*3/3
Let j(y) be the second derivative of y**8/5040 - y**7/1260 + y**6/1080 - 2*y**3/3 - 11*y. Let i(w) be the second derivative of j(w). Let i(b) = 0. What is b?
0, 1
Let m(d) be the second derivative of -1/300*d**6 + 0*d**4 - 1/75*d**5 + 0 - 7*d + 3/2*d**2 + 0*d**3. Let q(g) be the first derivative of m(g). Factor q(r).
-2*r**2*(r + 2)/5
Let f(i) be the second derivative of -3*i**5/20 - i**4 + 6*i**3 + 124*i. Determine k, given that f(k) = 0.
-6, 0, 2
Suppose 0 = 3*r + 9 + 33. Let l be 98/(-84)*8/r. Factor 0 - l*m + 1/3*m**2.
m*(m - 2)/3
Let m(g) = -4*g**4 - 2*g**3 - 8*g**2 - g. Let s(p) = -3*p**4 - 3*p**3 - 8*p**2 - 2*p. Let w = -12 - -15. Let q(b) = w*s(b) - 2*m(b). What is r in q(r) = 0?
-2, -1, 0
Factor 22*q**2 + 4*q**3 + 16 + 2*q**2 - 64*q + 100*q.
4*(q + 1)**2*(q + 4)
Suppose 14*c = 62 - 20. Factor 16*k + 16*k**2 + 9*k + 12 + 13*k - 10*k**c.
-2*(k - 3)*(k + 1)*(5*k + 2)
Solve -2/5*o**2 - 4/5*o + 6/5 = 0.
-3, 1
Let d be 33/7*4/((-16)/(-21)). Find m such that 45/2*m**3 - 27/4 + 3/4*m**5 - 69/2*m**2 - 27/4*m**4 + d*m = 0.
1, 3
Let c(d) be the first derivative of -d**6/24 - d**5/10 + d**4/2 - d**3/6 - 7*d**2/8 + d + 165. Factor c(j).
-(j - 1)**3*(j + 1)*(j + 4)/4
Let p(t) be the first derivative of -22*t**3/9 - 23*t**2/3 - 4*t/3 + 325. Factor p(y).
-2*(y + 2)*(11*y + 1)/3
Let t(d) be the second derivative of -d**5/50 + 21*d**4/10 - 64*d**3 - 1024*d**2/5 + 126*d. Factor t(q).
-2*(q - 32)**2*(q + 1)/5
Let i = 90641/80 + -1133. Let y(o) be the third derivative of 0*o**5 + 0 + 0*o**4 + 1/140*o**7 + i*o**6 + 0*o**3 - 4*o**2 + 0*o. Suppose y(z) = 0. What is z?
-1, 0
Let z(y) be the first derivative of -y**4/9 - 4*y**3/9 + 4*y**2/3 + 32*y/9 + 33. Factor z(d).
-4*(d - 2)*(d + 1)*(d + 4)/9
Let v be (44 + 7)*1/1. Let r = v + -35. Determine y, given that 5*y**4 + 0*y**4 + 2*y**3 + 10*y**3 - y**4 - r*y = 0.
-2, 0, 1
Let o(l) be the first derivative of l**6/6 - 17*l**5/15 + 4*l**4/3 + 8*l**3 + 3*l**2 - 5. Let f(x) be the second derivative of o(x). Factor f(a).
4*(a - 2)**2*(5*a + 3)
Let l(k) be the first derivative of -k**6/7 + 8*k**5/7 - 33*k**4/14 - 8*k**3/21 + 36*k**2/7 - 32*k/7 + 97. What is o in l(o) = 0?
-1, 2/3, 1, 2, 4
Let y(g) = -4*g**4 + 13*g**3 - 17*g**2 + 11*g + 3. Let d = -33 + 30. Let p(t) = -t**3 + t**2 + t + 1. Let l(k) = d*p(k) + y(k). Factor l(n).
-4*n*(n - 2)*(n - 1)**2
Let x(h) = -5*h**3 - 3*h**2 - 15*h - 5. Let j(v) = -9*v**3 - 7*v**2 - 30*v - 11. Let r(f) = 4*j(f) - 7*x(f). Factor r(w).
-(w + 1)*(w + 3)**2
Find q such that 15*q**2 - 48*q - 6 - 41*q - 43*q + 111*q + 12*q**3 = 0.
-2, -1/4, 1
Suppose 57*f + 189 = 360. Determine i, given that -2/5*i**5 - 18/5*i**4 - 66/5*i - 18/5 - 12*i**f - 92/5*i**2 = 0.
-3, -1
Let i(z) be the second derivative of 1/4*z**5 + 0 + 0*z**2 - 5/3*z**4 - 21*z + 10/3*z**3. Factor i(k).
5*k*(k - 2)**2
Let p(a) be the first derivative of a**8/2352 - a**7/245 + a**6/70 - 2*a**5/105 - 21*a**2/2 - 3. Let y(u) be the second derivative of p(u). Factor y(z).
z**2*(z - 2)**3/7
Let m(x) = 12*x - 60. Let r be m(5). Let o(g) be the second derivative of -2/3*g**2 + 1/60*g**5 + 7*g + 0 + r*g**3 + 1/12*g**4. Let o(u) = 0. What is u?
-2, 1
Let x(j) = -j**3 - j**2 + 1. Let b(u) = -36*u**2 + 48*u + 81. Let k(r) = -b(r) - 3*x(r). Determine h, given that k(h) = 0.
-14, -1, 2
Let w(t) be the third derivative of -t**6/60 + 8*t**5/3 - 559*t**4/4 + 1014*t**3 - 530*t**2. Factor w(j).
-2*(j - 39)**2*(j - 2)
Let z(y) be the third derivative of 0 + 1/96*y**5 + 1/96*y**4 + 0*y + 0*y**3 + 25*y**2 + 1/240*y**6 + 1/1680*y**7. What is i in z(i) = 0?
-2, -1, 0
Suppose -3*z + p - 4 + 14 = 0, 0 = -4*z - 3*p + 9. Let v = -263 - -276. Suppose -v + 9*x**z - 6*x**3 + 1 + 9*x**2 = 0. Calculate x.
-2, 1
Let l(g) be the second derivative of -g**5/60 - g**4/18 + 2*g - 157. Factor l(q).
-q**2*(q + 2)/3
Let y = 25/462 + 3/22. Let x(s) be the first derivative of 1/7*s**2 + 2 + 0*s - y*s**3 + 1/14*s**4. Let x(p) = 0. Calculate p.
0, 1
Let u(f) = f**3 - 24*f**2 + 66*f - 59. Let w be u(21). Let 15/4 - 3*m**2 - 3/4*m**w - 9/2*m + 9/2*m**3 = 0. What is m?
-1, 1, 5
Let n be (7 + 685/(-100))*44/11. Factor n*b + 3/5*b**5 - 3/5*b**4 - 3/5 + 6/5*b**2 - 6/5*b**3.
3*(b - 1)**3*(b + 1)**2/5
Solve -11/4*p**3 - 5/4*p**2 - 3/4 + 2*p**4 + 11/4*p = 0 for p.
-1, 3/8, 1
Let c = 145 - 143. Let g(r) be the second derivative of 1/10*r**4 - 1/75*r**6 - 3*r - 1/25*r**5 + 0 + 4/15*r**3 - 4/5*r**c. Factor g(l).
-2*(l - 1)**2*(l + 2)**2/5
Let d(n) = -n**2 + 18*n - 29. Suppose -3*f + 5*f = 4. Let k(l) = 7 - 5 - 7*l + 28 - 11*l. Let b(v) = f*k(v) + 3*d(v). Solve b(m) = 0 for m.
3
Solve -155 - 75*x**4 - 68*x + 855 - 355*x**3 + 308*x - 505*x**2 - 5*x**5 = 0 for x.
-7, -5, -2, 1
Suppose 0*w - 2*w = -4. Let h = 9 - 6. Factor h - 5 - b**2 + w - 2*b.
-b*(b + 2)
Let h = -1687 - -10129/6. What is c in -7/6*c**2 + 0 - 5/6*c**5 + 1/3*c + h*c**4 + 1/2*c**3 = 0?
-1, 0, 2/5, 1
Suppose -29 = -4*v - 13. Find x such that -2*x**v + 18*x**3 - 3*x**3 + x**5 + 7*x**2 + 11*x**4 = 0.
-7, -1, 0
Let y(d) = -d**2 + 11*d - 28. Suppose 5*v = k + 18, -5*v + 0*v = -25. Let q be y(k). Factor -5/3*x**3 + q + 2/3*x**4 + 4/3*x**2 - 1/3*x.
x*(x - 1)**2*(2*x - 1)/3
Let a(v) = 69*v**3 - 8*v**2 - 48*v - 4. Let x(m) = 72*m**3 - 9*m**2 - 49*m - 2. Let d(j) = 4*a(j) - 3*x(j). Solve d(u) = 0 for u.
-2/3, -1/4, 1
Let i = 1457/10 + -4051/30. Factor 0 - 2/3*b**3 - i*b + 16/3*b**2.
-2*b*(b - 4)**2/3
Let i be (-10)/40*(-3)/30. Let z(l) be the third derivative of 0*l + 0*l**3 + i*l**4 + 8*l**2 - 3/100*l**5 + 0 + 3/200*l**6 - 1/350*l**7. What is a in z(a) = 0?
0, 1
Let r(c) = -130*c**2 - 1370*c - 8640. Let h(m) = 11*m**2 + 114*m + 720. Let w(a) = -35*h(a) - 3*r(a). Suppose w(u) = 0. What is u?
-12
Let b(y) be the first derivative of -33*y**4/8 - 5*y**3 + 39*y**2/4 + 18*y + 92. Factor b(x).
-3*(x + 1)**2*(11*x - 12)/2
Let r = 152 - 149. Suppose -o = -r*d - 7, o + 1 = -0*o - 5*d. Suppose 1/2 - p**2 + 1/2*p**o - p**3 + 1/2*p**5 + 1/2*p = 0. Calculate p.
-1, 1
Let o = 24 - 21. Determine w, given that -20*w**4 - 14*w**3 + 11*w + 26*w**4 - o*w = 0.
-2/3, 0, 1, 2
Factor 12/7*k**2 + 256/7*k - 1/7*k**4 - 256/7 - 11/7*k**3.
-(k - 4)*(k - 1)*(k + 8)**2/7
Let v(i) be the first derivative of i**6/45 + i**5/30 + 6*i - 7. Let x(u) be the first derivative of v(u). Let x(b) = 0. What is b?
-1, 0
Let z(y) be the first derivative of -5*y**6/6 - 13*y**5 - 275*y**4/4 - 355*y**3/3 + 100*y**2 + 500*y - 45. Solve z(d) = 0.
-5, -2, 1
Suppose 2*n = -1 + 5. Let w be (1/(-28))/(13/(-156)). Find d, given that 0 + 3/7*d + w*d**n = 0.
-1, 0
Let x(u) = u**4 - u**3 - u**2 - 3*u. Let h(a) = -a**4 + 2*a. Let i(d) = 4*h(d) + 3*x(d). Factor i(o).
-o*(o + 1)**3
Let w(a) = 5*a**2 - 3*a - 8. Let r(x) = x**2 - 3. Let y(n) = -6*r(n) + w(n). Factor y(u).
-(u - 2)*(u + 5)
Suppose 0 + 21/5*y**3 + 3/5*y**2 - 21/5*y - 3/5*y**4 = 0. What is y?
-1, 0, 1, 7
Find f such that 88/3 + 47/3*f**2 + 134/3*f + 1/3*f**3 = 0.
-44, -2, -1
Let f(g) = -g**3 + g**2 + 2*g + 2. Let d be f(0). Suppose 6*t = -d*t. Let 0 - 3*p**3 + 9/2*p**4 - 3/2*p**5 + t*p**2 + 0*p = 0. Calculate p.
0, 1, 2
Let r(m) be the second derivative of m**6/840 - m**5/84 + m**4/28 - 7*m**2/2 - 11*m. Let x(p) be the first derivative of r(p). Suppose x(s) = 0. What is s?
0, 2, 3
Let q(u) = -11*u**5 + 48*u**4 - 52*u**3 + 6*u**2 + 2. Let g(h) = 33*h**5 - 145*h**4 + 156*h**3 - 17*h**2 - 7. Let j(m) = -2*g(m) - 7*q(m). Factor j(x).
x**2*(x - 2)**2*(11*x - 2)
Let j be (-4)/6*(4 + -4 + -3). Find l such that -20*l**3 + 21*l**3 + 4*l**2 - 2*l**j - 3*l**2 = 0.
0, 1
Let v(o) be the third derivative of o**5/270 + o**4/12 - 17*o**2 - 2. Determine k, given that v(k) = 0.
-9, 0
Let t(v) = -v**3 - 12*v**2 - 13*v - 16. Let k be t(-11). Let q be 1*(-3)/k + (-1)/(-2). Let 0*c + 2/3*c**2 + q = 0. What is c?
0
Let g = -267241/5 + 53450. Determine k so that 7*k + g + 23/5*k**2 - 3/5*k**3 = 0.
-1, -1/3, 9
Let 0*j + 0 + 0*j**3 - 2/3*j**4 + 2/3*j**2 = 0. What is j?
-1, 0, 1
Let h = 7 - 9. Let r be (-2 + 3)/(h/(-12)). Determine b so that -b**2 - 2*b**5 + 0*b**5 - 6*b**4 - r*b**2 + 5*b**2 - 6*b**3 = 0.
-1, 0
Factor 14 - 36*s**2 - 13 + 53*s + 15 + 11*s.
-4*(s - 2)*(9*s + 2)
Suppose 4*k - 48 - 32 = -4*a, -4 = a. Let z = k + -143/6. Factor 0*i**2 + 1/3*i**4 + 0*i + 0 - z*i**5 - 1/6*i**3.
-i**3*(i - 1)**2/6
Let g(t) be the first derivative of -1/1