suppose 14 = 2*l - 2*h, -17*l + 5 = -14*l + h. Find c such that -2/3*c + 0 + 16/3*c**2 - 32/3*c**l = 0.
0, 1/4
Let m be (-14)/192*2 - 0. Let w = 3/16 - m. Suppose -w*r**2 - 1/3 - 2/3*r = 0. What is r?
-1
Suppose -3*q + 10 = -5. Let z(s) be the third derivative of -2*s**2 + 1/6*s**3 - 1/60*s**q + 0 + 1/120*s**6 + 0*s - 1/24*s**4. Factor z(g).
(g - 1)**2*(g + 1)
Let y(x) = -8*x**2 - 43*x - 21. Let q(i) = 17*i**2 + 85*i + 42. Let n(u) = 2*q(u) + 5*y(u). Suppose n(a) = 0. Calculate a.
-7, -1/2
Let u(o) be the first derivative of -o**3 + 7*o**2/4 - o/2 - 12. Find m, given that u(m) = 0.
1/6, 1
Let a(z) be the first derivative of z**6/6 - 2*z**5/5 + z**4/4 - 4. Suppose a(l) = 0. What is l?
0, 1
Let q(a) be the third derivative of -a**6/90 + a**5/15 - 8*a**3/9 + 12*a**2. Determine k so that q(k) = 0.
-1, 2
Let v be 1*3 + 551/(-203). Let w be (2 - (-16)/(-7))*-2. Solve -2/7*j**4 + w*j - 8/7*j**3 - v + 4/7*j**2 + 4/7*j**5 = 0 for j.
-1, 1/2, 1
Suppose -c + 20 = 17. Let 3/2*r**3 + 0 - c*r**2 + 0*r = 0. Calculate r.
0, 2
Let c(s) be the third derivative of -s**9/22680 + s**8/5040 - s**7/3780 - s**4/12 + s**2. Let o(h) be the second derivative of c(h). Factor o(n).
-2*n**2*(n - 1)**2/3
Let v(c) be the third derivative of -c**7/105 + c**6/15 - c**5/5 + c**4/3 - c**3/3 + 9*c**2. Find t such that v(t) = 0.
1
Let p(x) be the third derivative of -1/240*x**6 - 1/120*x**5 + 0*x**3 + 3*x**2 + 0*x + 0*x**4 + 0. Suppose p(c) = 0. Calculate c.
-1, 0
Suppose -5*p + 22 + 3 = 0. Suppose 2*z + 3 = -4*c + 3*c, -p*z = -c + 18. Determine g, given that g**4 + 0*g**4 - 4*g**3 + 5*g**c = 0.
-1, 0
Let k(w) be the third derivative of -w**8/6720 - w**7/1260 - w**6/720 - w**4/8 - 4*w**2. Let r(b) be the second derivative of k(b). Solve r(o) = 0 for o.
-1, 0
Let l be (-13)/(-4) - (135/12)/9. Factor 0*m + 0 - 1/2*m**l.
-m**2/2
Let s be -1 + -1 + (-3 - -23). Solve 4*o**3 - 5*o**3 - 2 - 13*o - 8*o**3 - 6*o**2 - s*o**2 = 0.
-2, -1/3
Let q(p) be the second derivative of -p**6/360 - p**5/60 - p**4/24 + p**3/2 + 2*p. Let b(z) be the second derivative of q(z). Find g, given that b(g) = 0.
-1
Factor 24 + 8*i + 2/3*i**2.
2*(i + 6)**2/3
Let w(s) = 17*s**5 + 7*s**4 - s**3 - 3*s**2. Let u(z) = -z**5 + z**4 - z**3 + z**2. Suppose -3*o = 3 + 6. Let a(q) = o*u(q) - w(q). Factor a(i).
-2*i**3*(i + 1)*(7*i - 2)
Let m = -38/13 - -241/78. Factor 0*w - 1/6*w**4 + m*w**2 + 0 + 1/6*w**3 - 1/6*w**5.
-w**2*(w - 1)*(w + 1)**2/6
Factor 5*z - z**5 + 97*z**4 + 104*z**4 + 6*z**3 + 6*z + 3 - 202*z**4 + 14*z**2.
-(z - 3)*(z + 1)**4
Suppose 11 = 4*w + 5*j - 4*j, -2*w = -4*j - 10. Factor 0 + 0*d + 2/5*d**2 - 4/5*d**w + 2/5*d**4.
2*d**2*(d - 1)**2/5
Let n(f) be the first derivative of f**8/4200 + f**7/700 + f**6/300 + f**5/300 - 2*f**3/3 + 5. Let r(v) be the third derivative of n(v). Factor r(a).
2*a*(a + 1)**3/5
Let g(y) be the first derivative of -y**3/5 + 12*y**2/5 + 50. Factor g(x).
-3*x*(x - 8)/5
Let a = 1 + -5. Let q(y) = y**3 + 3*y**2 + 3. Let f(b) = b**3 + 4*b**2 + 4. Let x(o) = a*q(o) + 3*f(o). Let x(u) = 0. Calculate u.
0
Let o be (-1)/(((-8)/10)/4). Let s be (-28)/35*o/(-2). Determine n so that -4*n**3 + 2*n**2 - 3*n**s + 3*n**2 = 0.
0, 1/2
Factor -30*k + k + 3*k**3 + 11*k - 24 + 6*k**2 + 6*k.
3*(k - 2)*(k + 2)**2
Suppose -1 = -10*t + 19. Factor -4/3*y + t - 2/3*y**2.
-2*(y - 1)*(y + 3)/3
Let b(g) be the second derivative of -g**4/132 - 7*g**3/66 - 6*g**2/11 - 27*g. Suppose b(a) = 0. What is a?
-4, -3
Let b = 231 - 231. Factor b - 2/5*c**2 + 4/5*c.
-2*c*(c - 2)/5
Factor -8/3*i**2 - 14/3*i**4 + 0*i + 0 - 32/3*i**3.
-2*i**2*(i + 2)*(7*i + 2)/3
Let f = -12 + 3. Let p be (6/9)/((-3)/f). Find q such that -4/7*q**3 + 2/7 + 4/7*q - 2/7*q**4 + 0*q**p = 0.
-1, 1
Let l(r) be the second derivative of r**8/5880 + r**7/1470 + r**6/1260 + r**3/6 + 4*r. Let b(t) be the second derivative of l(t). Factor b(h).
2*h**2*(h + 1)**2/7
Let i(u) be the third derivative of 3*u**2 + 0 - 1/40*u**4 - 1/100*u**5 - 1/600*u**6 + 0*u - 1/30*u**3. Factor i(a).
-(a + 1)**3/5
Let w = 228485 + -20792571/91. Let x = w - -66/13. Factor -2/7*c + 4/7*c**2 + 4/7*c**3 - 2/7*c**5 - 2/7 - x*c**4.
-2*(c - 1)**2*(c + 1)**3/7
Let w(d) be the third derivative of 0*d + 1/15*d**5 + 1/36*d**6 - 1/12*d**4 + 4*d**2 + 5/6*d**3 + 0. Let s(o) be the first derivative of w(o). Solve s(h) = 0.
-1, 1/5
Let c(y) = -y**2 + 5*y - 1. Let k be c(3). Suppose 2*n**4 + n**5 - 4*n**k + 4*n**5 - n**4 = 0. Calculate n.
-1, 0
Let c = -282 - -285. Suppose 0 - 8/5*r**4 + 2/5*r - 12/5*r**c + 8/5*r**2 + 2*r**5 = 0. Calculate r.
-1, -1/5, 0, 1
Let a(s) be the first derivative of -s**5/25 - s**4/5 - s**3/3 - s**2/5 + 8. Factor a(j).
-j*(j + 1)**2*(j + 2)/5
Let r(d) = 4*d**3 - 11*d**2 - 4*d + 11. Let i(k) = -2*k**3 + 5*k**2 + 2*k - 5. Let b(x) = -x - 7. Let s be b(0). Let l(v) = s*i(v) - 3*r(v). Factor l(z).
2*(z - 1)**2*(z + 1)
Let z = 3 + 2. Let p be ((-1)/z)/((-7)/10). Solve p*q**4 + 2/7*q**2 + 0 + 0*q - 4/7*q**3 = 0.
0, 1
Let k(t) be the second derivative of -t**6/60 + t**5/30 + t**2/2 - 3*t. Let c(w) be the first derivative of k(w). Suppose c(n) = 0. What is n?
0, 1
Let g(w) be the first derivative of w**6/3 + 4*w**5/5 - 3*w**4/2 - 8*w**3/3 + 4*w**2 - 4. Find t such that g(t) = 0.
-2, 0, 1
Let o = 4 + 1. Suppose -o*l = -9*l. Find c, given that -c**2 + 1/2*c**3 + l + 1/2*c = 0.
0, 1
Let q(x) = x**3 + 15*x**2 - 12*x - 4. Let j(l) = -l**3 + l**2 - l + 1. Let c be (2 - 8)/(-2) + -6. Let f(v) = c*q(v) - 24*j(v). Factor f(y).
3*(y - 2)*(y - 1)*(7*y - 2)
Let d(r) = r**3 - 7*r**2 - 8*r. Let j be d(8). Determine w so that 0*w - 3*w**2 + 1 - 2*w + j*w + 0*w = 0.
-1, 1/3
Let d(x) be the first derivative of 6 + 9/8*x**2 + 11/12*x**3 - 1/2*x. Factor d(i).
(i + 1)*(11*i - 2)/4
Let k(o) be the first derivative of -o**7/420 + o**5/120 - 5*o**2/2 + 5. Let j(q) be the second derivative of k(q). Factor j(w).
-w**2*(w - 1)*(w + 1)/2
Let -t**3 + 6*t**2 - t**4 - 10*t**2 - 3*t**3 = 0. What is t?
-2, 0
Factor 9*s + 3/2*s**2 + 0.
3*s*(s + 6)/2
Let k = 9 + -7. Factor -a**2 + 3*a**4 - a**4 + a**2 - 2*a**k.
2*a**2*(a - 1)*(a + 1)
Let h(x) be the third derivative of -x**6/200 + x**5/150 - 5*x**2. Factor h(g).
-g**2*(3*g - 2)/5
Let j be 1703/975 - 4/50. Factor -2/3 + j*f + 1/3*f**3 - 4/3*f**2.
(f - 2)*(f - 1)**2/3
Factor -16/13*w**3 + 4/13*w**4 - 32/13*w**2 + 32/13*w + 64/13 + 2/13*w**5.
2*(w - 2)**2*(w + 2)**3/13
Let l(n) be the second derivative of -1/4*n**4 + 3*n + 0 - n**3 - 3/2*n**2. Factor l(j).
-3*(j + 1)**2
Factor -4/5 + 6/5*n**3 - 1/5*n**4 - 13/5*n**2 + 12/5*n.
-(n - 2)**2*(n - 1)**2/5
Let w(a) be the second derivative of a**9/52920 - a**8/5880 + a**7/1764 - a**6/1260 + a**4/4 + 2*a. Let n(c) be the third derivative of w(c). Factor n(m).
2*m*(m - 2)*(m - 1)**2/7
Let g(n) = -n**2 + 3. Let h be g(-3). Let d be 9/h*(-4)/15. Find w, given that 3/5*w**2 + d*w + 0 - w**3 = 0.
-2/5, 0, 1
Let o(a) be the second derivative of 1/8*a**2 - 2*a - 1/48*a**3 + 0 - 1/96*a**4. Find h such that o(h) = 0.
-2, 1
Let u(a) = a**2 + 15*a + 2. Let q be u(-15). Factor 1/2*o**3 + 0 + 0*o**q - 1/2*o.
o*(o - 1)*(o + 1)/2
Suppose -v + 5 = 5*i + 2*v, 0 = -2*v - 10. Let w**2 - 4 + 5 + 2 + 1 - i*w = 0. What is w?
2
Let y be -18 + 26 - (4 - -1). Factor 3/4*j**4 - 1/2*j**y - 1/2*j**2 - 1/4 + 3/4*j - 1/4*j**5.
-(j - 1)**4*(j + 1)/4
Let x(d) be the first derivative of d**6/33 + 6*d**5/55 + 3*d**4/22 + 2*d**3/33 + 24. Determine g so that x(g) = 0.
-1, 0
Let c = 27 - 23. Find o, given 