t l(m) be the second derivative of m**6/1800 - m**5/200 + m**4/60 - m**3/6 + 4*m. Let g(n) be the second derivative of l(n). Factor g(r).
(r - 2)*(r - 1)/5
Let w(j) = j**3 - 4*j**2 + 4*j - 1. Let b be w(3). Let s = -1/3 + 2/3. Find r, given that -1/3 + s*r**b + 0*r = 0.
-1, 1
Suppose 0 = 3*k - 6 - 0. Factor 6*m**3 - k*m**2 + 4*m - 4*m.
2*m**2*(3*m - 1)
Suppose 4*w + 40 = -4*i, 1 - 17 = 4*w. Let n be ((-30)/100)/(i/8). Suppose 2/5*u**3 - 2/5*u + n - 2/5*u**2 = 0. Calculate u.
-1, 1
Let x(d) be the first derivative of d**3/12 + d**2 - 9*d/4 - 68. Suppose x(k) = 0. What is k?
-9, 1
Let x(n) be the second derivative of 5*n**4/12 - 5*n**3/3 - 15*n**2/2 - 11*n. Solve x(i) = 0 for i.
-1, 3
Let v be ((-2)/93)/((-2)/(-6)). Let b = 68/93 + v. Find q, given that -1/3*q**4 - b*q**5 + 1/3*q**2 + q**3 + 0 - 1/3*q = 0.
-1, 0, 1/2, 1
Suppose 10*o + 4*r - 16 = 6*o, -5*r = -o + 4. Determine k so that 0 + 0*k + 2/7*k**2 + 2/7*k**o + 5/7*k**3 = 0.
-2, -1/2, 0
Let z(p) be the second derivative of -p**6/15 + 17*p**5/50 - 7*p**4/10 + 11*p**3/15 - 2*p**2/5 - 8*p. Suppose z(r) = 0. Calculate r.
2/5, 1
Let p = -28/9 - -149/45. Factor -p*y**3 + 1/5*y**2 + 0 + 0*y.
-y**2*(y - 1)/5
Let j be (2 - 1*-3) + -1. Suppose j*o + 3 = 19. Factor -9*q**3 + 2*q**3 + 2*q**2 + 0*q**3 + 8*q**o - 3*q**5.
-q**2*(q - 1)**2*(3*q - 2)
Suppose 4*m = 2*w - 34, 4*w - 3*m - 59 = -11. Suppose 0*k**3 + w*k**2 - 2*k**2 + 5*k**3 + 2*k = 0. Calculate k.
-1, -2/5, 0
Let a = 36 - 34. Let j(d) = d**2 + 4*d - 2. Let k be j(-6). Factor 8*q - 8/5 - k*q**a.
-2*(5*q - 2)**2/5
Let l(q) be the second derivative of 1/2*q**4 + 0 - 2*q + 0*q**2 - 1/3*q**3. Factor l(y).
2*y*(3*y - 1)
Let q be 7/(-20) + (-2)/(-5). Let r(v) be the third derivative of v**3 + 0 + 3*v**2 - 1/8*v**4 + 0*v - q*v**5. What is g in r(g) = 0?
-2, 1
Let m(z) be the third derivative of -z**6/480 - z**5/80 - z**4/32 - z**3/24 + 8*z**2. What is i in m(i) = 0?
-1
Let t(n) = 10*n**2 + 7*n - 1. Let v be t(-8). Let q = v + -6409/11. Factor q*d - 2/11 - 2/11*d**2.
-2*(d - 1)**2/11
Let f(u) = -2*u**2 - 11*u - 9. Let z(k) = 8*k**2 + 13*k + 9 - k - 5*k**2. Let q(a) = 6*f(a) + 5*z(a). Suppose q(w) = 0. What is w?
-1, 3
Let k = 13 - 10. Let l be (2/8)/(2/4). Suppose -l*q**4 - 3/2*q**k + 0 - 3/2*q**2 - 1/2*q = 0. Calculate q.
-1, 0
Let f(q) = -2*q - q**3 - 7 + q + 8 - q**2. Let i(b) = 2*b**4 + 4*b**3 + 6*b**2 + 6*b - 6. Let c(t) = 6*f(t) + i(t). Factor c(w).
2*w**3*(w - 1)
Let c(m) be the first derivative of -m**7/56 - m**6/20 + 3*m**5/80 + m**4/8 - m - 4. Let u(f) be the first derivative of c(f). Let u(q) = 0. Calculate q.
-2, -1, 0, 1
Let p(a) be the third derivative of -a**8/10080 + a**6/360 - a**5/30 + 2*a**2. Let y(c) be the third derivative of p(c). Determine i so that y(i) = 0.
-1, 1
Let a(i) = -3*i - 4. Let u be 5/2*(-8)/10. Let s be a(u). Determine t so that -1/2*t**4 + 1/2*t**s - 1/2*t**3 + 1/2*t + 0 = 0.
-1, 0, 1
Find w such that -1/2 + 1/6*w**2 - 1/3*w = 0.
-1, 3
Let f(g) = g**3 - 4*g**2 - 10*g + 4. Let o be f(6). Let a = o - 16. Factor s**3 + a*s + 0 - 3/4*s**4 - 1/4*s**2.
-s**2*(s - 1)*(3*s - 1)/4
Let r(k) be the first derivative of -2*k**2 - 6 + 0*k + 10/3*k**3. Factor r(i).
2*i*(5*i - 2)
Let z(q) = 5*q**2 + 15*q + 10. Let f(u) = -u**2 - 3*u - 2. Let m(d) = -11*f(d) - 2*z(d). Suppose m(n) = 0. Calculate n.
-2, -1
Let o be ((-16)/(-56))/(9/21). What is p in 8/3*p**2 - o*p**3 + 4/3 - 10/3*p = 0?
1, 2
Let d = -10 + 12. Let b(h) be the third derivative of 0 + 1/24*h**4 + 1/60*h**5 + 0*h**3 - 1/120*h**6 - d*h**2 - 1/210*h**7 + 0*h. Determine y so that b(y) = 0.
-1, 0, 1
Factor 2/3*o**2 + 4*o + 6.
2*(o + 3)**2/3
Suppose 4*j = 10 + 10. Factor i**5 + 2*i**5 - 7*i**j - 2*i**2 - 3*i**3 + 5*i**5.
i**2*(i - 2)*(i + 1)**2
Let d be 9/(-15)*(-5 - 0). Suppose d*l - 2 = 2*l. Factor -28 - l*k**2 + 28 + k + k**3.
k*(k - 1)**2
Let r(m) be the first derivative of 0*m**2 - 6 + 0*m + 2/33*m**3. Factor r(p).
2*p**2/11
Let n = -36/59 + 914/531. Suppose 2/9*s**3 - 8/9*s**2 - 4/9 + n*s = 0. What is s?
1, 2
Let v(o) be the second derivative of -1/18*o**3 - 1/60*o**5 + 0*o**2 + 0 + 1/18*o**4 + 2*o. Factor v(y).
-y*(y - 1)**2/3
Let w = -30 + 32. Suppose 4*d + 3*h = 23, -2*h - 7 = -d - 3*h. Find a such that w - a**d - 3*a**2 + a + 2*a**2 + a**2 = 0.
-1, 2
Let n = 71 - 67. Factor -13/3*b**n + 2/3*b + 1/3*b**2 - 3*b**3 - 5/3*b**5 + 0.
-b*(b + 1)**3*(5*b - 2)/3
What is h in 2/9*h**2 + 4/9 + 2/3*h = 0?
-2, -1
Let n be ((-1468)/10)/(1*-2). Let t = n - 73. Factor 0*a + t*a**5 + 0*a**4 + 0 + 0*a**3 + 0*a**2.
2*a**5/5
Let s(k) be the first derivative of -k**6/60 + k**5/40 + k**4/12 - 3*k - 1. Let d(o) be the first derivative of s(o). What is v in d(v) = 0?
-1, 0, 2
Let i(t) be the first derivative of 4*t**5/25 + 7*t**4/5 + 24*t**3/5 + 8*t**2 + 32*t/5 + 15. Factor i(u).
4*(u + 1)*(u + 2)**3/5
Let u(i) be the third derivative of 0*i + 0*i**3 + 0 - 3*i**2 - 1/90*i**5 + 0*i**4 + 1/180*i**6. Solve u(w) = 0.
0, 1
Let f(i) be the third derivative of -2*i**2 + 1/30*i**5 + 0*i + 2/3*i**3 + 1/4*i**4 + 0. Find v, given that f(v) = 0.
-2, -1
Factor 0 + 2/13*m**2 - 16/13*m.
2*m*(m - 8)/13
Let q(f) be the third derivative of -7*f**5/80 - 3*f**4/16 + f**3/8 - 5*f**2. Let q(w) = 0. What is w?
-1, 1/7
Let t(i) be the third derivative of -i**7/1680 - i**6/180 - i**5/60 + i**4/6 - 2*i**2. Let k(a) be the second derivative of t(a). What is q in k(q) = 0?
-2, -2/3
Let p = 2 - 0. Suppose -w + p*w**3 + 2*w**2 - w - 2 + 0*w = 0. What is w?
-1, 1
Let z = 311/5481 + -4/203. Let d(h) be the third derivative of -z*h**4 + 0 + 2*h**2 + 1/30*h**6 + 4/27*h**3 + 0*h - 1/18*h**5. Factor d(a).
2*(2*a + 1)*(3*a - 2)**2/9
Let n be (0 + 4)/(-2)*-4. Factor -8*s + n*s + 21*s**4 - 15*s**3 - 6*s**2.
3*s**2*(s - 1)*(7*s + 2)
Let h(q) be the first derivative of -1/6*q**3 + 0*q**2 - 1/12*q**6 - 2 + 1/8*q**4 + 0*q + 1/10*q**5. Factor h(j).
-j**2*(j - 1)**2*(j + 1)/2
Let u = 544 + -2718/5. Factor u*q**2 + 0 - 4/5*q.
2*q*(q - 2)/5
Suppose 3*j + j = 16. Solve 4*r - r**4 - 6*r**2 + 0*r**4 - 2 + 1 + j*r**3 = 0 for r.
1
Let k(z) = z**3 + 9*z**2 - 11*z - 8. Let g be k(-10). Let q(y) be the first derivative of -4/3*y**3 - 3*y**g + 2 - 2*y. Factor q(t).
-2*(t + 1)*(2*t + 1)
Let f(y) be the third derivative of -2/15*y**5 + 5/12*y**4 + 1/60*y**6 + y**2 - 2/3*y**3 + 0 + 0*y. Suppose f(a) = 0. Calculate a.
1, 2
Let m(s) be the third derivative of s**10/151200 + s**9/120960 - 7*s**5/60 - 10*s**2. Let w(a) be the third derivative of m(a). Solve w(j) = 0 for j.
-1/2, 0
Solve 0 - 2/5*g**5 - 1/5*g + 3/5*g**3 - 1/5*g**4 + 1/5*g**2 = 0 for g.
-1, 0, 1/2, 1
Let z(v) be the first derivative of -3/4*v**2 + 3/8*v**3 - 1/16*v**4 - 4*v - 1. Let k(g) be the first derivative of z(g). Solve k(u) = 0 for u.
1, 2
Let b = -1 - -1. Solve -4*o**3 + 2*o - 3*o**3 + 5*o**3 + b*o = 0.
-1, 0, 1
Let l be 66/70 + 10/50. Factor l*a + 8/7 - 2/7*a**2 - 2/7*a**3.
-2*(a - 2)*(a + 1)*(a + 2)/7
Let w = 7 + -5. Suppose 4 = w*g - 4. Factor 1/3*c**3 + 1/3*c**g + 0 + 0*c - 1/3*c**2 - 1/3*c**5.
-c**2*(c - 1)**2*(c + 1)/3
Let f(y) be the third derivative of 2*y**7/35 + y**6/15 + 2*y**2. What is p in f(p) = 0?
-2/3, 0
Let b = 185/2 + -903/10. Let x = b + -39/20. Suppose 0*k**3 + x*k**2 + 0*k - 1/4*k**4 + 0 = 0. Calculate k.
-1, 0, 1
Let s(o) be the first derivative of -o**6/10 + 3*o**5/4 - 3*o**4/2 - 2*o**3 + 12*o**2 - 8*o + 9. Let c(k) be the first derivative of s(k). Factor c(r).
-3*(r - 2)**3*(r + 1)
Let 3/8*y**2 + 3/4 + 9/8*y = 0. Calculate y.
-2, -1
Let y = 12 - 8. Factor -2*k**y + 24*k - 24*k + 2*k**2.
-2*k**2*(k - 1)*(k + 1)
Let u(q) be the third derivative of q**6/1980 + q**3/2 - 3*q**2. Let h(x) be the first derivative of u(x). Factor h(p).
2*p**2/11
Suppose 0*r = z + 4*r - 1, 0 = -5*z - 5*r + 20. Let v be (z + 1)/(15/10). Suppose -6*h**3 + 8*h**5 - h**2 + 4*h**5 + 5*h**2 + 3*h**4 - 13*h**v = 0. Calculate h.
-2/3, 0, 1/2, 1
Let k(c) = 10*c**2 + c + 1. Let a be k(-5). Let f = 1726/7 - a. Solve -2/7*i + f*i**2 + 0 - 2/7*i**3 = 0 for i.
0, 1
Factor 0 + 0*c + 1/6*c**3 + 1/3*c**2 - 2/3*c**4 - 1/2*c**5.
-c**2*(c + 1)**2*(3*c - 2)/6
Let x be (-5)/(-1) + (-6 - -3). Determine i so that -2/3*i**x - 4/3*i - 2/3 = 0.
-1
Let z be (1/8)/(2/4). Suppose -2*k + 8 = 4*v - 4*k, 4 = 4*v - k. Factor v + z*p - 1/2*p**2.
-p*(2*p - 1)/4
Let s(z) be the first derivative of -3*z**4/16 + 7*z