p so that j(p) = 0.
-2, -1, 0
Let j = 121 - 118. Let b(f) be the second derivative of 5*f - 1/3*f**2 + 0 + 4/9*f**j - 1/6*f**4. Solve b(i) = 0.
1/3, 1
Let n(r) be the third derivative of 2*r**7/105 - r**6/15 - 19*r**5/15 - 14*r**4/3 - 8*r**3 + r**2 + 184. Factor n(u).
4*(u - 6)*(u + 1)**2*(u + 2)
Let m be (3/(-15) + (-24)/840)*-7. Solve -2*o**2 - 2/5*o**4 - 4/5*o + 0 - m*o**3 = 0.
-2, -1, 0
Let v be ((-348)/36 - -8)/((-10)/36). Let z(l) be the first derivative of l**4 - 1/3*l**v + 0*l**3 + 7 - l**2 + 0*l + 0*l**5. Factor z(g).
-2*g*(g - 1)**2*(g + 1)**2
Determine n so that -242 - 2/9*n**2 + 44/3*n = 0.
33
Let k(h) be the second derivative of 0*h**2 + 0 - 1/54*h**4 - 4*h + 0*h**3 - 1/90*h**5. Determine l, given that k(l) = 0.
-1, 0
Suppose 15 - 4 = 3*v - a, -v + 17 = -3*a. Let w(l) be the second derivative of 0 + l**3 - 8*l + 1/6*l**4 + 2*l**v. Find c such that w(c) = 0.
-2, -1
Let r(q) be the first derivative of 2*q**5/3 - 13*q**4/6 + 2*q**3 + q**2/3 - 4*q/3 + 26. Factor r(l).
2*(l - 1)**3*(5*l + 2)/3
Let k(u) be the first derivative of -u**4/36 + u**3/3 - 5*u**2/6 - 25*u/9 + 97. Let k(b) = 0. Calculate b.
-1, 5
Let o(t) be the second derivative of t**10/2016 + t**9/756 + t**8/1008 - 7*t**4/12 - 9*t. Let n(p) be the third derivative of o(p). Factor n(j).
5*j**3*(3*j + 2)**2/3
Let v(w) = -10*w**3 - 80*w**2 - 792*w - 1304. Let l(s) = -8*s**3 - 79*s**2 - 792*s - 1302. Let r(k) = 4*l(k) - 3*v(k). Factor r(b).
-2*(b + 2)*(b + 18)**2
Let f(s) be the first derivative of s**5/15 - 13*s**4/12 - 14*s**3/9 + 368. Suppose f(q) = 0. What is q?
-1, 0, 14
Find o, given that -2*o - 3*o - 4*o**2 + 99 - 101 - o**3 = 0.
-2, -1
Let i = 94/133 + -8/19. Let l be (-1 + 18/14)*2. Factor 10/7*x**2 + 0 + 8/7*x**3 + l*x + i*x**4.
2*x*(x + 1)**2*(x + 2)/7
Let l = -217 + 240. Suppose 19*u - y = l*u - 2, 4 = 2*y. Determine a so that u*a**3 + 0 + 6/5*a - 21/5*a**2 + 27/5*a**4 = 0.
-1, 0, 1/3, 2/3
Let c(i) be the first derivative of -i**4/30 - 46*i**3/45 - 8*i**2 + 96*i/5 + 42. Determine z so that c(z) = 0.
-12, 1
Suppose -16*q - 54 + 54 = 0. Let d(m) be the third derivative of 4/15*m**6 + q*m - 10*m**2 + 0 + 0*m**4 + 2/3*m**3 - 2/35*m**7 - 2/5*m**5. Factor d(g).
-4*(g - 1)**3*(3*g + 1)
Let q(p) be the first derivative of -11*p**4/8 + 65*p**3/3 - 93*p**2 - 36*p + 148. Factor q(a).
-(a - 6)**2*(11*a + 2)/2
Let o be 3/(-12) + 16587/(-84). Let r = o - -198. Factor 2/7*v - r*v**3 + 2/7*v**2 - 2/7.
-2*(v - 1)**2*(v + 1)/7
Let x(c) = c**3 + 3*c**2 - 6*c - 4. Let d be x(-4). Suppose -6*g + g + 30 = -d*u, -u + 1 = 3*g. Let 3*v**g + 3*v**3 + 0*v**3 + 3*v**2 = 0. What is v?
-2, 0
Let l be (65 - 0) + 1/3*0. Let t = 65 - l. Suppose -1/4*m + t - 1/4*m**3 + 1/2*m**2 = 0. What is m?
0, 1
Determine m, given that 44*m**3 - 2406*m**4 + 4818*m**4 + 45*m**2 - 2413*m**4 = 0.
-1, 0, 45
Let j(i) be the third derivative of -i**10/105840 - i**9/26460 + 2*i**4/3 - 16*i**2. Let u(v) be the second derivative of j(v). Factor u(a).
-2*a**4*(a + 2)/7
Let t(b) = b**5 + 21*b**4 + 5*b**3 - 5*b**2 - 5*b + 5. Let i(m) = 12*m**4 + 3*m**3 - 3*m**2 - 3*m + 3. Let g(c) = 5*i(c) - 3*t(c). What is q in g(q) = 0?
-1, 0
Factor -1/3*w - 1/3*w**2 + 0.
-w*(w + 1)/3
Let z(c) be the second derivative of -c**4/8 - 51*c**3/2 - 7803*c**2/4 + 180*c. Find u such that z(u) = 0.
-51
Let w(r) be the second derivative of -1/126*r**7 + 13/90*r**6 + 4 - 145/36*r**4 - 19/60*r**5 - 32/3*r**2 - 88/9*r**3 + r. Factor w(p).
-(p - 8)**2*(p + 1)**3/3
Let z(i) be the second derivative of i**7/840 + i**6/80 + i**5/20 + 2*i**4/3 + 2*i. Let j(d) be the third derivative of z(d). Factor j(w).
3*(w + 1)*(w + 2)
Let l(c) = -2*c + 2. Let p(s) = 3*s - 5. Let n(w) = 15*l(w) + 6*p(w). Let a(u) = u**2 + 11*u. Let d(v) = -4*a(v) - 5*n(v). Factor d(f).
-4*f*(f - 4)
Factor 12/7*y + 0 - 12/7*y**3 + 2/7*y**2 - 2/7*y**4.
-2*y*(y - 1)*(y + 1)*(y + 6)/7
Let f(a) be the first derivative of 7*a**4/26 - 32*a**3/39 + 11*a**2/13 - 4*a/13 + 68. Factor f(m).
2*(m - 1)**2*(7*m - 2)/13
Let t(m) be the first derivative of -m**6/6 + 8*m**5/5 - 13*m**4/4 - 26*m**3/3 + 32*m**2 - 32*m - 285. Suppose t(d) = 0. What is d?
-2, 1, 4
Let t(u) be the first derivative of u**7/840 - u**6/45 + 13*u**5/120 - u**4/4 - 3*u**3 + 4. Let x(w) be the third derivative of t(w). Solve x(v) = 0.
1, 6
Let r(c) = 17*c - 10*c - 21 - 9*c - 11*c - c**2. Let i be r(-10). Factor i*z**2 - 12/5*z**3 - 9/5 - 24/5*z.
-3*(z - 3)*(z - 1)*(4*z + 1)/5
Let m = 1179 + -15325/13. Solve 0*l + m*l**3 + 0 + 4/13*l**2 = 0.
-2, 0
Let z(q) be the second derivative of q**5/20 + 5*q**4/6 - 11*q**3/6 + q**2 + 3*q. Let y be z(-11). Solve 10*i + 2*i - y*i**2 - 8*i = 0.
0, 2
Solve 8/3*f - 22/3*f**2 + 0 - 7/3*f**3 + f**4 = 0.
-2, 0, 1/3, 4
Let n(m) be the third derivative of 5/336*m**8 + 1/42*m**7 - 1/24*m**6 + 0 - 9*m**2 + 0*m**4 + 0*m - 1/12*m**5 + 0*m**3. Solve n(x) = 0 for x.
-1, 0, 1
Let u(r) = -r**2 + 1. Suppose 2*b + 9 = -3*b - 4*y, y = b. Let n(s) = 8*s**2 - 30*s - 3. Let f(x) = b*n(x) - 3*u(x). Factor f(g).
-5*g*(g - 6)
Let s(t) = -5*t**2 + 35*t - 22. Let y(l) = l**2 - 7*l + 4. Let v(u) = 2*s(u) + 11*y(u). Factor v(c).
c*(c - 7)
Suppose 17*q - 29 = 22. Suppose w**2 - q + 47*w - 98*w + 49*w = 0. What is w?
-1, 3
Let w(l) be the second derivative of 30*l - 2/9*l**4 - 4/9*l**3 + 0 + 0*l**2 - 1/30*l**5. Find d such that w(d) = 0.
-2, 0
Suppose -11 = -4*o + 1. Suppose -2*k + 30 = o*k. Factor -8*z + k*z**3 + 2 + 2*z + 8*z**4 - 2*z**2 - 8*z**2.
2*(z - 1)*(z + 1)**2*(4*z - 1)
Suppose t - 4*t = -3*f - 93, 53 = 3*t + 5*f. Let j = t - 23. Let 0 - 8/3*a - 8/3*a**2 - 2/3*a**j = 0. Calculate a.
-2, 0
Let b(h) be the first derivative of 0*h**2 + 4 - 2*h**3 + 0*h + 3/5*h**5 + 3/4*h**4. Factor b(f).
3*f**2*(f - 1)*(f + 2)
Let v be ((-3)/(-2))/((-15)/(-10)). Let q be (2 - -1)*(v + 14/(-15)). Factor -1/5*k**2 + q*k + 0.
-k*(k - 1)/5
Let g(h) be the third derivative of 0*h + 7/15*h**6 - 3/2*h**4 - 2/21*h**8 + 10*h**2 + 8/35*h**7 - 4/3*h**3 + 0 - 7/15*h**5. Find u, given that g(u) = 0.
-1/2, 1, 2
Let h(z) = -z**2 - 8*z - 10. Let f be h(-8). Let m be (-1)/5 + (-32)/f. Factor -5*d**2 + d**4 - 6*d**3 - m*d**4 - d**2 + d - 3*d.
-2*d*(d + 1)**3
Let r(s) be the third derivative of -s**7/105 + s**6/30 - s**4/6 + s**3/3 - 2*s**2 + 57. Factor r(t).
-2*(t - 1)**3*(t + 1)
Let h = 16/23 - 2/69. Let b = 20623 - 61868/3. Factor 0 - h*i + b*i**3 - i**4 + i**2 + 1/3*i**5.
i*(i - 2)*(i - 1)**2*(i + 1)/3
Let l(f) be the first derivative of f**7/441 + 2*f**6/315 - f**4/63 - f**3/63 + 49*f + 25. Let s(i) be the first derivative of l(i). Factor s(d).
2*d*(d - 1)*(d + 1)**3/21
Let x(h) = h**2 - 4*h. Let y(d) = 3*d**2 - 32*d - 28. Let q(z) = 4*x(z) - y(z). Let q(b) = 0. Calculate b.
-14, -2
Let t(s) = 7*s**4 - 8*s**3 + 15*s**2 - 18*s - 32. Let z(n) = -n**4 + n**3 + n + 1. Let m(l) = -5*t(l) - 40*z(l). Determine h, given that m(h) = 0.
-4, -1, 2, 3
Find w, given that 2*w**2 + 2/13*w**4 + 0 + 12/13*w + 16/13*w**3 = 0.
-6, -1, 0
Let q be (88/16 + -5)/(2/36). Let m be (9 - q)/((-2)/(0 - -2)). Factor m - 1/7*b - 1/7*b**3 + 2/7*b**2.
-b*(b - 1)**2/7
Let n = -19 + 23. Suppose -8*j**2 + 0*j - 9*j**5 - 8*j**4 + n + 4*j - 8*j**3 + 13*j**5 + 12*j**4 = 0. What is j?
-1, 1
Let t be -3 + 11/3 + 1. Let n be ((-2)/6)/(-1) + 103/309. Factor -n - z + t*z**2.
(z - 1)*(5*z + 2)/3
Let n(g) = 57*g**2 + 15*g + 18*g**2 + 21*g**3 - 4 - 39*g**2. Let q(x) = 230*x**3 + 395*x**2 + 165*x - 45. Let u(y) = -45*n(y) + 4*q(y). Factor u(s).
-5*s*(s + 1)*(5*s + 3)
Let k be 15/3*-1*-1. Let z = 56 - 45. Let 3*g**4 - 6*g**2 - 6*g**3 - 2 - 8*g + 3*g**k + 5 + z*g = 0. What is g?
-1, 1
Factor 100/3*o + 0 + 0*o**2 - 4/3*o**3.
-4*o*(o - 5)*(o + 5)/3
Let f = -185 - -190. Let i(j) be the third derivative of 0*j**3 + 0*j**f - 4*j**2 + 0 + 0*j**6 + 0*j**4 - 1/210*j**7 - 1/336*j**8 + 0*j. Factor i(s).
-s**4*(s + 1)
Let r(o) = 2*o**2 + 4*o. Let l be r(-3). Suppose 0 = -4*m + d + l, 0*m + 2*m - 5*d + 6 = 0. Factor 2/3 - q + 1/3*q**m.
(q - 2)*(q - 1)/3
Let d(w) = w**5 + w**4 + w**3 + w**2 + w. Let j(a) = 6*a**5 - 2*a**4 - 10*a**3 + 34*a**2 + 40*a. Let h(v) = -4*d(v) + j(v). Find b such that h(b) = 0.
-2, -1, 0, 3
Let r be 306/60 - (-30)/(-100). Let l(z) = z + 7. Let x be l(-5). Find d, given that 0*d + 0*d**x + 0 + r*d**4 + 48/5*d**3 + 3/5*d**5 = 0.
-4, 0
Let i(r) = 2*r**2 + 182*r + 588. Let l(q) = q**2 +