 - 1/75*b**6 + 1/210*b**7 + 0*b**2 + 0*b**3 + 1/100*b**5. Factor u(l).
l**3*(l - 1)**2/5
Suppose 36728*s = 36867*s - 278. Determine j, given that -j**s - 1/3*j**3 + 3*j - 5/3 = 0.
-5, 1
Suppose -7221*i - 52 = -7247*i. Let t(s) be the third derivative of 0*s**3 - 1/8*s**5 + 0*s**4 + 0*s + 0 + 19*s**i - 1/48*s**6. Factor t(o).
-5*o**2*(o + 3)/2
Determine g so that -4/5*g**2 + 0 + 148/5*g = 0.
0, 37
Let p(m) be the first derivative of -15*m**4/32 - 241*m**3/8 - 9*m**2 + 2113. Find b such that p(b) = 0.
-48, -1/5, 0
Let y = 425701/150 + -2838. Let w(k) be the second derivative of -y*k**6 - 2/15*k**3 - 1/10*k**4 - 8*k + 4/5*k**2 + 1/20*k**5 + 0. Factor w(s).
-(s - 2)**3*(s + 1)/5
Factor 50/7*u**2 - 2/7 + 26/7*u**3 + 22/7*u.
2*(u + 1)**2*(13*u - 1)/7
Let z be (-130)/(-10) - 52/4. Let s(u) be the third derivative of z*u + 5/78*u**4 + 1/390*u**5 + 14*u**2 + 0 + 25/39*u**3. Factor s(b).
2*(b + 5)**2/13
Let l(b) be the second derivative of -b**4/12 + 7*b**3/24 - 3*b**2/8 - 2020*b. Let l(r) = 0. Calculate r.
3/4, 1
Suppose 0 = 25*u - 222 + 47. Factor -5*k**3 - 10*k**2 - 40*k + 60 + 3*k**3 - 15*k**2 + u*k**3.
5*(k - 6)*(k - 1)*(k + 2)
Factor -51/4*g**4 + 243*g**2 + 3/8*g**5 + 0*g + 189/2*g**3 + 0.
3*g**2*(g - 18)**2*(g + 2)/8
Let i(w) be the third derivative of 0 + 44*w**2 - w**3 + 3/8*w**4 + 0*w - 1/40*w**6 + 0*w**5. Determine j so that i(j) = 0.
-2, 1
Factor 0 + 55/2*g**2 + 35/4*g + 30*g**3 + 5/4*g**5 + 25/2*g**4.
5*g*(g + 1)**3*(g + 7)/4
Factor 1254*x - 372*x + 514*x + 524*x - 3110018 + 3068*x - 2*x**2.
-2*(x - 1247)**2
Let z = 464 - 459. What is s in -4*s**z + 20*s**3 - 20*s**4 + 70*s**2 - 18*s**2 + 8*s**3 - 32*s**2 - 24*s = 0?
-6, -1, 0, 1
Let g(j) be the second derivative of 3/13*j**2 - 8/39*j**3 - 1/26*j**4 - j + 31. Factor g(h).
-2*(h + 3)*(3*h - 1)/13
Let z(s) be the third derivative of -s**10/272160 - s**9/68040 - s**8/60480 - 13*s**4/6 - 22*s**2. Let o(b) be the second derivative of z(b). Factor o(k).
-k**3*(k + 1)**2/9
Let u(p) be the second derivative of p**4/12 + 1175*p**3/3 + 1380625*p**2/2 - 2*p + 1269. Factor u(t).
(t + 1175)**2
Solve -272*p**3 - 1292 + 1516*p**2 - 105*p**3 + 748*p - 371*p**3 + 568 - 4*p**4 - 788 = 0.
-189, -1, 1, 2
Let b be (((-8200)/(-250))/(-41))/(55/(-75)). Let b*v + 6/11*v**4 + 0 + 30/11*v**2 + 24/11*v**3 = 0. What is v?
-2, -1, 0
Let o(a) be the first derivative of -66 + 12/7*a - a**2 + 2/21*a**3. Factor o(s).
2*(s - 6)*(s - 1)/7
Let h(w) = 7*w**2 - 11*w - 14. Let l = -104 + 100. Let i(g) = 2*g**2 + 1. Let z(b) = l*i(b) + h(b). What is x in z(x) = 0?
-9, -2
Factor 1080/11*j**2 + 4/11 + 24786/11*j**3 - 182/11*j.
2*(17*j + 2)*(27*j - 1)**2/11
Let k(q) be the second derivative of q**4/3 - 418*q**3/3 + 416*q**2 - 662*q. Factor k(n).
4*(n - 208)*(n - 1)
Let a(n) = -12*n**2 + 66*n - 19. Let p(v) = -2*v**2 + 13*v - 3. Let t(i) = -6*a(i) + 33*p(i). Factor t(c).
3*(c + 5)*(2*c + 1)
Factor -1/5*s**3 + 33/5*s**2 + 80 - 216/5*s.
-(s - 25)*(s - 4)**2/5
Let i = -20210 - -20212. Let d be (1 - 2)/((-2)/6). What is q in 2/9 - 2/9*q - 2/9*q**i + 2/9*q**d = 0?
-1, 1
Suppose -624 = 11*i + 2*i. Let z be (5/(-30))/(36/i). Factor 2/9 + z*m**2 - 4/9*m.
2*(m - 1)**2/9
Let p(k) be the first derivative of -k**6/9 - 16*k**5/5 - 125*k**4/6 + 108*k**3 + 1152*k**2 + 2880*k + 6395. Suppose p(x) = 0. What is x?
-12, -3, -2, 5
Let v = -174 - -178. Let m be (-2)/(1/((-6)/v)). Factor 1/6*c - 1/6*c**m + 1/3 - 1/3*c**2.
-(c - 1)*(c + 1)*(c + 2)/6
Let c(j) be the second derivative of -11/30*j**6 - 2*j - 13 + 1/42*j**7 - 15/2*j**4 + 27/2*j**3 + 23/10*j**5 - 27/2*j**2. Factor c(q).
(q - 3)**3*(q - 1)**2
Let s(l) be the first derivative of -27*l**7/140 - l**6/5 - l**5/15 + 29*l**3/3 + l**2/2 + 17. Let c(o) be the third derivative of s(o). Factor c(n).
-2*n*(9*n + 2)**2
Suppose 20 = -62*t + 66*t. Factor -15*h**3 - 7*h**5 + 17*h**t - 7*h**5 + h**5 - 16*h**2 + 0*h**2 - 4*h + 4*h**4.
h*(h - 2)*(h + 2)*(2*h + 1)**2
Let b(z) be the third derivative of -z**7/630 - z**6/360 + z**5/180 + z**4/72 + 182*z**2 - z. Let b(n) = 0. What is n?
-1, 0, 1
Suppose 2*u - 7*u - 2*k = -1715, -2*u - 4*k + 686 = 0. Let d = u - 683/2. What is l in 1/2*l**3 + d - 3/2*l**2 - 1/2*l = 0?
-1, 1, 3
Let l(q) be the second derivative of -q**6/195 - 7*q**5/65 - 10*q**4/13 - 24*q**3/13 + 971*q - 3. Factor l(n).
-2*n*(n + 2)*(n + 6)**2/13
Let m be 15/((-18)/(3 - 9)). Suppose -2*v + 27*s + 24 = 23*s, 30 = m*v - 4*s. Find p, given that -2*p**2 + 2/3*p**3 - 2/3 + v*p = 0.
1
Suppose 18 = -4*c + 3*t, 613*t - 618*t + 30 = -4*c. Solve c + 1/5*n**5 + 0*n**2 + 1/5*n**3 - 2/5*n**4 + 0*n = 0 for n.
0, 1
Let t = -292 + 297. Factor -15*y**4 + y**t - y**5 - 3*y**5 + 46*y**3 - 58*y**3.
-3*y**3*(y + 1)*(y + 4)
Let d(q) = 393*q + 77031. Let m be d(-196). Factor -5/3*f**m + 5/3 + 5/3*f - 5/3*f**2.
-5*(f - 1)*(f + 1)**2/3
Let y(r) = 9*r - 5. Let m be y(1). Suppose 2*f = k - 6, 3*k + 7*f + m = 2*f. Find a such that 0*a - 12*a + 6*a + 3*a**k + 3*a**3 = 0.
-2, 0, 1
Let v(m) = -22*m**3 + 80*m**2 + 599*m + 267. Let i(f) = 16*f**3 - 82*f**2 - 594*f - 268. Let w(n) = -6*i(n) - 4*v(n). Suppose w(p) = 0. Calculate p.
-5, -1/2, 27
Suppose 0 = -9*g + 10*g + 9. Let c be ((-48)/g)/((-8)/(-12)). Factor r + c + 2*r**2 - 3*r - 4 + 8*r.
2*(r + 1)*(r + 2)
Let -1/2*y**2 - 306*y - 46818 = 0. What is y?
-306
Let l(m) be the second derivative of -m**7/504 + m**5/24 - m**4/2 + 26*m + 1. Let i(s) be the third derivative of l(s). Suppose i(x) = 0. Calculate x.
-1, 1
Let p(i) be the second derivative of i**5/25 + 133*i**4/30 - 73*i**3/15 - 402*i**2/5 + 5807*i. Factor p(j).
2*(j - 2)*(j + 67)*(2*j + 3)/5
Suppose 12*i - 1476 = -4*w, -10*i + 4*w = -14*i + 452. Factor 144*t - 33/2*t**2 - i + 1/2*t**3.
(t - 16)**2*(t - 1)/2
Let t be ((-18)/(-60))/(84/260750). Let r = t + -931. Factor 3/4*a**2 - a + 0 + r*a**3.
a*(a - 1)*(a + 4)/4
Let x = 201609 - 201607. Solve -n**3 + 0 + 3*n**x - 5/3*n - 1/3*n**4 = 0 for n.
-5, 0, 1
Let x be (-4)/(-22) + (-84)/(-1232). Let w be 1/4*((-9)/(-63) + (-69)/(-7)). Factor 27/2*z**2 + x*z**5 + 27/4*z + w*z**4 + 9*z**3 + 0.
z*(z + 1)*(z + 3)**3/4
Let b(d) = 9*d**3 + 2*d**2 - 15*d + 7. Let a be b(3). Suppose -8*x + 239 = a. Suppose -3/4*v**3 - 3/2*v**x + 3/2 + 3/4*v = 0. Calculate v.
-2, -1, 1
Determine n, given that 1188025/8*n**2 + 1/2 + 911250*n**4 + 732375*n**3 + 1085/2*n = 0.
-2/5, -1/540
Let q(k) be the first derivative of 0*k + 22*k**2 + 4/3*k**3 + 28. Factor q(m).
4*m*(m + 11)
Let f(m) be the first derivative of 4/9*m**3 + 0*m - 52 - 86/3*m**2. Factor f(a).
4*a*(a - 43)/3
Suppose 92 = -v - 104. Let c be 3/7 - 504/v. Factor 1/5*d**c - 4/5 + 3/5*d**2 + 0*d.
(d - 1)*(d + 2)**2/5
Let c be (-16 - (-1188)/77)/((-2)/28). Suppose -4*w - 4*a = -c, -w + a - 4*a = -2. Factor -40*t**w - 8/3 - 56/3*t + 125/6*t**4 - 50/3*t**3.
(t - 2)*(5*t + 2)**3/6
Solve 1721*w - 430*w - 3*w**2 - 714 + 368 - 1571 + 629*w = 0.
1, 639
Let l(y) be the second derivative of -7*y**6/165 - 8*y**5/55 + y**4/22 + 16*y**3/33 + 4*y**2/11 + 674*y. Suppose l(x) = 0. Calculate x.
-2, -1, -2/7, 1
Find v, given that -4*v - 452*v**2 - 8237*v**3 + 182 + 8241*v**3 + 270 = 0.
-1, 1, 113
Factor 0*x + 0 + 0*x**3 - 67/4*x**4 + 1/4*x**5 + 0*x**2.
x**4*(x - 67)/4
Factor -1/2 - 29/8*g - 7/8*g**2.
-(g + 4)*(7*g + 1)/8
What is d in -29/2*d**2 + 65/4 + 1/4*d**5 - 7/4*d**4 + 73/4*d - 37/2*d**3 = 0?
-5, -1, 1, 13
Let i(r) = 7 - 260*r + 241*r - 1. Let j be i(0). Factor 0 + j*c**2 + 14/3*c**4 + 2/3*c**5 + 10*c**3 + 0*c.
2*c**2*(c + 1)*(c + 3)**2/3
Let c(n) be the first derivative of -17*n**4/24 - 83*n**3/18 + 5*n**2/6 - 13967. Solve c(j) = 0 for j.
-5, 0, 2/17
Let t = -73/33 + 52699/23793. Let j = t - -8618/12257. Find r such that -14/17*r + 2/17*r**2 + j = 0.
1, 6
Factor 27*h**2 - 6435 - 21*h + 6411 + 194*h**3 - 173*h**3 - 3*h**4.
-3*(h - 8)*(h - 1)*(h + 1)**2
Let j(c) be the first derivative of -c**9/756 - c**8/105 - c**7/70 - 151*c**3/3 - 44. Let v(q) be the third derivative of j(q). Factor v(d).
-4*d**3*(d + 1)*(d + 3)
Suppose -2893*n - 4866 + 5017 = -17816 - 5177. Factor -n*z + 32 - 2*z**2 + 1/2*z**3.
(z - 4)**2*(z + 4)/2
Let t = 348 + -366. Let n be 60/(-150)*(0 - (-10)/t). Factor -n*u**2 + 0 - 2/9*u.
-2*u*(u + 1)/9
Let n = 6942 - 41651/6. Let r(j) be the second derivative of 0 + 21*j + 1/40*j**5 + 0*j**2 - n*j**3 + 1/24*j**4. Factor r(s).
s*(s - 1)*(s + 2)/2
Le