given that 0*d**3 - 2*d**3 + t*d**3 = 0.
0
Let c = 5 + -5. Suppose 5*q - 3*q = -4*a + 22, -a - 3*q + 18 = c. Find j, given that 0 + 2/7*j**5 + 4/7*j**4 + 0*j**a - 2/7*j - 4/7*j**2 = 0.
-1, 0, 1
Let x(j) = -j - 15. Let m be x(-15). Let g(s) be the third derivative of -1/30*s**5 + 0 + 1/60*s**6 + 0*s**3 + m*s - s**2 + 0*s**4. Factor g(n).
2*n**2*(n - 1)
Suppose 6*d**3 - 8*d - 2*d**4 + 12*d**3 - 16*d**3 + 4*d**3 = 0. What is d?
-1, 0, 2
Let t(w) be the first derivative of 0*w**3 + 0*w + 0*w**2 - 1/7*w**6 - 8/35*w**5 - 1/14*w**4 + 4. Let t(f) = 0. Calculate f.
-1, -1/3, 0
Let h(b) be the first derivative of 2/5*b - 7/10*b**4 + 2 + 6/25*b**5 - 1/30*b**6 + 16/15*b**3 - 9/10*b**2. Factor h(i).
-(i - 2)*(i - 1)**4/5
Let o(n) be the second derivative of 0 + 0*n**4 + 1/189*n**7 + 0*n**3 - 3*n - 2/135*n**6 + 0*n**2 + 1/90*n**5. Determine v so that o(v) = 0.
0, 1
Let p = -1 - 1. Let d be (6/(-45))/(p/10). What is y in 0*y + 0 + 2/3*y**3 + d*y**5 + 0*y**2 + 4/3*y**4 = 0?
-1, 0
Let r be ((-16)/(-4) - 2) + 1. Determine p, given that -r*p**5 - 4*p**5 + 9*p**5 + 2*p**4 = 0.
-1, 0
Let d be 6/16*4/6. Let t(a) = a**3 - 29*a**2 - 62*a + 2. Let b be t(31). Factor 1/2*u - d*u**b - 1/4.
-(u - 1)**2/4
Let i(s) be the first derivative of -243*s**4/8 - 18*s**3 - 3*s**2 + 11. Suppose i(v) = 0. What is v?
-2/9, 0
Let x be (-1)/(-1) + 1 - (-15)/(-10). Determine n, given that -1/4*n**3 + 1/4*n + 1/2 - x*n**2 = 0.
-2, -1, 1
Let m be 1/(-1) - (11 - -4). Let x be (-1)/3 - m/12. Let 3*v**2 + v**3 - v - 2*v - 2*v**3 + x = 0. Calculate v.
1
Let f = 7 + -8. Let i = f - -4. Factor -7/4*w**5 + 15/2*w**4 - 25/2*w**i + 1/2 + 10*w**2 - 15/4*w.
-(w - 1)**4*(7*w - 2)/4
Let d(o) = o - 1. Let m be (3/(-2))/((-1)/4). Let a(g) = -g**3 + 2*g**2 + 5*g - 6. Let z(x) = m*d(x) - a(x). Let z(n) = 0. Calculate n.
0, 1
Let l(d) = 4*d + 3*d + 3 - 2 - 6*d - d**3. Let q(f) = -2*f**5 + 6*f**4 - 12*f**3 + 2*f**2 + 6*f + 6. Let u(n) = 6*l(n) - q(n). Factor u(h).
2*h**2*(h - 1)**3
Suppose 0 = -4*k - k + 20. Factor 0*y**2 + 0 - 4/3*y**3 + 2/3*y**5 + 2/3*y + 0*y**k.
2*y*(y - 1)**2*(y + 1)**2/3
Let a(d) = -2*d**2 + 2*d - 2. Let m(q) = 2. Let c(f) = -1. Let h(g) = 3*c(g) + 2*m(g). Let t(z) = -a(z) - 6*h(z). Find w, given that t(w) = 0.
-1, 2
Let r = -164 - -164. Solve 1/3*q**2 + 0*q + r = 0 for q.
0
Let r(b) = -3*b**3 + 3*b**2 + 9*b + 6. Let p(h) = 9*h**3 - 8*h**2 - 27*h - 18. Let m(a) = 3*p(a) + 8*r(a). Determine i so that m(i) = 0.
-1, 2
Let o(k) = k + 4. Let s be o(0). Factor -4 + d**3 + 3*d + s - 4*d.
d*(d - 1)*(d + 1)
Let o(n) be the first derivative of 3*n**5/50 + n**4/6 - 4*n**3/15 - 4*n**2/5 + 2*n + 2. Let h(s) be the first derivative of o(s). Factor h(r).
2*(r - 1)*(r + 2)*(3*r + 2)/5
Suppose 2/9*g**4 + 10/9*g - 2/9*g**3 - 4/9 - 2/3*g**2 = 0. What is g?
-2, 1
Let z be 1 - (6 + -3 + -2). Suppose -4*v = -2*i - 12, -v = -0*i - 4*i - 3. Let 6/5*k - 3/5*k**4 + 0 + 9/5*k**2 + z*k**v = 0. What is k?
-1, 0, 2
Let d(y) be the first derivative of -8 + 2*y - 1/2*y**2 - 1/3*y**3. Suppose d(z) = 0. Calculate z.
-2, 1
Let h = -2 + 2. Let j(s) be the third derivative of -s**2 + 0 + 0*s**4 + 0*s**3 + h*s**5 - 1/120*s**6 + 0*s. Factor j(k).
-k**3
Suppose 0 = 5*i - 6*i - 28. Let c = i + 30. Suppose 0 + 0*r**c + 0*r**3 + 3/4*r**4 + 0*r = 0. What is r?
0
Let v(b) be the third derivative of -b**9/241920 + b**8/40320 - b**7/20160 - b**5/20 - 3*b**2. Let k(x) be the third derivative of v(x). Factor k(d).
-d*(d - 1)**2/4
Let s(m) be the first derivative of m**5 + 11*m**4/4 - 3*m**3 - 1. Let p(j) = -2*j**4 - 5*j**3 + 4*j**2. Let h(c) = 14*p(c) + 6*s(c). Let h(a) = 0. Calculate a.
0, 1
Factor -1/4*i**2 + 1/4 - 1/4*i + 1/4*i**3.
(i - 1)**2*(i + 1)/4
Let a be (12/(-9))/((-2)/6). Let r(n) be the second derivative of -n + 0 + 3/4*n**2 + 1/2*n**3 + 1/8*n**a. Solve r(x) = 0.
-1
Let v(s) be the third derivative of s**8/2352 + 2*s**7/735 + s**6/280 + 9*s**2. Factor v(c).
c**3*(c + 1)*(c + 3)/7
Let j(z) be the first derivative of 1/20*z**4 + 0*z + 4/25*z**5 - 3 - 4/15*z**3 - 1/10*z**2. Let j(q) = 0. Calculate q.
-1, -1/4, 0, 1
Let z be (-2)/(-12) - 10/108. Let c(p) be the second derivative of z*p**3 + 0 + 1/6*p**4 + 0*p**2 + 3*p. Factor c(y).
2*y*(9*y + 2)/9
Suppose -4*x + 4*b - 12 = 9*b, 4*b + 26 = 5*x. Let n(c) be the first derivative of 1 + 0*c**x + 0*c - 1/6*c**3 + 1/16*c**4. Factor n(l).
l**2*(l - 2)/4
Solve 44/7*j + 2/7*j**2 + 242/7 = 0 for j.
-11
Let y = 7 + -11. Let p(q) = q**5 - q**4 - q**3 - q**2. Let d(l) = 13*l**5 - 19*l**4 - l**3 - l**2. Let x(g) = y*p(g) + d(g). Factor x(o).
3*o**2*(o - 1)**2*(3*o + 1)
Suppose -10 = -3*o + 2. Let s = 6 - o. Find t, given that -t**3 + 2*t**2 + 2*t**s - 2*t - t**3 = 0.
0, 1
Let p(y) be the second derivative of -y**4/42 + y**3/21 + 2*y**2/7 + 8*y. Factor p(s).
-2*(s - 2)*(s + 1)/7
Let g(j) = j + 12. Let f be g(-12). Let l(n) be the second derivative of -1/60*n**5 + 0 + 0*n**2 + f*n**4 + n + 0*n**3. Factor l(s).
-s**3/3
Let y = -4/35 - -47/105. Let w(u) be the first derivative of 1 + 4*u + y*u**3 - 2*u**2. Suppose w(i) = 0. Calculate i.
2
Suppose 2*l - l = a - 4, 3*l = 4*a - 14. Factor 3*z**3 - 4*z + 5*z + z**a - z**3 - 3*z**3 - z**4.
-z*(z - 1)*(z + 1)**2
Let m(s) be the third derivative of -s**7/420 + s**6/80 - s**5/40 + s**4/48 + 17*s**2. Factor m(l).
-l*(l - 1)**3/2
Let d = -1 - 0. Let z be -6*((-2)/(-4) + d). Factor -2*m**2 - m**z - 2*m**3 - m**3.
-2*m**2*(2*m + 1)
Let v be 1/(-2) - 15/(-6). Solve 1/4*t**v - 1/4*t**4 + 0 + 0*t + 0*t**3 = 0.
-1, 0, 1
Let u(p) = p**3 - p - 1. Let r(f) = 5*f**3 + f**2 - 5*f - 5. Let a(x) = r(x) - 4*u(x). Let a(y) = 0. Calculate y.
-1, 1
Find k, given that 0 - k**3 + 0*k - 4/5*k**4 - 1/5*k**2 = 0.
-1, -1/4, 0
Let t = -58953/524 + 230/131. Let d = -107 - t. Find j, given that 9/4*j**2 + d*j**3 + 0 + 3/4*j**5 + 1/2*j + 11/4*j**4 = 0.
-1, -2/3, 0
Let -4*o + 19*o**2 - 4 - 5*o**2 - 4*o**2 - 2*o = 0. Calculate o.
-2/5, 1
Let g(a) be the first derivative of a**8/1344 - a**7/280 + a**6/160 - a**5/240 + a**3 - 3. Let b(p) be the third derivative of g(p). Let b(k) = 0. What is k?
0, 2/5, 1
Let n(k) be the third derivative of 2*k**2 + 0 + 4/3*k**3 + 1/3*k**4 + 0*k + 1/30*k**5. Find r such that n(r) = 0.
-2
Let b(v) = 13*v**2 - 11*v - 2. Let i(l) = -12*l**2 + 12*l + 3. Let u(s) = 4*b(s) + 3*i(s). Suppose u(a) = 0. What is a?
1/4
Factor 9/2*s**3 + 0*s + 0 - 3/2*s**4 + 0*s**2.
-3*s**3*(s - 3)/2
Let j be (12/378)/(40/6). Let c(x) be the third derivative of -x**2 + j*x**5 + 0*x - 1/84*x**4 + 0*x**3 + 0. Determine b so that c(b) = 0.
0, 1
Let y be (2 + 2)/(8/20). Let o = y - 6. Factor 0*f**5 + o*f**3 - 5*f**3 + f**5.
f**3*(f - 1)*(f + 1)
Let a(h) = -h**2 + h + 1. Let c(z) = -100*z**4 - 180*z**3 - 102*z**2 - 10*z + 6. Let s(x) = 6*a(x) - c(x). Let s(b) = 0. Calculate b.
-1, -2/5, 0
Suppose 3*d - 25 = -19. Factor 3/2 + 1/2*j**2 - d*j.
(j - 3)*(j - 1)/2
Factor -1/6*q - 1/6*q**2 + 1/6*q**4 + 0 + 1/6*q**3.
q*(q - 1)*(q + 1)**2/6
Let c = -63 + 66. Let d(g) be the second derivative of -1/3*g**c - 2*g - 1/15*g**6 + 1/10*g**5 + 1/6*g**4 + 0*g**2 + 0. Suppose d(h) = 0. Calculate h.
-1, 0, 1
Let i be (-4)/14 + (-27)/(-21). Let z(a) = -1. Let g(f) = f**3 + f**2 - 2*f - 1. Let q(l) = i*z(l) - g(l). Let q(w) = 0. Calculate w.
-2, 0, 1
Suppose -5*r - 20 + 30 = 0. Let 0*c + 1/5*c**r + 0 + 1/5*c**3 = 0. What is c?
-1, 0
Let a(c) be the second derivative of 0*c**3 - 6*c + 1/4*c**4 + 0*c**2 + 0. Factor a(x).
3*x**2
Let w(d) = -16*d**3 - 49*d**2 - 251*d - 309. Let r(f) = 50*f + 10*f**2 - 9*f**2 + 62 + 9*f**2 + 3*f**3. Let q(m) = 33*r(m) + 6*w(m). Factor q(z).
3*(z + 4)**3
Let u(f) = -f**2 - 6*f + 2. Let k be u(-6). Let t(p) be the third derivative of 0 + 3/80*p**6 + 2*p**k + 7/48*p**4 + 1/12*p**3 + 0*p + 1/8*p**5. Factor t(s).
(s + 1)*(3*s + 1)**2/2
Factor a**4 - 5*a**2 - 2*a**4 + 5*a**4 + a**2.
4*a**2*(a - 1)*(a + 1)
Let k(b) be the first derivative of b**5/120 + b**4/24 + b**3/12 - b**2/2 + 3. Let h(n) be the second derivative of k(n). Factor h(c).
(c + 1)**2/2
Let h = 0 - -4. Suppose -3*m - 11 = -4*u - h, -4*m = 4*u - 28. Factor b**3 + 1/2*b**u + 0*b**2 + 0*b + 0.
b**3*(b + 2)/2
Let k(i) be the second derivative of i**5/20 + i**4/4 + i**3/2 + i**2/2 + 14*i. Find w such that k(w) = 0.
-1
Let v(m) be the third derivative of -5*m**8/84 + m**7/42 + m**6 - 19*m**5/6 + 25*m**4/6 - 5*m**3/2 - 