-m**6/10 + 3*m**5/5 - 21*m**4/20 + 3*m**3/5 + 115. Suppose f(r) = 0. What is r?
0, 1, 3
Let m(d) be the first derivative of 25/4*d**6 - 42*d**2 + 417/8*d**4 + 43 - 67/2*d**3 + 93/2*d**5 + 30*d. Let m(j) = 0. What is j?
-5, -1, 2/5
Let o(h) be the second derivative of -h**6/225 - h**5/25 + 4*h**4/15 + 224*h**3/45 + 128*h**2/5 + 2*h - 536. Factor o(g).
-2*(g - 6)*(g + 4)**3/15
Let d(s) = s - 6. Let h be d(-9). Let k be h/(-42)*52/65. Find m such that -34/7*m**4 + 8/7*m**5 - k + 8*m**3 - 44/7*m**2 + 16/7*m = 0.
1/4, 1
Suppose 5*c = 1 + 9. Let p = -241 - -263. Factor -8 + 5 - 29 - c*m**3 - 16*m - p*m**2 + 36*m**2.
-2*(m - 4)**2*(m + 1)
Let f(x) = -3*x + 6. Let q be f(1). Let l(p) be the second derivative of q*p + 3*p**2 + 0 - 1/2*p**4 - 9/20*p**5 + 3/2*p**3. Factor l(z).
-3*(z - 1)*(z + 1)*(3*z + 2)
Let u(d) be the first derivative of 2*d**5/65 + 11*d**4/13 + 9. Factor u(o).
2*o**3*(o + 22)/13
What is x in 2/3*x**5 - 4/3*x**3 + 11/3*x**2 - 4/3 - 5/3*x**4 + 4/3*x = 0?
-1, 1/2, 2
Let x(a) be the second derivative of a**5/10 - 45*a**4/2 + 1541*a**3 - 4489*a**2 - 315*a. Factor x(z).
2*(z - 67)**2*(z - 1)
Let b(g) be the second derivative of -2*g**6/15 + 4*g**5/5 + 2*g**4 - 8*g**3/3 - 10*g**2 + 10*g - 5. Factor b(t).
-4*(t - 5)*(t - 1)*(t + 1)**2
Let k(h) be the third derivative of -h**7/840 - h**6/80 - h**5/30 - 302*h**2. What is f in k(f) = 0?
-4, -2, 0
Let r(g) be the first derivative of 3*g**4/4 + 9*g**3 - 75*g**2/2 - 99*g + 224. Factor r(b).
3*(b - 3)*(b + 1)*(b + 11)
Let k(r) be the first derivative of 5/3*r**3 + 8 + 80*r - 20*r**2. Solve k(u) = 0 for u.
4
Suppose -5*g + 1465 = -0*g. Let d = -95 - -388. Let -d*z + g*z + 2*z**2 = 0. Calculate z.
0
Let o = -69/16 + 393/80. Let k(d) be the first derivative of 2/3*d**6 - 12 + 0*d - d**3 + 1/2*d**2 - 5/4*d**4 + o*d**5. What is v in k(v) = 0?
-1, 0, 1/4, 1
Let a(c) be the second derivative of -2*c**6/15 + 7*c**5/5 + c**4 - 46*c**3/3 + 28*c**2 - 133*c - 2. Determine i, given that a(i) = 0.
-2, 1, 7
Let j(q) be the first derivative of -q**4/12 + 2*q**3/3 - 2*q**2 + 13*q + 1. Let f(b) be the first derivative of j(b). Determine w, given that f(w) = 0.
2
Let f(y) be the second derivative of 9*y**2 + 2*y**3 + 0 - 2*y + 1/6*y**4. Solve f(v) = 0.
-3
Let -6/5*w + 2/5*w**5 - 16/5*w**2 - 12/5*w**3 + 0 + 0*w**4 = 0. What is w?
-1, 0, 3
Let i be (-4)/8*9/(-117)*13. Factor -p + 1/2*p**5 + i*p**3 + 3/2*p**2 + 0 - 3/2*p**4.
p*(p - 2)*(p - 1)**2*(p + 1)/2
Let p be 115*-3*((-40)/6 - 1). Factor 2*h**3 + 2645*h - 3*h**5 - 5*h**4 - p*h.
-h**3*(h + 2)*(3*h - 1)
Factor 0*v**3 - 8 + 25*v - 7 + 0*v**3 + 5*v**3 + 5 - 20*v**2.
5*(v - 2)*(v - 1)**2
Let 0*w + 0 + 1/2*w**3 - 1/8*w**5 - 1/2*w**2 + 1/8*w**4 = 0. What is w?
-2, 0, 1, 2
Let t(m) = -m**3 + 18*m**2 - 43*m + 41. Let p(l) = -l**2 - l - 1. Let z(o) = -5*p(o) - t(o). What is s in z(s) = 0?
1, 6
Let -3360/19*d - 162/19*d**2 - 2/19*d**3 - 3200/19 = 0. Calculate d.
-40, -1
Factor 2/7*j**4 + 663552/7 + 110592/7*j + 6912/7*j**2 + 192/7*j**3.
2*(j + 24)**4/7
Solve -16/5*p + 8/5 - 2/5*p**4 - 2/5*p**5 + 2*p**3 + 2/5*p**2 = 0 for p.
-2, 1
Suppose -38*x - 9 = -41*x. Let l = 3 + -1. Factor -4*w**2 - 4*w**x + 3*w**l - 3*w**2.
-4*w**2*(w + 1)
Suppose -64 + 52*u**4 - 224*u**3 - 384*u - 309*u**2 - 88*u**4 - 55*u**2 - 116*u**2 = 0. What is u?
-2, -2/9
Let y(w) be the second derivative of w**7/294 - w**6/42 + 3*w**5/140 + 5*w**4/84 - 2*w**3/21 + 14*w + 13. Suppose y(r) = 0. What is r?
-1, 0, 1, 4
Let f(y) be the second derivative of 5/2*y**2 + 0 - 5/6*y**3 + 1/4*y**5 - 5/12*y**4 + 7*y. Factor f(d).
5*(d - 1)**2*(d + 1)
Factor -2*i - 12 + 2/3*i**2.
2*(i - 6)*(i + 3)/3
Determine f so that -23*f**2 + 0 - 1/2*f**4 + 13/2*f**3 + 24*f = 0.
0, 2, 3, 8
Let b = -321/5 - -65. Let c(z) be the third derivative of b*z**5 + 0*z**3 - 1/8*z**6 + 0 - 1/2*z**4 - 4*z**2 + 0*z - 5/14*z**7. Solve c(v) = 0 for v.
-1, 0, 2/5
Let r(v) be the first derivative of v**6/18 - v**4/4 - 2*v**3/9 + 422. Factor r(p).
p**2*(p - 2)*(p + 1)**2/3
Let q(b) be the third derivative of -b**6/300 + 13*b**5/30 - 341*b**4/20 - 363*b**3/5 + 7*b**2 + 6. Factor q(h).
-2*(h - 33)**2*(h + 1)/5
Factor -58*x**2 - 24 - 4*x**4 + 2*x + 2*x**4 - 13*x + 75*x + 20*x**3.
-2*(x - 6)*(x - 2)*(x - 1)**2
Let d(r) be the third derivative of r**4/4 + r**3/2 + 4*r**2. Let g be d(7). Factor -g*l**4 + 12*l**2 - 15*l**3 - 12*l**5 - 15 + 15 - 21*l**3.
-3*l**2*(l + 2)**2*(4*l - 1)
Let -38412*t + 0*t**2 + 38276*t + 4*t**2 = 0. Calculate t.
0, 34
Let c(k) = -39*k**5 + 123*k**4 - 60*k**3 - 150*k**2 - 18. Let z(x) = -11*x**5 + 35*x**4 - 17*x**3 - 43*x**2 - 5. Let l(p) = 5*c(p) - 18*z(p). Factor l(f).
3*f**2*(f - 4)*(f - 2)*(f + 1)
Let l(n) = -97*n**2 - 194*n. Let k be l(-2). Suppose 0*y**3 + y**2 + k - 1/3*y**4 + 2/3*y = 0. Calculate y.
-1, 0, 2
Let m(j) be the third derivative of 3*j**8/8960 + j**7/840 + j**6/960 - 3*j**4/8 + 17*j**2. Let r(z) be the second derivative of m(z). Factor r(l).
3*l*(l + 1)*(3*l + 1)/4
Let i(n) = -n**5 - n**4 - n**3 + n**2 - n + 1. Let j = -23 - -25. Let m(g) = 3*g**5 + g**4 - 2*g**2 + 2*g - 2. Let q(w) = j*m(w) + 4*i(w). Factor q(a).
2*a**3*(a - 2)*(a + 1)
Let a(z) = -27*z**3 - 77*z**2 + 22*z. Let q(o) = 54*o**3 + 155*o**2 - 46*o. Let y(t) = -5*a(t) - 2*q(t). Suppose y(n) = 0. Calculate n.
-3, 0, 2/9
Let i(x) be the second derivative of 2*x**6/15 - x**5/5 - 5*x**4/3 - 2*x**3 - 110*x. Factor i(m).
4*m*(m - 3)*(m + 1)**2
Let g(f) be the third derivative of f**7/70 + 5*f**6 + 500*f**5 - f**2 + 222. Factor g(k).
3*k**2*(k + 100)**2
Let x(y) be the first derivative of y**6/810 + y**5/135 + y**4/54 + 7*y**3/3 + 5. Let g(l) be the third derivative of x(l). Determine h, given that g(h) = 0.
-1
Let w(r) be the second derivative of -20*r**4/3 + 3*r**3 + 9*r**2 + r - 11. Determine o so that w(o) = 0.
-3/8, 3/5
Let i(q) be the second derivative of -q**7/56 - q**6/40 + 3*q**5/40 + q**4/8 - q**3/8 - 3*q**2/8 - 2*q - 5. What is o in i(o) = 0?
-1, 1
Suppose -5*u + 23 = -27. Factor -494 + 5*t**3 + u*t**2 + 25*t**5 + 494 - 40*t**4.
5*t**2*(t - 1)**2*(5*t + 2)
Let z = 13757 - 13755. Let 2/5*o**z - 8/5 + 6/5*o = 0. Calculate o.
-4, 1
Let a = -200 - -5001/25. Let d(g) be the second derivative of -2*g - a*g**5 + 2/15*g**4 - 2/15*g**3 + 0*g**2 + 0. Factor d(b).
-4*b*(b - 1)**2/5
Let b(w) be the third derivative of 5*w**7/42 + 55*w**6/24 + 58*w**5/5 - 11*w**4/6 - 56*w**3/3 - 6*w**2 + 34*w. Let b(f) = 0. What is f?
-7, -4, -2/5, 2/5
Let m(i) be the third derivative of 0*i**6 + 1/72*i**4 - 1/315*i**7 - 1/1008*i**8 + 0*i**3 + 0*i + 1/90*i**5 - 18*i**2 + 0. What is a in m(a) = 0?
-1, 0, 1
Suppose 9*c + 168 = 17*c. Let u(s) be the first derivative of 6 - 176/3*s**3 + 58*s**2 + c*s**4 - 24*s. Factor u(a).
4*(a - 1)*(3*a - 2)*(7*a - 3)
Let q(g) be the first derivative of -24 - 28*g**2 - 4/3*g**3 - 196*g. Factor q(r).
-4*(r + 7)**2
Let p = -530 - -530. Factor p*y + 0 - 1/8*y**2 - 1/4*y**4 - 3/8*y**3.
-y**2*(y + 1)*(2*y + 1)/8
Suppose x + 131 = 146. Let 4 - 47*r + 21*r**3 - 16 - x*r**2 - r = 0. Calculate r.
-1, -2/7, 2
Factor 3/5*k**5 - 12/5*k**4 + 3*k**3 + 0*k - 6/5*k**2 + 0.
3*k**2*(k - 2)*(k - 1)**2/5
Let p(t) = -15*t**3 + 18*t**2 - 11*t + 10. Let i be p(1). Solve -10/3*m**2 - i*m**3 + 2/3 - 2/3*m = 0.
-1, 1/3
Let x(d) = 2*d**2. Let v = -10 + 9. Let m be x(v). Find q, given that m + q - q**2 + 5*q - 7*q = 0.
-2, 1
Let o(r) = 3*r - 7. Let a be o(4). Suppose -5*h + 5*k = -9 - 6, -a*h = 3*k - 15. Suppose -1/3*t**h + 0 - 1/3*t**2 + 0*t = 0. What is t?
-1, 0
Suppose 89 = 5*k + 69. Let a(l) be the first derivative of 1 + 1/6*l**2 + 0*l + 1/12*l**k - 2/9*l**3. Factor a(v).
v*(v - 1)**2/3
Let p = 167 + -167. Let i(u) be the third derivative of -1/90*u**5 + 1/180*u**6 + 1/9*u**3 + 0 + p*u - 4*u**2 - 1/36*u**4. Factor i(f).
2*(f - 1)**2*(f + 1)/3
Let m(j) be the third derivative of -j**7/70 - j**6/40 + j**5/10 + 3*j**2 + 7. Factor m(x).
-3*x**2*(x - 1)*(x + 2)
Let h = -493/4 + 124. Let o(b) be the first derivative of 0*b + 1/2*b**6 + 0*b**3 + 0*b**2 + 2 - h*b**4 + 0*b**5. Factor o(m).
3*m**3*(m - 1)*(m + 1)
Let c be (432/648)/(2/12). Factor 0 - 2/13*u**3 + 2/13*u**5 + 0*u**c + 0*u + 0*u**2.
2*u**3*(u - 1)*(u + 1)/13
Find k such that -7952*k - 2/5*k**3 - 7840 - 562/5*k**2 = 0.
-140, -1
Let x(k) = k**3 + 8*k**2 - 2*k - 5. Let s be x(-5). Determine v, given that -11*v + 1