*2/11
Let v(t) = 2*t**3 - 8*t**2 - 20*t + 23. Let b(m) = m**3 + m**2 - 1. Let p(q) = -3*b(q) - v(q). Determine w so that p(w) = 0.
-2, 1, 2
Let w = 43685/153 - -2954/51. Let f = -343 + w. Factor 2/9 + f*a + 2/9*a**2.
2*(a + 1)**2/9
Let t be (0 - -2) + 2 + -2. Factor d**t - d**2 - 2*d + 2*d**2.
2*d*(d - 1)
Let -t**2 - 2*t**2 + 4*t + 4*t - t**2 = 0. What is t?
0, 2
Let o(p) be the first derivative of 0*p + 1/9*p**3 - 2 + 0*p**2. Let o(j) = 0. Calculate j.
0
Let n = 207/5 + -41. Factor 4/5*j**3 + 0*j - 2/5*j**2 - n*j**4 + 0.
-2*j**2*(j - 1)**2/5
Suppose n + m = 9 - 4, -5*m = -n - 25. Let 2 + n + 10*u + 20*u**3 + u**5 + 20*u**2 + u**4 + 9*u**4 + u**5 = 0. Calculate u.
-1
Suppose -2*c + 2 = -6. Let d(m) be the third derivative of 0*m**6 + 0*m**c + 0 - 1/20*m**5 + 1/70*m**7 + 0*m + 0*m**3 + m**2. Let d(r) = 0. Calculate r.
-1, 0, 1
Let m(c) be the second derivative of c**5/100 - c**4/20 + c**3/15 + 48*c. Find d such that m(d) = 0.
0, 1, 2
Factor -8/7 + 4/7*z**2 - 4/7*z.
4*(z - 2)*(z + 1)/7
Factor -6*h - 3*h**3 + 6*h**3 + 3*h**2 + h**2 - h**2.
3*h*(h - 1)*(h + 2)
Let m(w) = -5*w**3 - 12*w**2 - 10*w - 3. Let b(n) = n + 1. Let x(y) = -4*b(y) - 4*m(y). Factor x(u).
4*(u + 1)**2*(5*u + 2)
Let z = -1/289 - -313/6936. Let f(u) be the third derivative of -2*u**2 + 1/60*u**5 + 0*u + 0 + 0*u**3 + z*u**4. What is y in f(y) = 0?
-1, 0
Let m(h) be the first derivative of h**4/2 + 2*h**3/3 - h**2/4 - h/2 - 7. Solve m(a) = 0 for a.
-1, -1/2, 1/2
Let p(t) = 5*t + 29. Let o be p(-5). Let k(g) be the first derivative of 0*g + 1 + 0*g**2 - 1/6*g**3 + 1/10*g**5 + 1/12*g**6 - 1/8*g**o. Solve k(w) = 0.
-1, 0, 1
Let a = 57/5 - 11. Find c such that 0*c + 0 + a*c**3 + 0*c**2 - 2/5*c**5 + 0*c**4 = 0.
-1, 0, 1
Suppose 8*h = 4*h + 2*a, 3*h + 14 = 5*a. Suppose 2/5*s - 8/5*s**h + 8/5*s**4 - 8/5*s**5 + 0 + 6/5*s**3 = 0. What is s?
-1, 0, 1/2, 1
Let a be (-325)/15*(-6)/(-4). Let f = -32 - a. Suppose -1/2*q**4 + 0 - 1/2*q**5 + 0*q + 1/2*q**2 + f*q**3 = 0. What is q?
-1, 0, 1
Let z(w) = 3*w**3 + 16*w**2 + 7*w - 19. Suppose 0 = 2*v - v + 14. Let r(k) = k**3 + 5*k**2 + 2*k - 6. Let u(d) = v*r(d) + 4*z(d). Suppose u(h) = 0. Calculate h.
-2, 1
Let h be (5*1)/(7 - 36/8). Factor -2/5*c**h - 2/5*c**3 + 0*c + 0.
-2*c**2*(c + 1)/5
Let k(v) be the second derivative of v**7/147 - v**5/70 - 4*v. Factor k(c).
2*c**3*(c - 1)*(c + 1)/7
Let o(g) be the third derivative of -g**7/2520 - g**6/540 - g**5/360 - g**3/3 - 3*g**2. Let p(z) be the first derivative of o(z). Let p(w) = 0. What is w?
-1, 0
Let o(b) = -76*b**3 - 112*b**2 + 48*b - 16. Let w(r) = -25*r**3 - 37*r**2 + 16*r - 5. Let k(n) = -5*o(n) + 16*w(n). Factor k(x).
-4*x*(x + 2)*(5*x - 2)
Determine w so that -1/3*w - 4/3*w**2 + 0 = 0.
-1/4, 0
Let b(l) be the first derivative of 2/5*l**4 + 16/15*l**3 + 1 + 2/5*l + l**2. Factor b(j).
2*(j + 1)*(2*j + 1)**2/5
Let b(j) be the third derivative of j**8/20160 - j**6/720 - j**5/20 + j**2. Let s(r) be the third derivative of b(r). Factor s(k).
(k - 1)*(k + 1)
Let b be 10/(-24)*(-31)/(1085/98). Factor -4/3*c**2 - 1/3*c**3 + 1/3*c**4 - 1/3 + 1/6*c**5 - b*c.
(c - 2)*(c + 1)**4/6
Let p = 808/35 - 114/5. Let 0 - 2/7*a**3 + 2/7*a - 2/7*a**2 + p*a**4 = 0. What is a?
-1, 0, 1
Let t = 6/5 - 7/10. Let s(x) be the first derivative of -x + t*x**2 + 1/3*x**3 - 1/4*x**4 + 2. Factor s(a).
-(a - 1)**2*(a + 1)
Let n = 3035/528 + -63/11. Let k(r) be the third derivative of 0 - 1/240*r**6 + 0*r**3 + 2*r**2 + 0*r - n*r**4 + 1/60*r**5. What is b in k(b) = 0?
0, 1
Let p(h) be the second derivative of -2*h**6/105 - 3*h**5/35 + 2*h**4/21 + 8*h**3/7 + 16*h**2/7 - 7*h. Determine u, given that p(u) = 0.
-2, -1, 2
Factor 1/5*c**2 + 0*c - 1/5*c**3 + 0.
-c**2*(c - 1)/5
Let 2/5*s**3 - 2/5*s + 2/5 - 2/5*s**2 = 0. What is s?
-1, 1
Let r(h) be the first derivative of -h**6/3 + 2*h**5/5 + h**4/2 - 2*h**3/3 + 9. Factor r(a).
-2*a**2*(a - 1)**2*(a + 1)
Let n(v) = v**3 + 29*v**2 + 61*v - 3. Let o(c) = 4*c**3 + 144*c**2 + 304*c - 16. Let z(i) = 16*n(i) - 3*o(i). Suppose z(p) = 0. Calculate p.
-4, 0
Let o(l) be the first derivative of l**6/2160 - l**5/240 + l**4/72 - l**3 - 5. Let k(q) be the third derivative of o(q). Find z, given that k(z) = 0.
1, 2
Let l(k) be the first derivative of k**8/168 - k**7/105 - k**6/20 + k**5/6 - k**4/6 - 3*k**2/2 - 2. Let u(i) be the second derivative of l(i). Solve u(h) = 0.
-2, 0, 1
Let g(m) be the third derivative of -m**7/35 + 11*m**6/120 - m**5/15 - m**4/24 + 34*m**2. Solve g(x) = 0 for x.
-1/6, 0, 1
Let a(p) = -p**3 + 17*p**2 - 6. Let b be a(17). Let n(m) = 6*m**2 + 25*m + 54. Let t(i) = 3*i**2 + 12*i + 27. Let o(f) = b*n(f) + 11*t(f). Factor o(d).
-3*(d + 3)**2
Let w(m) be the second derivative of -m**5/30 - m**4/9 - 23*m. Factor w(o).
-2*o**2*(o + 2)/3
Suppose 2*b - 1 = 7. Let v = 6/7 - 4/7. Factor v*s**3 + 0 - 2/7*s - 2/7*s**b + 2/7*s**2.
-2*s*(s - 1)**2*(s + 1)/7
Let f = 9 + -9. Suppose -4*l + f = -y - 2, 4*y - 3 = 5*l. Let d + 1/4*d**y + 1 = 0. What is d?
-2
Let o be 3/111*(-10)/15. Let f = 41/222 + o. Let -f*s**2 + 1/2*s - 1/3 = 0. Calculate s.
1, 2
Suppose 25 + 15 = 10*c. Factor 26/7*t + 4/7 + 54/7*t**2 + 2*t**c + 46/7*t**3.
2*(t + 1)**3*(7*t + 2)/7
Let z(g) = g**3 + 1. Let y(r) = 4*r**3 + r**2 + 5. Let o = -5 + 9. Suppose 3*i + o = -i. Let u(n) = i*y(n) + 5*z(n). Factor u(f).
f**2*(f - 1)
Factor -2*n**2 + 0 + 28*n + 18*n**2 - 8 + 0*n.
4*(n + 2)*(4*n - 1)
Let a(y) be the second derivative of -5*y**5/4 + 10*y**4/3 - 5*y**3/6 - 5*y**2 + 8*y. Determine k so that a(k) = 0.
-2/5, 1
Let n(i) be the first derivative of 3*i**5/5 + 6*i**4 + 22*i**3 + 36*i**2 + 27*i - 30. Solve n(t) = 0.
-3, -1
Let d(n) be the second derivative of -n**4/12 + n**3/6 - 6*n. Factor d(b).
-b*(b - 1)
Let b be 1 + -1 + 0 - -4. What is y in -4*y + 4 + 1 - b*y**2 + 3 = 0?
-2, 1
Let y be (-6)/10 - (-47)/70. Let x(d) be the first derivative of 1/7*d**2 - 2/21*d**3 - 2 + 0*d - y*d**4 + 2/35*d**5. Let x(f) = 0. What is f?
-1, 0, 1
Suppose 2*l = r + 7, 0*l + 3*r - 11 = -2*l. Suppose -3*x + o + 3 = 0, -l*o + 5*o = 4*x - 5. Factor d**5 + d**4 - 2*d**x + 2*d**2.
d**4*(d + 1)
Let x(d) = -9*d**3 - 20*d**2 + 7*d - 11. Let b(p) = -3*p**3 + 2 + p + 6*p**2 + p - 13*p**2 - 6. Let n(g) = 11*b(g) - 4*x(g). Factor n(a).
3*a*(a - 1)*(a + 2)
Let h(x) be the third derivative of x**7/5460 + x**6/2340 + 4*x**3/3 - 7*x**2. Let g(i) be the first derivative of h(i). Factor g(t).
2*t**2*(t + 1)/13
Let p(k) be the first derivative of -k**8/168 + k**6/30 - k**4/12 - k**2 - 2. Let q(h) be the second derivative of p(h). Find c such that q(c) = 0.
-1, 0, 1
Let h(y) = -y**3 - 2*y**2 + 2*y + 3. Let w be h(-3). Suppose 4*z + 14 = 4*q + w*z, -12 = -4*z. Factor 1/5*f + 0 + 1/5*f**q.
f*(f + 1)/5
Let q(l) be the first derivative of -l**7/1260 + l**6/540 + l**5/180 - l**4/36 - l**3 - 1. Let o(m) be the third derivative of q(m). Factor o(s).
-2*(s - 1)**2*(s + 1)/3
Let b(l) be the first derivative of -35*l**6/6 + 12*l**5 - 15*l**4/4 - 10*l**3/3 + 20. Let b(d) = 0. What is d?
-2/7, 0, 1
Let g(x) be the second derivative of -9*x**6/10 - 3*x**5/10 + 9*x**4/4 + x**3 - 17*x. Solve g(i) = 0.
-1, -2/9, 0, 1
Let b(s) be the second derivative of 0 - 1/24*s**4 + 0*s**2 - 4/15*s**6 - s + 0*s**3 + 1/5*s**5. What is l in b(l) = 0?
0, 1/4
Let g(l) = -l**2 - l + 2. Let s be g(0). Factor 2*a**2 + 4*a**s + 3*a - 3*a**4 + a**4 + a.
-2*a*(a - 2)*(a + 1)**2
Let m(a) = a**3 + 10*a**2 + 7*a - 3. Let w be m(-9). Let l be w/18 + 1/(-3). Factor 1/4*s**2 + l + 3/4*s.
(s + 1)*(s + 2)/4
Let w(k) = 2*k**2 + 4*k + 3. Let q = 9 + -6. Let y(i) = -3*i**2 - 5*i - 4. Let a(g) = q*y(g) + 4*w(g). Factor a(z).
-z*(z - 1)
Let c(t) be the second derivative of 0 - 2/27*t**3 + 4*t + 1/9*t**2 + 1/54*t**4. Let c(u) = 0. What is u?
1
Factor -11*w**2 - 1 - 8*w - 9*w**4 - 24*w**3 - 9*w**2 - 9*w**2 + 7*w**2.
-(w + 1)**2*(3*w + 1)**2
Suppose 229*d = 222*d. Let z be (-3)/(-4)*(-8)/(-9). Suppose 2/3*b**3 + 0*b - 2/3*b**5 + d + 2/3*b**2 - z*b**4 = 0. Calculate b.
-1, 0, 1
Let m(w) = 21*w**3 + 27*w**2 + 15*w - 9. Let p(g) = 5*g**3 + 7*g**2 + 4*g - 2. Let u(l) = -2*m(l) + 9*p(l). Determine r, given that u(r) = 0.
-2, -1, 0
Let m = -317 + 2223/7. Find u such that m - 2/7*u - 2/7*u**2 = 0.
-2, 1
Suppose 36 = -3*t + 6*t. Suppose 5*q = 3*q - 4*v - t, 0 = 2*q + 5*v + 16. Factor 3*c**2 + 4*c**3 - 2 - 4*c + q*c**4 - 3*c**2.
2*