-1, 0, 1/3
Let j(i) be the second derivative of -i**8/84 + i**6/10 + 2*i**5/15 - 3*i**2/2 + 16*i. Let o(w) be the first derivative of j(w). Let o(r) = 0. What is r?
-1, 0, 2
Let y(n) be the second derivative of n**4/6 - 5*n**3/3 - 24*n**2 + 18*n. Suppose y(d) = 0. Calculate d.
-3, 8
Suppose -28 = -4*i + 16. Let n = i - 9. Find o such that 3*o + 4 + 7*o**n - 4*o**2 - 11*o = 0.
2/3, 2
Suppose -7*z = -11*z + 12. Suppose 2*m - 4*h = 12, 3*h = z*m - 11 - 1. Determine j so that -18/5*j - m*j**3 + 24/5*j**2 + 4/5 = 0.
2/5, 1
Let b(q) be the first derivative of 2*q**5/25 + q**4/2 + 16*q**3/15 + 4*q**2/5 - 80. Solve b(x) = 0 for x.
-2, -1, 0
Find a, given that a**2 + 20*a + 24*a + 0*a - 65*a = 0.
0, 21
Let 0*w**2 + 0 + 0*w - 3/10*w**3 + 1/10*w**4 = 0. Calculate w.
0, 3
Let i(z) be the first derivative of z**6/30 + z**5/10 - z**4/4 + 14*z + 14. Let m(h) be the first derivative of i(h). Let m(k) = 0. Calculate k.
-3, 0, 1
Let g be (2/4)/(3/2)*9. What is d in 3*d**3 - 2*d**2 + 5*d**2 - d - g - 2*d = 0?
-1, 1
Let r(j) = 7*j**2 + 16*j + 4. Let f(v) = -6*v**2 - 15*v - 6. Let l(w) = -4*f(w) - 3*r(w). Suppose l(p) = 0. What is p?
-2
Determine h, given that 231*h**2 - 185856*h + 94*h**3 + 9129244 + 825*h**2 - 96*h**3 - 1755698 + 3530006 = 0.
176
Factor -12/5 + 36*i - 135*i**2.
-3*(15*i - 2)**2/5
Let y(x) be the second derivative of -7/9*x**3 + 5/18*x**4 - 1/30*x**5 + 0 + x**2 - 7*x. Factor y(j).
-2*(j - 3)*(j - 1)**2/3
Let 12/5 + 2*h + 2/5*h**2 = 0. Calculate h.
-3, -2
Let y be -7*2 + ((-12)/(-4) - 1). Let o be (8 + y)*(0 - 1/8). Factor 3/2*c + 1/2*c**3 - o - 3/2*c**2.
(c - 1)**3/2
Let c = -28/109 - -1117/3924. Let h(i) be the second derivative of 0*i**2 + c*i**4 - 10*i + 0 - 1/6*i**3. Factor h(y).
y*(y - 3)/3
Let y(b) be the second derivative of -b**4/15 + 8*b**3/15 + 24*b**2/5 - 7*b + 4. Factor y(m).
-4*(m - 6)*(m + 2)/5
Let n(p) be the second derivative of -p**4/30 - 14*p**3/15 + 19*p**2 + 244*p. Factor n(c).
-2*(c - 5)*(c + 19)/5
Suppose 2*i = -5*m + 1, m + 5*i - 16 = -2. Let c be (4 - -2) + -2 + 0 + m. Suppose -c*y + 9/2 + 1/2*y**2 = 0. Calculate y.
3
Suppose 25 = 15*m - 10*m. Factor 40*l**2 + 27*l**3 + l**m + 53*l**3 + 10*l**5 + 5*l**5 - 4 + 60*l**4.
4*(l + 1)**4*(4*l - 1)
Let t be 182/(-21)*(-3)/(-2). Let l(n) = 7*n**2 - 2*n - 5. Let o(r) = -15*r**2 + 4*r + 11. Let w(b) = t*l(b) - 6*o(b). Let w(a) = 0. What is a?
1
Let u(d) be the third derivative of d**8/1008 + d**7/210 - d**6/360 - 7*d**5/180 + 2*d**3/9 - 8*d**2 + 6*d. Determine c, given that u(c) = 0.
-2, -1, 1
Suppose -31 = 2*p - 35. Let z(c) = -c**3 - c - 1. Let w(u) = 6*u**3 + 6*u**2 - 4*u - 2. Let d(h) = p*w(h) - 4*z(h). Factor d(t).
4*t*(t + 1)*(4*t - 1)
Factor 0*f + 0*f**2 + 0 - 2/9*f**5 + 4/9*f**3 + 2/9*f**4.
-2*f**3*(f - 2)*(f + 1)/9
Let o(c) be the first derivative of -c**5/2 + 37*c**4/8 + 38*c**3/3 - 9*c**2 + 221. What is y in o(y) = 0?
-2, 0, 2/5, 9
Factor -8064*h - 9216 + 1104*h**2 - 142/3*h**3 + 2/3*h**4.
2*(h - 24)**3*(h + 1)/3
Let x(n) be the second derivative of 0 + 2/5*n**2 + 1/10*n**4 + 1/3*n**3 - n. Suppose x(m) = 0. Calculate m.
-1, -2/3
Let p(c) be the first derivative of -1/34*c**4 - 4/51*c**3 + 4/17*c + 1/17*c**2 + 5. What is d in p(d) = 0?
-2, -1, 1
Let y(c) = c**5 + c**3 - c - 1. Let g = -15 - -17. Let r(d) = 3*d**5 + 3*d**4 + 4*d**3 - 2*d - 2. Let j(z) = g*y(z) - r(z). Find i such that j(i) = 0.
-2, -1, 0
Let z(a) = a**3 + 7*a**2 - 8*a + 4. Let h be z(-8). Solve h*o**3 + 2*o**4 - 4*o**5 - 2*o**4 - 4*o**2 + 4*o**4 = 0 for o.
-1, 0, 1
Suppose 3*d**2 + 10*d - 4*d - 33 - 10*d + 34*d = 0. Calculate d.
-11, 1
Suppose -3*p + p - x = 7, -5*p = -3*x + 34. Let b(s) = 2*s + 10. Let g be b(p). Find j such that -1/4*j + 1/2*j**4 - 3/4*j**5 + g + j**3 - 1/2*j**2 = 0.
-1, -1/3, 0, 1
Let a(v) = 14*v**2 + 86*v + 12. Let u(o) = o**3 - 5*o**2 - 28*o - 4. Let k(j) = -6*a(j) - 20*u(j). Factor k(m).
-4*(m - 2)*(m + 1)*(5*m + 1)
Let y(b) = -b**2 + 11*b - 11. Let l be y(9). Suppose 0 = a + 2*j + l, 3*j = -5*a + j + 5. Factor 11 - 5 + 9*p**2 + a*p**3 - 3*p - 15*p**2.
3*(p - 2)*(p - 1)*(p + 1)
Suppose 0 = -2*g - 5*l + 6, -2*g + 6*l + 6 = 3*l. Let k(z) be the second derivative of 1/6*z**4 + 0*z**g + 0 + 5*z + 0*z**2. Factor k(q).
2*q**2
Let t = 177/428 - 35/214. Factor -7/2*o - 49/4 - t*o**2.
-(o + 7)**2/4
Let z(a) be the first derivative of -a**6/9 - 2*a**5/15 + a**4 + 28*a**3/9 + 11*a**2/3 + 2*a - 662. Let z(u) = 0. What is u?
-1, 3
Let t(s) = -5*s**2 - 10*s + 78. Let m(k) = 14*k**2 + 31*k - 229. Let c(x) = -6*m(x) - 17*t(x). Determine h, given that c(h) = 0.
4, 12
Factor -9*h**4 + 1/2*h**5 + 8 - 33/2*h + h**2 + 16*h**3.
(h - 16)*(h - 1)**3*(h + 1)/2
Suppose 96*h - 3 = 95*h - 0. Solve -128/21 - 8/7*n**2 - 2/21*n**h - 32/7*n = 0 for n.
-4
Let i(p) be the second derivative of -p**7/3360 + p**6/480 - p**4/24 - 7*p**3/6 + 3*p**2/2 + 24*p - 2. Let g(c) be the second derivative of i(c). Factor g(m).
-(m - 2)**2*(m + 1)/4
Factor -24 - 68*o + 2*o**2 + 121*o - 55*o.
2*(o - 4)*(o + 3)
Determine q so that -853*q + 4*q**4 + 901*q - 44*q**2 - 8*q**3 + 185 - 41 = 0.
-2, 3
Let u(j) = 33*j**2 - 96*j - 54. Let n(o) = 2*o**2 - 3. Let p(b) = 18*n(b) - u(b). Determine w, given that p(w) = 0.
-32, 0
Let p = -859/10 - -86. Let s = p - -17/30. Factor 0*g**2 - s*g**3 + 2/3*g**4 + 0 + 0*g.
2*g**3*(g - 1)/3
Let j(f) be the second derivative of -f**6/6 - f**5/4 + 5*f**4/4 + 5*f**3/6 - 5*f**2 + 104*f. Factor j(u).
-5*(u - 1)**2*(u + 1)*(u + 2)
Let s(o) = 10*o**2 + 7*o - 31. Let g(b) = -7*b**2 - 4*b + 21. Let p(q) = 7*g(q) + 5*s(q). Factor p(j).
(j - 1)*(j + 8)
Let a be 36/(-63) - (-28)/49. Let d(u) be the third derivative of 1/420*u**6 - 1/84*u**4 + 0 + 0*u + a*u**5 + 2*u**2 + 0*u**3. Suppose d(o) = 0. Calculate o.
-1, 0, 1
Let c(w) be the third derivative of -w**7/840 - 3*w**6/160 - w**5/16 - 7*w**4/96 - w**2 + 12. Factor c(y).
-y*(y + 1)**2*(y + 7)/4
Let o(c) = -10*c - 230. Let u be o(-23). Find a, given that 3/2*a**3 + 0 - 3/2*a**4 + 0*a**2 + u*a = 0.
0, 1
Let i(z) be the second derivative of 2*z**7/105 + 3*z**6/25 + 6*z**5/25 + 2*z**4/15 + 9*z. Factor i(r).
2*r**2*(r + 2)**2*(2*r + 1)/5
Solve s - 48*s**2 - 179*s**5 + 11*s**3 + 42*s**2 - s - 4*s**4 + 178*s**5 = 0.
-6, 0, 1
Suppose -z + 5*a + 24 = 8*a, 5*z = -a + 8. Factor 2*x**4 + 0 + z*x**2 - 2/3*x**5 + 0*x - 4/3*x**3.
-2*x**3*(x - 2)*(x - 1)/3
Let h be -1 - 4/((-8)/62). Suppose -4*d + h = 22. Factor 5*q + 23 - 11 + 8 + 5*q**d + 15*q.
5*(q + 2)**2
Factor -37 - 57*a**3 - a**5 + 17 - 54*a - 103*a**2 - 34*a - 13*a**4 - 8 + 2*a**3.
-(a + 1)**2*(a + 2)**2*(a + 7)
Let g(f) = -f**2 + 4*f + 7. Let x(m) = -4*m**2 + 13*m + 24. Let w(h) = -14*g(h) + 4*x(h). Factor w(q).
-2*(q + 1)**2
Let z(k) = 55*k**2 - 125*k + 110. Let m(c) = -8*c**2 + 18*c - 16. Let i(p) = -20*m(p) - 3*z(p). Factor i(r).
-5*(r - 2)*(r - 1)
Let u(r) be the second derivative of r**4/16 - 21*r**3/8 - 81*r - 1. Factor u(d).
3*d*(d - 21)/4
Let f(c) = 2*c + 15. Let i(a) = a + 8. Let g(w) = -2*f(w) + 5*i(w). Let u be g(-7). Factor 13 - 13 + 3*b**u - b**3 - 4*b**2.
2*b**2*(b - 2)
Factor -26/3*k**2 + 2/3*k**4 + 2*k**3 - 24 - 34*k.
2*(k - 4)*(k + 1)*(k + 3)**2/3
Let f(a) be the third derivative of -5*a**8/336 - 5*a**7/42 - a**6/6 - 428*a**2. Factor f(u).
-5*u**3*(u + 1)*(u + 4)
Let x(j) be the third derivative of j**8/16800 - j**7/630 + j**6/72 + 5*j**4/24 - 12*j**2. Let n(z) be the second derivative of x(z). Factor n(q).
2*q*(q - 5)**2/5
Let g(q) be the second derivative of 1/3*q**3 + 0 - 1/8*q**4 + 1/60*q**5 + q - 5/2*q**2. Let p(s) be the first derivative of g(s). Factor p(x).
(x - 2)*(x - 1)
Suppose 2/13*t**2 + 4 - 54/13*t = 0. Calculate t.
1, 26
Let j(l) = 307*l**2 - 612*l**2 + 2 + 306*l**2 + 3*l. Let t be j(0). Factor -4/7 + 2*h**3 + 4/7*h**t - 2*h.
2*(h - 1)*(h + 1)*(7*h + 2)/7
Let i(v) be the third derivative of v**5/135 - 4*v**4/27 - 22*v**3/9 + 3*v**2 + 42. Factor i(k).
4*(k - 11)*(k + 3)/9
Let z(g) be the second derivative of -7*g**4/36 - 985*g**3/18 + 47*g**2 + 952*g. What is t in z(t) = 0?
-141, 2/7
Let q(p) be the first derivative of 2/3*p**2 - 2*p - 22 + 8/9*p**3 - 2/15*p**5 - 1/3*p**4. Solve q(n) = 0 for n.
-3, -1, 1
Let m(u) = 115*u - 55 - 55*u**2 - u**3 + 5*u**3 + 11*u**3. Let l(s) = -7*s**3 + 28*s**2 - 57*s + 28. Let o(z) = -5*l(z) - 2*m(z). Factor o(w).
5*(w - 3)*(w - 2)*(w - 1)
Let g be 7*(-6)/(-126