 - -51). Let l(m) be the third derivative of 0*m - 1/10*m**6 + 0 + g*m**3 + 0*m**4 + 1/20*m**5 + 9*m**2. Suppose l(v) = 0. What is v?
0, 1/4
Let j(u) be the second derivative of u**6/600 + u**5/200 + 2*u**3 - 14*u. Let i(m) be the second derivative of j(m). Suppose i(f) = 0. What is f?
-1, 0
Let u(g) be the first derivative of -g**6/6 + g**5/4 + 5*g**4/4 - 25*g**3/6 + 5*g**2 - 8*g - 10. Let h(r) be the first derivative of u(r). Solve h(i) = 0.
-2, 1
Let a = -1 + 4. Let d be ((-84)/(-24))/(12/36 - -2). Factor 0 + 0*i + 3/2*i**a + d*i**2.
3*i**2*(i + 1)/2
Suppose 0 = 2*f - 6. Suppose -8*c - 9 = -f*c + 3*i, 6 = -3*c - 2*i. Factor -2*z**2 + c*z**2 + 2*z - z + z**3.
z*(z - 1)**2
Let k = 14 - 10. Suppose -k*w + 72 = -8. Factor 8*j**4 + 80*j**2 - 6*j**4 + 4*j**3 + 32*j - 38*j**4 + w*j**3.
-4*j*(j - 2)*(3*j + 2)**2
Factor 998*y - 974*y + 2 - 2*y**2 - 42 + 0*y**2.
-2*(y - 10)*(y - 2)
Let u(a) be the first derivative of 25*a**2 - 7/2*a**4 - 19 + 12*a + 8*a**3. Factor u(r).
-2*(r - 3)*(r + 1)*(7*r + 2)
Let t = 1875 - 5624/3. Factor t*w**2 + 1/3*w + 0.
w*(w + 1)/3
Let g(t) = 9*t**2 + 22*t + 29. Let d(n) = 8*n**2 + 12*n + 28. Let q(x) = 5*d(x) - 4*g(x). Solve q(r) = 0.
1, 6
Let f = 22 + -15. Suppose -f = -2*o + 9. Find b such that -2 + 6 - 8*b - o*b + 17*b**2 - 5*b**3 = 0.
2/5, 1, 2
Let p(b) = -b + 14. Let w be p(9). Let 0*f**5 + 21*f + 50*f**2 - 40 - 5*f**w - 5*f**3 - 20*f**4 - f = 0. Calculate f.
-2, 1
Suppose o - 46 + 35 = 0. Let i be 8/o + (-52)/286. Factor i*r**5 + 14/11*r**3 + 0*r + 0 + 16/11*r**4 + 4/11*r**2.
2*r**2*(r + 1)**2*(3*r + 2)/11
Let a(c) = -c**2 - 13*c + 33. Let u be a(-15). Factor 4*i**4 + 2*i**5 - 3*i**5 - 14*i - 4*i**3 + u*i**5 - 16*i**2 - 4.
2*(i - 2)*(i + 1)**4
Let p(r) be the second derivative of r**6/120 + r**5/20 - 3*r**4/8 - r**3/3 + 9*r. Let f(v) be the second derivative of p(v). Suppose f(w) = 0. Calculate w.
-3, 1
Let r be 1 + 2 + 4 + -1 - 4. Let n(m) be the second derivative of 0*m**r + 1/66*m**4 + 0 + 4*m + 1/33*m**3. Suppose n(f) = 0. Calculate f.
-1, 0
Let t(n) be the second derivative of 0 + 0*n**4 - 9*n - 1/20*n**5 + 0*n**2 + 1/60*n**6 + 0*n**3. Factor t(h).
h**3*(h - 2)/2
Let -8/11*k - 12/11 - 1/11*k**2 = 0. What is k?
-6, -2
Let z(h) = -h**4 + h**3 + h**2 - 2*h - 1. Let f(b) = 6*b**4 - 16*b**3 - 25*b**2 + 18*b + 31. Let c(r) = 2*f(r) + 14*z(r). Factor c(m).
-2*(m - 1)*(m + 2)**2*(m + 6)
Let w(a) be the third derivative of -3*a**5/20 - 25*a**4/8 - 4*a**3 - 6*a**2 - 32. Factor w(m).
-3*(m + 8)*(3*m + 1)
Suppose 5*s - 4*t = -4, 0*s + 1 = 5*s + t. Let w be 15/(-5) - (-5 - 0). Factor -3/5*m**w + 3/5*m**5 + 0*m + 9/5*m**3 - 9/5*m**4 + s.
3*m**2*(m - 1)**3/5
Let d = 8 - 2. Factor 2*k**4 + d*k**3 - 2*k**5 - k**3 - k**3.
-2*k**3*(k - 2)*(k + 1)
Let v(a) be the second derivative of -a**6/120 + 3*a**5/40 - a**4/12 - a**3/4 + 5*a**2/8 + 258*a. Factor v(n).
-(n - 5)*(n - 1)**2*(n + 1)/4
Let a(p) be the second derivative of p**6/1440 - p**5/480 - 13*p**3/6 + 13*p. Let u(q) be the second derivative of a(q). Suppose u(d) = 0. What is d?
0, 1
Let n be ((-2304)/40320)/(1/10*-1). Factor 2/7*v**2 - 6/7 + n*v.
2*(v - 1)*(v + 3)/7
Suppose -4*y = -u - 43, -5*u - 1 = -2*y - 2. Find j such that -8*j + y + 4/3*j**2 = 0.
3
Let n = -2/13157 - -39479/52628. Factor 1/2*p + 1/4*p**2 - n.
(p - 1)*(p + 3)/4
Determine d so that -64/13 + 18/13*d**3 - 64/13*d + 12/13*d**2 = 0.
-4/3, 2
Let a be 0/(2*2/4). Suppose a = -3*n - 2*h + 4, -6 = -2*h - 2. Factor 3*q**3 + 2 - 4 + n*q - q + 4*q**2.
(q + 1)**2*(3*q - 2)
Let f(y) be the first derivative of 0*y**4 + 0*y**2 + 2/105*y**5 + 0*y - 22 - 2/63*y**3. Solve f(v) = 0 for v.
-1, 0, 1
Let t(j) be the second derivative of j**6/1800 + j**5/300 - j**4/40 - j**3/6 + 3*j. Let p(q) be the second derivative of t(q). Factor p(m).
(m - 1)*(m + 3)/5
Suppose 0 = 22*y - 5*y - 34. Let g(p) be the second derivative of -1/36*p**4 + 0*p**y + 7*p + 0 - 1/18*p**3. Determine c, given that g(c) = 0.
-1, 0
Let z(r) be the second derivative of -r**6/225 + 119*r**5/150 - 116*r**4/3 - 80*r**3 + 11*r - 4. Factor z(s).
-2*s*(s - 60)**2*(s + 1)/15
Let y = -437 - -440. Let p(z) be the second derivative of 0 + 1/10*z**y + 9/100*z**5 + 0*z**2 - 3/20*z**4 - 1/50*z**6 + 2*z. Factor p(w).
-3*w*(w - 1)**3/5
Let q(k) = k**3 - k**2 - 4*k + 4. Let y(z) = -z**2 + z - 1. Suppose -4*v = -2*v - 5*f + 35, 5*v + f = -101. Let n(i) = v*y(i) - 5*q(i). Factor n(u).
-5*u**2*(u - 5)
Let h(w) be the third derivative of -w**6/360 + w**5/10 - 17*w**4/72 - w**2 - 159. Determine t, given that h(t) = 0.
0, 1, 17
Let o = 92 + -87. Suppose o*a = -3 + 13. Solve -4/3*g**a + 0 + 8/3*g = 0.
0, 2
Let w be (-38)/57*6/(-25)*15/6. Suppose 2/5*g**3 - 8/5*g - w*g**2 + 8/5 = 0. What is g?
-2, 1, 2
Let l(u) be the first derivative of -u**3 + 3/2*u**2 + 0*u + 6 - 3/4*u**4 + 3/5*u**5. Factor l(m).
3*m*(m - 1)**2*(m + 1)
Let x(r) be the third derivative of 0*r**3 - 7/80*r**6 + 1/14*r**8 + 1/40*r**5 + 27*r**2 + 2/35*r**7 + 0 + 0*r + 0*r**4. Find m, given that x(m) = 0.
-1, 0, 1/4
Let q(o) be the third derivative of o**6/780 - o**5/390 + 7*o**3 + 15*o**2. Let n(u) be the first derivative of q(u). Find k, given that n(k) = 0.
0, 2/3
Let f = 9751/9 + -1083. Determine w so that 16/9*w**2 + 0 + 1/3*w + 17/9*w**3 + f*w**4 = 0.
-3, -1, -1/4, 0
Let q(i) = -i**5 - 20*i**4 + 43*i**3 - 24*i**2 + 2. Let a(l) = -8*l**5 - 138*l**4 + 300*l**3 - 169*l**2 + 15. Let o(j) = -2*a(j) + 15*q(j). Factor o(y).
y**2*(y - 22)*(y - 1)**2
Let q(p) be the first derivative of p**6/18 - 4*p**5/15 - p**4/6 + 4*p**3/3 + 3*p**2/2 + 122. Factor q(m).
m*(m - 3)**2*(m + 1)**2/3
Let m be (4800/1440)/((-5)/(-6)). Find b such that -2/3*b**2 - 16/3 - m*b = 0.
-4, -2
Let v = 474 + -474. Let h(s) be the third derivative of v*s**3 + 1/100*s**5 - 1/20*s**4 + 0 + 6*s**2 + 0*s. Let h(k) = 0. What is k?
0, 2
Let f(i) = i**2 - 22*i + 49. Let r be f(20). Suppose 5*v - r = 6. Find m, given that -5/3*m - 1/3*m**v - 2/3 - 4/3*m**2 = 0.
-2, -1
Let z(y) be the second derivative of y**7/14 - 9*y**6/10 - 68*y. Suppose z(k) = 0. What is k?
0, 9
Let z(y) be the second derivative of -y**4/21 - 4*y**3/21 + 30*y**2/7 - 28*y. Factor z(t).
-4*(t - 3)*(t + 5)/7
Let z(f) = 76*f**3 - f**2 - 3*f - 1. Let c be z(-1). Let n be c/30*(-2)/20. Determine b, given that 1/4 + n*b**2 - 1/2*b = 0.
1
Determine k so that -9*k**3 + 7/2*k**4 - 1/4*k**5 + 17/2*k**2 - 11/4*k + 0 = 0.
0, 1, 11
Let s(p) be the first derivative of 4*p - 1/9*p**4 + 0*p**2 - 4/9*p**3 + 8. Let h(y) be the first derivative of s(y). Factor h(q).
-4*q*(q + 2)/3
Let r(t) be the first derivative of -15 + 9*t**4 - 8*t**2 + 0*t + 64/3*t**3. Suppose r(p) = 0. Calculate p.
-2, 0, 2/9
Let d(r) = -r**2 - 10*r. Let u = 8 + -10. Let x(a) = a**2 + a. Let i(z) = u*x(z) + d(z). Factor i(s).
-3*s*(s + 4)
Let u be 30/(-40) - 55/(-60). Let q(v) be the second derivative of -1/2*v**2 - u*v**4 - v + 5/12*v**3 + 1/40*v**5 + 0. Factor q(s).
(s - 2)*(s - 1)**2/2
Let j(b) be the second derivative of -1/2*b**2 + 1/36*b**4 + 0 - 1/9*b**3 - 5*b. Factor j(f).
(f - 3)*(f + 1)/3
Let b be ((-1)/(-2))/(3/(-36)). Let j(c) = -c**2 - 6*c + 4. Let d be j(b). Factor 4*n**4 - 3*n**4 + n**d.
2*n**4
Let t(x) = x**2 + 2*x - 3. Let h be t(-3). Suppose -4*i + 9 + 27 = h. Factor -i*w**2 + 0*w**2 - 5*w + 21*w**4 + 9*w**3 - w + 6*w**5 + 3*w**5.
3*w*(w + 1)**3*(3*w - 2)
Let l be 2*10/8*2. Let r = l + -3. Factor -3 - 2 - 3 - r*f**2 - 8*f.
-2*(f + 2)**2
Suppose 8*c - 7 - 33 = 0. Let w = 7 - c. Determine h so that 0*h + 0 - 2/9*h**w = 0.
0
Let i(v) be the third derivative of v**9/7560 + v**8/3360 - v**7/1260 - v**6/360 + 7*v**4/24 + 12*v**2. Let d(g) be the second derivative of i(g). Factor d(q).
2*q*(q - 1)*(q + 1)**2
Let v be ((-8)/(-9))/(16/12). Let f = -11/4 + 37/12. Factor -1/3*m**2 + v - f*m.
-(m - 1)*(m + 2)/3
Suppose z = -u + 1, -5*z + 4*u = 50 - 10. Let t be (5/(550/z))/((-1)/5). Solve t*v**2 + 0 - 2/11*v = 0.
0, 1
Let b(g) be the third derivative of -g**10/75600 - g**9/18900 + g**8/2100 + 5*g**4/6 + 21*g**2. Let c(u) be the second derivative of b(u). Factor c(h).
-2*h**3*(h - 2)*(h + 4)/5
Let x(g) be the first derivative of -18*g**5/35 - 17*g**4/7 + 106*g**3/21 - 10*g**2/7 + 104. What is v in x(v) = 0?
-5, 0, 2/9, 1
Let g = -235/132 + 100/33. Factor 3/4 + 1/4*j**2 - g*j + 1/4*j**3.
(j - 1)**2*(j + 3)/4
Let z be (20/8 + 3/(-6