et j(l) be the second derivative of -l**6/30 + 159*l**5/10 - 25597*l**4/12 + 8374*l**3 - 12482*l**2 - 70*l - 1. What is m in j(m) = 0?
1, 158
Suppose -6305*a**2 + 1249*a - 4*a**5 + 2015*a + 168*a**4 + 1740*a**3 + 11137*a**2 = 0. Calculate a.
-4, -1, 0, 51
Factor 30*w + 5 + 52*w**2 + 16 - 29 - 5*w + 19*w.
4*(w + 1)*(13*w - 2)
Suppose -21*o + 1/8*o**2 + 83/2 = 0. What is o?
2, 166
Let w be (-3)/(3/(-27)*1). Suppose 40*p - 39 = w*p. Factor 2*a**5 + 1/2 + 9/4*a + 7/4*a**2 - 7/2*a**3 - p*a**4.
(a - 2)*(a - 1)*(2*a + 1)**3/4
Suppose 3*m = -4*i + 2, -28*m = i - 33*m - 12. Let c(b) be the first derivative of -b**2 - i*b**4 - 13 + 13/3*b**3 - 48/5*b**5 + 0*b. Factor c(l).
-l*(3*l + 2)*(4*l - 1)**2
Let p(k) be the first derivative of k**6/30 - k**5/60 - 3*k**4/2 + 3*k**3/2 + k**2/2 + 7*k - 234. Let w(o) be the second derivative of p(o). Factor w(s).
(s - 3)*(s + 3)*(4*s - 1)
Let d(f) be the second derivative of 1/13*f**4 + 1 + 8/13*f**2 + 1/130*f**5 + 14*f + 4/13*f**3. Solve d(a) = 0 for a.
-2
Factor 24*w - 42*w**2 - 3*w**4 + 2409*w**3 - 790*w**3 - 796*w**3 - 802*w**3.
-3*w*(w - 4)*(w - 2)*(w - 1)
Let f(w) be the first derivative of -w**4/4 - 1001*w**3 - 3006003*w**2/2 - 1003003001*w + 6960. Factor f(d).
-(d + 1001)**3
Let n(h) = -2*h - 7. Let i(c) = 2*c**4 - 6*c**3 - 6*c**2 + 12*c - 47. Let s(y) = i(y) - 5*n(y). Solve s(p) = 0.
-2, 1, 3
Let o(f) be the second derivative of 45*f**7/14 - 45*f**6/2 - 9*f**5/2 + 245*f**4/6 - 205*f**3/6 + 25*f**2/2 + 10*f + 93. Factor o(g).
5*(g - 5)*(g + 1)*(3*g - 1)**3
Let p(h) be the second derivative of h**4/18 - 466*h**3/9 + 54289*h**2/3 - 29*h + 6. Factor p(s).
2*(s - 233)**2/3
Let v(f) be the third derivative of f**7/630 - 7*f**6/72 + 11*f**5/5 - 18*f**4 - 96*f**3 - 906*f**2. Factor v(i).
(i - 12)**3*(i + 1)/3
Let u(a) be the third derivative of -a**6/120 - 13*a**5/60 - 5*a**4/8 - 17*a**3/6 + a**2. Let x be u(-12). Factor x*q + 25*q - 42*q + 2*q**2 - 4.
2*(q - 1)*(q + 2)
Solve 3/2*k**5 - 1653*k**2 - 12*k**4 - 1575 - 5835/2*k - 324*k**3 = 0 for k.
-5, -2, -1, 21
Let w(q) = -q**2 + 92*q - 1945. Let r be w(59). Let l(u) be the second derivative of 1/12*u**4 + 0 - 1/6*u**3 + 33*u - u**r. Determine c so that l(c) = 0.
-1, 2
Suppose -24301 + 24989 = 43*g. Suppose 0*u + 16*u**2 + 1/2*u**5 + g*u**3 + 5*u**4 + 0 = 0. What is u?
-4, -2, 0
Let a(d) be the third derivative of 1/24*d**4 - 1/60*d**5 + 2*d**2 + 0*d + 1/3*d**3 + 15. Factor a(v).
-(v - 2)*(v + 1)
Let f(d) = 5*d**2 + 163*d - 1404. Let p(q) = -5*q**2 - 162*q + 1406. Let n(k) = 3*f(k) + 2*p(k). Solve n(v) = 0.
-40, 7
Let m(f) be the first derivative of f**6/30 - 3*f**5/25 - 7*f**4/20 + 7*f**3/15 + 9*f**2/5 + 8*f/5 + 1009. Factor m(b).
(b - 4)*(b - 2)*(b + 1)**3/5
Let c = 40 + -16. Let b = 49 - c. Find g such that -15*g**5 - 21*g**4 - 16*g**4 - b*g**4 + 52*g**4 = 0.
-2/3, 0
Let d(g) = 12*g**4 - 8*g**3 - 62*g**2 + 130*g + 4. Let s(f) = 4*f**4 + f**2 + f + 2. Let o(x) = d(x) - 2*s(x). Factor o(c).
4*c*(c - 4)*(c - 2)*(c + 4)
Let s = 20334 - 20329. Let c(f) be the third derivative of 0 + 1/120*f**6 - 1/36*f**s + 0*f**3 - 1/36*f**4 + 0*f - 5*f**2. Solve c(h) = 0.
-1/3, 0, 2
Let h(u) be the third derivative of 0 + 1/180*u**5 + 14*u + 1/360*u**6 - 1/8*u**4 - u**2 - 1/2*u**3. Factor h(v).
(v - 3)*(v + 1)*(v + 3)/3
Let t(w) be the third derivative of -1/300*w**6 - w - 4*w**2 + 7/15*w**3 + 1/60*w**4 - 7/150*w**5 + 0. Factor t(b).
-2*(b - 1)*(b + 1)*(b + 7)/5
Determine m so that 22/7*m**3 + 0 - 62/7*m**4 + 22/7*m**2 - 12/7*m + 30/7*m**5 = 0.
-3/5, 0, 2/3, 1
Factor -4*v**4 + 2472*v**2 - 629*v + 848 - 1051*v - 2629*v**2 - 192*v**3 + 1185*v**2.
-4*(v - 2)**2*(v - 1)*(v + 53)
Let t(o) be the third derivative of o**6/160 + o**5/80 + 659*o**2. Suppose t(q) = 0. What is q?
-1, 0
Let h be (-517)/2585*(-2 - -1). Factor -1/5*m**2 + h + 0*m.
-(m - 1)*(m + 1)/5
Let b(f) = -5*f**3 - f**2 - 293*f - 293. Let u be b(-1). Factor 10/3*t - u + 2/3*t**2.
2*(t - 1)*(t + 6)/3
Let p(i) be the first derivative of -i**6/15 - 4*i**5/25 + 4*i**4/5 + 32*i**3/15 - 16*i**2/5 - 64*i/5 - 1397. Find o, given that p(o) = 0.
-2, 2
Let i be 9812/223 + 10 + -54. What is t in i - 4/9*t**3 - 40/9*t**2 + 44/9*t = 0?
-11, 0, 1
Let y(g) be the third derivative of -g**6/720 + 901*g**5/40 - 2435403*g**4/16 + 2194298103*g**3/4 - 372*g**2 - 2*g. Factor y(f).
-(f - 2703)**3/6
Let -20*b + 37*b**2 + 53/9*b**3 + 0 + 2/9*b**4 = 0. What is b?
-15, -12, 0, 1/2
Let k(h) = -525 - 72 - 354 - 137*h + 68 + h**2 + 27. Let s be k(-6). Solve 15/2*f**3 - 111/2*f**s + 93/2*f + 21/2*f**4 - 9 = 0 for f.
-3, 2/7, 1
Let h(i) be the first derivative of 2/3*i**2 + 49 - 2/9*i**3 - 2/3*i. Factor h(t).
-2*(t - 1)**2/3
Let l(m) = 63*m - 626. Suppose 2*k - s - 25 = 0, 46*k + 25 = 51*k + 5*s. Let r be l(k). Factor -3/4*h + 0 - 3/2*h**3 + 25/8*h**2 - 7/8*h**r.
-h*(h - 1)*(h + 3)*(7*h - 2)/8
Let k(i) = 6*i**4 - 34*i**3 - 56*i**2 + 386*i - 452. Let n(r) = 2*r**4 - 11*r**3 - 19*r**2 + 129*r - 150. Let c(w) = 6*k(w) - 20*n(w). Factor c(o).
-4*(o - 3)**2*(o - 2)*(o + 4)
Let n = 59006/5 + -11801. Let g(q) be the second derivative of -33*q + 0 + 2/25*q**5 + 1/15*q**4 - n*q**3 - 1/105*q**7 - 2/5*q**2 + 0*q**6. Solve g(y) = 0.
-1, 1, 2
Let r(n) = -11*n**3 + 224*n**2 - 121*n - 157. Let y(m) = 16*m**3 - 336*m**2 + 184*m + 236. Let g(l) = -20*r(l) - 13*y(l). Solve g(s) = 0.
-2/3, 1, 9
Suppose 3*u - 17 = 4*q - 52, -36*q = u - 399. Determine x so that 6/7 + 33/7*x**3 - 27/7*x**4 - 33/7*x + u*x**2 = 0.
-1, 2/9, 1
What is w in -1372/3*w + 0 + 1/3*w**3 + 457*w**2 = 0?
-1372, 0, 1
Let r be 8/(-72 - -8)*-16. Let q(h) be the first derivative of 11 - 1/48*h**6 + 5/16*h**r - 1/8*h**4 + 1/12*h**3 - 1/10*h**5 + 1/4*h. Factor q(v).
-(v - 1)*(v + 1)**3*(v + 2)/8
Let p(c) be the first derivative of 2*c - 2/9*c**3 + 73 - 2/3*c**2. Find t, given that p(t) = 0.
-3, 1
Let p = -45951/28 + 11500/7. Factor 5/2 + 1/4*j**2 - p*j.
(j - 5)*(j - 2)/4
Let k = 152 - 118. Let p be (-4)/k + (-7)/476*-8. Factor p + 4/13*y - 2/13*y**2.
-2*y*(y - 2)/13
Suppose 2627 = 583*g - 11365. Factor -6272 - g*t**2 + 672*t + 2/7*t**3.
2*(t - 28)**3/7
Suppose -956*j - 2*m = -958*j + 28, -4*j - 4*m = 40. Solve 2/3*z**3 - j - 2/3*z**2 - 10/3*z = 0.
-1, 3
Suppose -6*s - 2 = -8*s - 2*l, s - l = 3. Factor 2 - 4*v + 8*v**s - 28*v**3 + 32*v**3 - 10.
4*(v - 1)*(v + 1)*(v + 2)
Let z(s) = 371*s + 203. Let d be z(2). Let q be (-4)/18 + 2640/d. Factor -q + 0*i + 2/7*i**2.
2*(i - 3)*(i + 3)/7
Let n = -363/20 - -297/5. Let t = n + -327/8. Factor -t*b**3 + 3/4*b + 0 + 3/8*b**2.
-3*b*(b - 2)*(b + 1)/8
Suppose -5*f - t + 9 = 0, -t - 3*t = -3*f - 13. Let s(v) = -7*v**2 - 6*v - 3. Let l(u) = -2*u**2 - u. Let y(b) = f*s(b) - 4*l(b). Factor y(c).
(c - 3)*(c + 1)
Let o(z) be the first derivative of -17/7*z**2 + 0*z - 38 + 2/21*z**3. Factor o(l).
2*l*(l - 17)/7
Let d(s) be the first derivative of 0*s + 0*s**2 + 11/2*s**6 - 138/5*s**5 + 39*s**4 - 8*s**3 + 68. Factor d(b).
3*b**2*(b - 2)**2*(11*b - 2)
Suppose -4*d + 118 = 2*y, 4*y + 43 = d + 9*y. Let w be (50/35 + d/49)/1. Find h, given that 40/3*h + 14/3*h**3 + 16/3 - 52/3*h**w = 0.
-2/7, 2
Suppose 16*a + 25*a + 2 = 42*a. Let n(w) be the second derivative of -5/18*w**3 + 0 + 1/60*w**5 + 1/2*w**a - 14*w + 1/36*w**4. Let n(s) = 0. What is s?
-3, 1
Let c be (-4)/10 + 3*(-1461)/(-45). Let f = -82 + c. Suppose f*v**4 - 25*v**3 + 5*v + 27*v**2 - 9*v**2 - 13*v**2 = 0. Calculate v.
-1/3, 0, 1
Let s(y) be the second derivative of y**6/120 - 9*y**5/20 + 129*y**4/16 - 140*y**3/3 + 96*y**2 - 109*y + 2. Let s(m) = 0. What is m?
1, 3, 16
Let w(j) be the third derivative of -1 - 5/12*j**6 + 25/2*j**4 + 0*j + 13/12*j**5 + 28*j**2 + 1/42*j**7 + 30*j**3. Factor w(n).
5*(n - 6)**2*(n + 1)**2
Let v(k) be the second derivative of 3*k**5/100 + 31*k**4/10 - 64*k**3/5 - 1628*k. Factor v(o).
3*o*(o - 2)*(o + 64)/5
Let o(h) be the first derivative of 2*h**3/51 - 756*h**2/17 + 285768*h/17 + 1769. Factor o(y).
2*(y - 378)**2/17
Let u(i) be the second derivative of i**5/60 + i**4/8 - 2*i**3/3 + 61*i**2/2 + 2*i + 35. Let b(k) be the first derivative of u(k). Factor b(v).
(v - 1)*(v + 4)
Let u(o) be the second derivative of o**5/90 + 8*o**4/9 - 11*o**3/3 + 50*o**2/9 + 279*o. Let u(b) = 0. What is b?
-50, 1
Determine m so that -17/2*m**2 + 15*m + 1/2*m**3 + 0 = 0.
0, 2, 15
Let t = 215 - 207. Factor 4047*i - 6*i**