2/9, 1/2
Let a be (2419/(-738)*9 - -30)*(-6)/(-7). Determine j so that -7500/7 - 300/7*j - a*j**2 = 0.
-50
Let x(n) be the first derivative of -n**4/4 - 23*n**3/2 - 63*n**2 + 305*n - 218. Let w(y) be the first derivative of x(y). Factor w(c).
-3*(c + 2)*(c + 21)
Let s = 101512/118433 + 2/118433. Suppose -2/7*y**3 - 4/7*y - s*y**2 + 0 = 0. What is y?
-2, -1, 0
Factor -15/2*h**2 + 93/2 - 1/4*h**3 + 37/4*h.
-(h - 3)*(h + 2)*(h + 31)/4
Let k(y) be the third derivative of -y**5/30 + 97*y**4/12 - 32*y**3 + 428*y**2 - 3*y + 1. Factor k(t).
-2*(t - 96)*(t - 1)
Factor 5751*k - 14*k**3 - k**4 + 5732*k - 25*k**2 - 11495*k.
-k*(k + 1)**2*(k + 12)
Let j(f) be the first derivative of -f**5/3 + 325*f**4/12 - 1535*f**3/9 + 705*f**2/2 - 300*f - 7122. Suppose j(h) = 0. Calculate h.
1, 3, 60
Let s(m) be the first derivative of m**4/2 + 562*m**3/3 + 19599*m**2 - 39762*m + 1196. Factor s(f).
2*(f - 1)*(f + 141)**2
Let 54*x**2 + 2*x**3 + 264 + 223*x + 126*x - 117*x = 0. What is x?
-22, -3, -2
Let -1404/7*r + 1402/7 + 2/7*r**2 = 0. Calculate r.
1, 701
Let o(i) be the third derivative of i**7/1680 + i**6/720 - i**5/120 + 42*i**3 + 45*i**2. Let m(j) be the first derivative of o(j). Find p, given that m(p) = 0.
-2, 0, 1
Let j(d) be the first derivative of -d**6/33 - 112*d**5/55 + 299*d**4/22 - 740*d**3/33 - 236*d**2/11 + 976*d/11 + 1491. Find a, given that j(a) = 0.
-61, -1, 2
Let f(v) = 30*v**2 - 121*v - 292. Let p(r) = 51*r**2 - 201*r - 486. Let t(c) = -12*f(c) + 7*p(c). Determine b, given that t(b) = 0.
-2, 17
Suppose a - 4*x + 40 = 0, -5*a - 17890*x + 17895*x = 35. Find b such that 0*b**3 + 0*b**2 + 0*b + 0 + 4/7*b**5 - 4/7*b**a = 0.
0, 1
Let g = -161 + 157. Let m(l) = 22*l**2 + 89*l + 8. Let k be m(g). Factor 10/11*i**3 - 2/11*i**2 - 8/11*i**k + 0 + 0*i.
-2*i**2*(i - 1)*(4*i - 1)/11
Let d(t) be the first derivative of -7*t**2 + 0*t - 1/24*t**4 - 1/4*t**3 + 1/120*t**5 + 5. Let l(n) be the second derivative of d(n). Factor l(u).
(u - 3)*(u + 1)/2
Let v(w) be the first derivative of -w**6/24 + 7*w**5/20 + 9*w**4/8 + w**3/6 - 17*w**2/8 - 9*w/4 + 153. Find z, given that v(z) = 0.
-1, 1, 9
Let o(m) be the first derivative of -m**4 - 268*m**3/3 - 262*m**2 - 260*m - 6678. Suppose o(i) = 0. Calculate i.
-65, -1
Suppose 5*h - 20 = -5*x, 3*x + 20 = -h + 8*x. Suppose 14*f - 9*f - 125 = h. Solve -10*y**4 - 57*y**2 - 34*y**3 - 8*y - 3 + 3 + f*y**2 = 0.
-2, -1, -2/5, 0
Suppose 8*o + 6 + 2 = 0. Let a be (o + -2)*(33/(-22) - 2). Solve 21/2*y**4 + 0 - a*y**3 - 3*y**5 + 0*y + 3*y**2 = 0 for y.
0, 1/2, 1, 2
Let q(l) = l**3 - 15*l**2 - 8*l - 69. Let v be q(15). Let o be 6 - 16/(576/v). What is j in 0 + 0*j - o*j**2 - 5/4*j**4 - 15/2*j**3 = 0?
-3, 0
Suppose 67*a = 78*a. Let u(d) be the second derivative of 1/3*d**4 - 2*d + 3/10*d**5 + a + 0*d**2 + 0*d**3. Determine j, given that u(j) = 0.
-2/3, 0
Let z = 21 - 16. Let b = z + -5. Determine d, given that -4*d**2 + 2*d + 5*d**2 + b*d - 2*d**2 = 0.
0, 2
Solve 104*x + x**4 + 142*x + 53*x**3 + 77*x**3 + 44*x + 425*x**2 - 6*x**4 = 0 for x.
-2, -1, 0, 29
Let b(u) be the first derivative of -5/3*u**3 + 0*u - 25/2*u**2 + 47. Solve b(k) = 0.
-5, 0
Determine j, given that 398/9*j + 2/9*j**3 + 404/9*j**2 - 268/3 = 0.
-201, -2, 1
Let w = 568/521 - 1751/2084. Factor 0 - 1/4*j**4 + 1/2*j**3 + w*j**2 - 1/2*j.
-j*(j - 2)*(j - 1)*(j + 1)/4
Let a(q) be the third derivative of q**8/1008 - q**7/315 - q**6/18 + 31*q**5/90 - 61*q**4/72 + 10*q**3/9 - 1593*q**2 - q - 1. Determine d so that a(d) = 0.
-5, 1, 4
Let b(u) be the first derivative of -u**5/5 + 33*u**4/4 - 136*u**3 + 1120*u**2 - 4608*u - 564. Determine t, given that b(t) = 0.
8, 9
Let y be (-82 - -83)*(0 + 80)/(-2). Let t = y + 45. What is c in 68/9*c**2 + 4/3*c + 112/9*c**4 + 32/9*c**t + 0 + 136/9*c**3 = 0?
-3/2, -1, -1/2, 0
Factor -80*z**3 - 14*z**3 - 20*z**2 + 32*z**2 + 81*z**2 + z**4.
z**2*(z - 93)*(z - 1)
Solve -28*j**2 - 98*j**2 - 276*j**2 - 7*j**3 + 4*j**3 + 405*j = 0.
-135, 0, 1
Let i(u) = u**2 - 62*u + 795. Let n be i(18). Let -7/4*a**2 - 1/4*a**n - 3 - 4*a = 0. What is a?
-3, -2
Let t(j) be the first derivative of j**5/35 - 31*j**4/28 + 85*j**3/7 - 225*j**2/14 + 4315. Factor t(w).
w*(w - 15)**2*(w - 1)/7
Factor 236 - 3*y**2 - 714 + 238 + 240 - 5319*y.
-3*y*(y + 1773)
Let p be 2/(-76)*2834/(-327) + (-6)/(-57). Factor -5/3*n + p*n**2 + 0.
n*(n - 5)/3
Let r = 2/119 + -1692/1547. Let o = 8/65 - r. Factor -4/5*p**2 + 2/5*p**5 + 0 + 0*p**4 + 0*p - o*p**3.
2*p**2*(p - 2)*(p + 1)**2/5
Let h(f) = -11*f**2 - 43*f + 9. Let r be h(-4). Suppose 5*l**r - 8*l - 8*l**4 + 10*l**2 - 14*l - 7*l + 24*l - 2*l**4 = 0. Calculate l.
-1, 0, 1
Let t(u) be the third derivative of 23/40*u**4 - 1/25*u**6 - 11*u + 9*u**2 + 0 - u**3 + 1/560*u**8 - 1/10*u**5 + 2/175*u**7. Determine a so that t(a) = 0.
-5, -2, 1
Let y(s) be the second derivative of -s**6/180 + s**5/12 + s**4/2 + 47*s**3/6 - 11*s. Let u(d) be the second derivative of y(d). Factor u(w).
-2*(w - 6)*(w + 1)
Let h(f) be the third derivative of 0*f**3 + 1/120*f**6 - 1/10*f**5 - 88*f**2 + 0 + 5/24*f**4 + 0*f. Let h(m) = 0. What is m?
0, 1, 5
Suppose 646 - 1010 = -555*j + 746. Determine s, given that 0 + 3/2*s**5 - 6*s**j + 4*s**3 + 0*s + 13/2*s**4 = 0.
-3, -2, 0, 2/3
Let k(j) be the first derivative of -4*j + 76 - 1/3*j**3 + 2*j**2. Factor k(u).
-(u - 2)**2
Let u(b) be the second derivative of 25*b**4/12 + 4670*b**3/3 - 1870*b**2 + 5794*b. Solve u(k) = 0.
-374, 2/5
Let j(m) be the third derivative of m**6/210 - 2*m**5/15 - 5*m**4/14 - 496*m**2 + 2. Factor j(d).
4*d*(d - 15)*(d + 1)/7
Let h = 7236 + -7212. Let d(t) be the first derivative of -h - 3/5*t**5 + 0*t - 3/4*t**4 + 0*t**2 + t**3 + 1/2*t**6. Let d(n) = 0. Calculate n.
-1, 0, 1
Suppose -2 + 8 = 2*b + 2*v, -38*v = -7 - 107. Let -y**2 + 1/3*y**3 + b - 4/3*y = 0. Calculate y.
-1, 0, 4
Factor 1135*k + 5/2*k**2 - 2275/2.
5*(k - 1)*(k + 455)/2
Suppose -26 = 7*l + 107. Let o(b) = 19*b + 364. Let s be o(l). Find j, given that 53/10*j**2 + 21/10*j + 27/10*j**s - 9/10 + 2/5*j**4 = 0.
-3, -1, 1/4
Let h(o) be the third derivative of 1/315*o**7 + 0*o**3 + 37*o**2 - 1/144*o**4 + 0*o - 1/2016*o**8 + 1/90*o**5 + 0 - 1/120*o**6. Solve h(s) = 0 for s.
0, 1
Let h(u) be the first derivative of -u**3/12 + 11*u**2/2 - 43*u/4 + 141. Factor h(r).
-(r - 43)*(r - 1)/4
Let q be (19*-1)/(168/2268). Let l = 257 + q. Factor 5/2*u**3 + 3/2*u + 0 + 7/2*u**2 + l*u**4.
u*(u + 1)**2*(u + 3)/2
Let z(q) be the second derivative of 1/120*q**4 + 0 - 3/20*q**2 - 23*q + 1/30*q**3. Factor z(s).
(s - 1)*(s + 3)/10
Let a(q) be the second derivative of q**4/36 - 175*q**3/3 - 299*q + 1. Find o such that a(o) = 0.
0, 1050
Let z = 401739 + -401736. Determine m so that 1/4*m**z - 5/4*m**2 - 1/8*m + 5/8 + 5/8*m**4 - 1/8*m**5 = 0.
-1, 1, 5
Let t be 20/8*(2*-1 - 0). Let a(o) = 12*o**2 + 11*o + 7. Let q(x) be the first derivative of x**3/3 + x**2/2 + x + 12. Let r(c) = t*a(c) + 35*q(c). Factor r(l).
-5*l*(5*l + 4)
Let x(d) = -d**3 - 9*d**2 - 66*d - 44. Let u be x(-19). Factor -u + 7*g**2 + 65*g - 2400 + 315*g - 12*g**2.
-5*(g - 38)**2
Let c(h) be the second derivative of -5/6*h**3 - 18 + 2*h + 45/2*h**2 + 1/4*h**5 - 15/4*h**4. Find i such that c(i) = 0.
-1, 1, 9
Let u(j) be the second derivative of 28/9*j**3 - 4/3*j**2 - 35/18*j**4 + 11/30*j**5 + 0 - 76*j. Factor u(n).
2*(n - 2)*(n - 1)*(11*n - 2)/3
Let t(x) be the first derivative of x**5/5 + 143*x**4/4 - 145*x**3 + 437*x**2/2 - 146*x + 2918. Factor t(s).
(s - 1)**3*(s + 146)
Let b be 3 - 4 - -8 - (-135)/(-30). Let t(c) be the third derivative of 10*c**2 + 0 - 1/12*c**5 + b*c**3 + 0*c - 5/12*c**4. Factor t(u).
-5*(u - 1)*(u + 3)
Factor 2532*q**3 + 3*q**4 + 288*q**2 - 5132*q**3 + 2534*q**3 + 864*q.
3*q*(q - 12)**2*(q + 2)
Let i(z) be the first derivative of z**3/9 + 13*z**2/6 - 66*z + 8192. Factor i(n).
(n - 9)*(n + 22)/3
Find l, given that -76/5*l**3 + 0 - 104/5*l**2 - 48/5*l - 22/5*l**4 - 2/5*l**5 = 0.
-6, -2, -1, 0
Let t(r) = -32*r**2 - 4*r - 10. Let o(j) = -10*j**2 - 2*j - 3. Let n(l) = 10*o(l) - 3*t(l). Factor n(x).
-4*x*(x + 2)
Let v(j) be the second derivative of -j**6/10 + 9*j**4/4 - 2*j**3 - 18*j**2 - 3*j + 129. Factor v(u).
-3*(u - 2)**2*(u + 1)*(u + 3)
Let t = -3430 + 6861/2. Let i(g) be the first derivative of 1/2*g**3 + t*g**2 + 1/20*g**5 + 18 + 1/4*g + 1/4*g**4. Suppose i(m) = 0. Calculate m.