et x(a) be the first derivative of -2*a**5/45 + 2*a**3/9 + 2*a**2/9 + 809. Suppose x(c) = 0. What is c?
-1, 0, 2
Suppose 6*g + 4 = 70. Suppose -26*u**4 + 15*u**4 - 5*u - 5*u**5 + 10*u**3 + g*u**4 = 0. What is u?
-1, 0, 1
Let s(o) be the first derivative of 3 + 0*o**3 + 0*o**2 - 1/4*o**4 + 2*o. Let t(g) be the first derivative of s(g). Factor t(h).
-3*h**2
Let q(y) be the third derivative of -y**7/560 + 13*y**6/960 - y**5/30 + y**4/48 - 51*y**2. Factor q(a).
-a*(a - 2)**2*(3*a - 1)/8
Determine t, given that -2/3*t**3 + 2/3*t**2 - 4/3 + 14/9*t - 2/9*t**4 = 0.
-3, -2, 1
Let r(p) = -124*p - p**3 + 6*p**2 + 126*p - p**3 - 5*p**3 - 1. Let w(j) = 8*j**3 - 6*j**2 - 2*j. Let h(v) = -6*r(v) - 5*w(v). Factor h(f).
2*(f - 3)*(f - 1)*(f + 1)
Determine q, given that 85*q**2 - 70*q**2 + 5*q**4 + 28*q**3 - 8*q**3 = 0.
-3, -1, 0
Let c(u) = u**2 + 159*u + 920. Let t be c(-6). Solve 1/10*g + 7/10*g**t - 3/5 = 0.
-1, 6/7
Let q(a) be the first derivative of 0*a**3 - 1/6*a**4 + 4/3*a + 14 + a**2. Factor q(z).
-2*(z - 2)*(z + 1)**2/3
Let u(p) be the second derivative of -1/18*p**4 + 0*p**2 - 1/60*p**5 + 0 + 0*p**3 + 8*p. Factor u(y).
-y**2*(y + 2)/3
Suppose f + 2*l = 3*f - 2, -5*f + 8 = -2*l. Find g such that 0*g + f*g**3 - g - 3*g - 6*g**4 - 12*g**2 - g**5 - 15*g**3 = 0.
-2, -1, 0
Let f = 3/6695 + 11959/3193515. Let v = f + 8560/6201. Factor -40/13*u**2 + 2*u + v*u**3 - 4/13.
2*(u - 1)**2*(9*u - 2)/13
Let w(o) be the second derivative of 2*o**6/3 - 2*o**5/5 - o**4 - 129*o. Factor w(g).
4*g**2*(g - 1)*(5*g + 3)
Let a(w) be the second derivative of 3*w**5/10 + 11*w**4/3 + 32*w**3/3 - 32*w**2 + 110*w - 1. Let a(d) = 0. Calculate d.
-4, 2/3
Factor -50 - 5/3*o**2 - 65/3*o.
-5*(o + 3)*(o + 10)/3
Suppose x + 5*a - 7 = 0, x - 7*a + 3*a - 16 = 0. Suppose -3*f - 22 = -5*h, 2*h - 4*h - 2*f = -x. Factor -4*t**2 + 2*t**2 - t + t**5 + 0*t**h + 2*t**4.
t*(t - 1)*(t + 1)**3
Let x(j) be the first derivative of -j**6/6 + 5*j**5/4 - 15*j**4/4 + 35*j**3/6 - 5*j**2 + 5*j - 4. Let t(l) be the first derivative of x(l). Solve t(u) = 0.
1, 2
Let p be (-10)/(-65) + 72/39. What is d in 3*d**5 + 6*d**2 - 9*d**4 - 2*d**p - 6*d**5 + 5*d**2 + 3*d**3 = 0?
-3, -1, 0, 1
Let s(p) = 7*p + 32. Let v be s(-4). Let x(z) be the third derivative of 0*z - 1/3*z**3 + 0 - 1/120*z**5 - 1/12*z**v - z**2. Let x(k) = 0. Calculate k.
-2
Let o be (-6)/2 + 4 + 3. Let s(r) be the first derivative of 0*r + 2/13*r**2 + 3/26*r**o + 10/39*r**3 - 1. Solve s(d) = 0 for d.
-1, -2/3, 0
Factor 14/13*j**2 - 2/13*j**3 + 0*j + 0.
-2*j**2*(j - 7)/13
Let c be ((-4)/(-6))/(6/(-126)). Let j be (-7)/21 - c/6. Factor -6 + 8 + 3*o**j - 3*o - 2.
3*o*(o - 1)
Let k(g) = -11*g - 138. Let o be k(-13). Let s(f) be the first derivative of -4*f - 1/8*f**4 + f**2 - o + 1/3*f**3. Let s(z) = 0. Calculate z.
-2, 2
Let b(a) be the third derivative of 0*a**4 + 0*a - 1/600*a**6 + 0 - 1/1680*a**8 + 26*a**2 + 0*a**3 - 1/525*a**7 + 0*a**5. Factor b(q).
-q**3*(q + 1)**2/5
Let -3/5*d**4 + 21/5*d**2 - 6/5*d**5 + 6/5*d + 18/5*d**3 + 0 = 0. Calculate d.
-1, -1/2, 0, 2
Let p(c) be the third derivative of 2*c**7/525 - 4*c**6/75 + 2*c**5/25 + 4*c**4/3 + 10*c**3/3 + 47*c**2. Factor p(h).
4*(h - 5)**2*(h + 1)**2/5
Let x be (-1048)/(-48) - (1 - 7/6). Let d = -22 + x. Factor 4/9*v**2 + d + 0*v - 2/9*v**3.
-2*v**2*(v - 2)/9
Let x = 75 - 75. Determine i, given that -18*i + 0 + 841*i**2 - 838*i**2 + x = 0.
0, 6
Let b(v) = 5*v**2 - 2*v**2 + 2*v**2 - 4*v**2 + 3 - 7*v. Let k be b(7). Solve -t**4 + 0*t**2 + t**2 - 3*t**5 + t**3 + t**k + t**3 = 0 for t.
-1, -1/3, 0, 1
Let z(i) be the second derivative of 0 - 1/9*i**3 + 1/108*i**4 + 1/180*i**5 - 17*i + 0*i**2. What is m in z(m) = 0?
-3, 0, 2
Let i(r) = -2*r**2 - 8*r + 9. Let y be i(-7). Let d = -30 - y. Find o, given that -1 - 6*o**d + 7/2*o + 7/2*o**2 = 0.
-2/3, 1/4, 1
Let h = -964 - -243890/253. Let i = 1018/759 + h. Factor 2*v**3 + i*v**5 + 0*v + 0 + 1/3*v**2 + 3*v**4.
v**2*(v + 1)**2*(4*v + 1)/3
Let 0*r + 35/2*r**2 + 45/2*r**4 - 75/2*r**3 + 0 - 5/2*r**5 = 0. What is r?
0, 1, 7
Let l = 138324/17 - 8136. Determine p, given that -l*p**2 - 40/17*p - 16/17 + 18/17*p**3 = 0.
-2/3, 2
Let r(n) = n**2 - 1. Let g(y) = -9*y**4 + 60*y**3 + 28*y**2 - 36*y + 5. Let k(q) = g(q) - 2*r(q). Determine m, given that k(m) = 0.
-1, 1/3, 7
Let h = -248378/9 - -27608. Suppose -64/3*p - h*p**3 - 8 - 2/9*p**5 - 194/9*p**2 - 22/9*p**4 = 0. Calculate p.
-3, -2, -1
Let p(b) be the second derivative of -1/30*b**4 + 0 + 0*b**2 - 3*b + 1/50*b**5 + 0*b**3. Solve p(r) = 0 for r.
0, 1
Factor 2/9*z**5 - 40/9*z**2 - 14/9*z**4 + 4*z**3 + 16/9*z + 0.
2*z*(z - 2)**3*(z - 1)/9
Factor -285/11*i - 1/11*i**3 - 32/11*i**2 - 450/11.
-(i + 2)*(i + 15)**2/11
Let c(h) = 7*h**3 - 512*h**2 + 9439*h + 2734. Let k(p) = p**2 + p - 1. Let u(t) = c(t) - 4*k(t). Factor u(s).
(s - 37)**2*(7*s + 2)
Let z(k) = 70*k - 140. Let r be z(2). Factor -26/9*w**2 - 2/9*w**3 + r - 8/3*w.
-2*w*(w + 1)*(w + 12)/9
Let z(l) be the first derivative of 25*l**3/3 - 25*l**2/2 + 10. Let p(t) = -t + 1. Let y(i) = -2*p(i) - z(i). Factor y(m).
-(m - 1)*(25*m - 2)
Suppose 19 - 103*c**2 - 1824 + 190*c + 98*c**2 = 0. What is c?
19
Let h(p) be the first derivative of 29 + 4/3*p - 1/3*p**2 + 1/6*p**4 - 4/9*p**3. Factor h(j).
2*(j - 2)*(j - 1)*(j + 1)/3
Let p(a) = a**2 - 3*a - 1. Let h(s) = -6*s**2 + 1723*s - 147919. Let y(d) = -h(d) - p(d). Factor y(t).
5*(t - 172)**2
Let g(z) = z**3 + 74*z**2 + 210*z - 9. Let y be g(-3). Factor y + 12*o**3 - 6/5*o + 21/5*o**2 + 33/5*o**4.
3*o*(o + 1)**2*(11*o - 2)/5
Let m be (-1 - -1)*(-130)/520. Determine x so that 5/6*x**3 + 0*x**2 + m + 0*x**4 + 0*x - 5/6*x**5 = 0.
-1, 0, 1
Let y be ((-42)/6 + 7)*7/(-21). Let g(w) be the third derivative of 0 - 6*w**2 + 0*w**4 - 2*w**3 - 1/40*w**6 + 3/20*w**5 + y*w. Suppose g(a) = 0. What is a?
-1, 2
Factor -9*y**4 - 108*y**3 + 22*y**4 + 108*y - 6*y**4 + 4*y**2 - 11*y**4.
-4*y*(y - 1)*(y + 1)*(y + 27)
Let y be (0*4/32)/1. Let w = 123/20 - 23/4. Determine q, given that 2/5*q**4 - w*q**2 + 0*q**3 - 1/5*q**5 + y + 1/5*q = 0.
-1, 0, 1
Suppose 7*i - 13*i = -18. Factor -52*n**2 + 52*n**2 - i*n**3 + 9*n + 6.
-3*(n - 2)*(n + 1)**2
Let k(n) = -2*n**4 - 5*n**3 - 2*n**2 + 5*n + 3. Let o(l) = -l**3 + l + 1. Let d = -5 + -6. Let g = d - -10. Let j(u) = g*k(u) - o(u). Factor j(w).
2*(w - 1)*(w + 1)**2*(w + 2)
Let r(s) = -16*s + 130. Let g be r(8). Let h(x) be the first derivative of -2/3*x**3 - 3*x**g + 0*x + 5. Suppose h(l) = 0. What is l?
-3, 0
Let r(v) be the second derivative of -v**4/3 + 76*v**3/3 - 74*v**2 + 162*v. Find m, given that r(m) = 0.
1, 37
Let t(r) be the first derivative of 0*r - 7 - 1/3*r**3 + r**2 + 1/5*r**5 - 1/2*r**4. Determine m so that t(m) = 0.
-1, 0, 1, 2
Let a(g) be the second derivative of g**6/1080 + g**5/45 + 2*g**4/9 + 2*g**3 + 6*g. Let b(y) be the second derivative of a(y). Suppose b(x) = 0. Calculate x.
-4
Let o be (45/10)/((-6)/(-4)). Factor 16*s + 2*s**3 + 2*s**4 - 1 - 26*s - 6*s**2 - o.
2*(s - 2)*(s + 1)**3
Factor 2 + 2/3*q**2 - 2/3*q**3 + 10/3*q.
-2*(q - 3)*(q + 1)**2/3
Let t(j) be the second derivative of j**7/1260 - j**6/180 + j**5/60 - 11*j**4/3 - 30*j. Let k(w) be the third derivative of t(w). Factor k(q).
2*(q - 1)**2
Let b(f) be the first derivative of -f**5/180 + f**4/24 - f**3/9 - 7*f**2/2 + 5. Let y(x) be the second derivative of b(x). Factor y(l).
-(l - 2)*(l - 1)/3
Let x(g) be the second derivative of g**2 + g**3 - 19/40*g**5 - 13/24*g**4 + 0 + 3/20*g**6 + 1/12*g**7 + 4*g. Suppose x(l) = 0. What is l?
-2, -1, -2/7, 1
Let l(d) be the first derivative of d**4/10 - 6*d**3/5 + 14*d**2/5 + 49. Factor l(v).
2*v*(v - 7)*(v - 2)/5
Let s(x) be the third derivative of x**7/2415 + 7*x**6/1380 - 3*x**5/115 + 36*x**2 - 5*x. Factor s(z).
2*z**2*(z - 2)*(z + 9)/23
Let f(d) be the second derivative of 3*d**5/10 + 3*d**4/4 - 3*d - 5. Factor f(o).
3*o**2*(2*o + 3)
Let q(b) be the first derivative of -b - 23/8*b**2 - 5/2*b**3 - 29 + 9/16*b**4. Let q(k) = 0. What is k?
-1/3, 4
Suppose k - 20 + 15 = 0. Let l(s) be the second derivative of 0 + 4*s + 0*s**2 + 9/100*s**k - 11/60*s**4 + 1/15*s**3. Find o, given that l(o) = 0.
0, 2/9, 1
Let y be (80/168)/(110/154). Suppose -14/3 + y*p**2 - 4*p = 0. Calculate p.
-1, 7
Let b(h) be the first derivative of h**6/120 - h**5/80 - h**4/16 + h**3/24 + h**2/4 - 15*h - 9. Let z(j) b