second derivative of -l**5/10 - 10*l**4/3 + 7*l**3 - 2330*l. Determine d, given that u(d) = 0.
-21, 0, 1
Let m = 2450 + -1461. Let y = 989 - m. Determine u, given that -32/9*u - 4/9*u**2 + y = 0.
-8, 0
Find h, given that -3/8*h**2 + 9/2*h - 15/2 = 0.
2, 10
Suppose 5*a = -4*t + 6, 4*t + 2*a - 5 - 7 = 0. Let c(v) = -v**3 + 4*v**2 + 3*v. Let j be c(t). Let -j*b - 51 - 46 + 97 + 4*b**2 = 0. What is b?
0, 3
Suppose 37338 = m + 3*j, -8*m + 5*m = -3*j - 112074. Let r = m + -258015/7. Find d, given that r - 2/7*d**3 - 864/7*d + 72/7*d**2 = 0.
12
Let j be 14/(-6) - (-42)/18. Let a(h) be the third derivative of -3/5*h**3 + 11/40*h**4 - 9*h**2 + 0 + j*h - 3/100*h**5. Factor a(y).
-3*(y - 3)*(3*y - 2)/5
Let a(h) be the first derivative of h**3/33 + 23*h**2/22 + 2*h - 604. Factor a(l).
(l + 1)*(l + 22)/11
Let s(t) be the third derivative of 0*t**3 - 109*t**2 - 1/15*t**5 + 0*t + 0*t**4 + 0 + 1/30*t**6. Factor s(b).
4*b**2*(b - 1)
Let h = 4094924/15 + -1364973/5. Factor -2/3*t**2 + 1/3*t**5 + 0*t + 0 + 2/3*t**4 - h*t**3.
t**2*(t - 1)*(t + 1)*(t + 2)/3
Let t(m) = m**4 - 39*m**3 + 367*m**2 - 609*m + 286. Let d(x) = x**4 - 40*x**3 + 370*x**2 - 608*x + 285. Let h(y) = 3*d(y) - 4*t(y). Factor h(q).
-(q - 17)**2*(q - 1)**2
Let w(c) be the third derivative of -c**8/112 + c**7/35 + c**6/20 - c**5/5 - c**4/8 + c**3 + 121*c**2 - 2*c. Determine y, given that w(y) = 0.
-1, 1, 2
Let c(z) be the first derivative of z**6/2 - 99*z**5/20 - 39*z**4/4 + 365*z**3/2 + 225*z**2 - 66*z - 33. Let r(n) be the first derivative of c(n). Factor r(f).
3*(f - 5)**2*(f + 3)*(5*f + 2)
Let u(w) be the second derivative of -7*w**4/72 + 145*w**3/36 + 7*w**2/2 - 694*w. Factor u(g).
-(g - 21)*(7*g + 2)/6
Let t(u) = 2*u**2 - 4*u + 9. Let x be t(4). Let d = 31 - x. Factor l**3 + d*l - 3*l - 7*l**3 + 3*l**5.
3*l*(l - 1)**2*(l + 1)**2
Suppose 2679 = -4*l + 3179. Factor 5*p**2 + 54*p**3 - 53*p**3 + l*p + 44*p + 23*p**2 - 2*p**2.
p*(p + 13)**2
Let i(c) be the second derivative of 0 + 1/14*c**2 + 1/42*c**3 - 1/84*c**4 - 1/140*c**5 - 83*c. Find x such that i(x) = 0.
-1, 1
Solve 62/3 - 175*s - 17/3*s**2 = 0.
-31, 2/17
Let d(o) be the first derivative of -o**3/27 + 2018*o**2/9 - 4072324*o/9 + 7657. Let d(r) = 0. Calculate r.
2018
Let c(m) be the second derivative of -m**6/360 - m**5/30 - 5*m**3/6 - 4*m**2 + m - 23. Let t(v) be the second derivative of c(v). Let t(h) = 0. Calculate h.
-4, 0
Let w(o) be the second derivative of -3*o**5/140 + 5*o**4/14 - 23*o**3/14 + 3*o**2 - 5610*o. Factor w(i).
-3*(i - 7)*(i - 2)*(i - 1)/7
Suppose 8*l - 18 = 2*l. Factor -8*a**4 - 5*a**3 - 2*a**l + 11*a**4 - 2*a**3.
3*a**3*(a - 3)
Let z(j) = -4*j**2 - 6*j**4 - 5*j**5 + 5*j + 9*j**3 + 6*j**5 + 0*j**4 - 3*j - 4*j. Let o(g) = -g. Let k(h) = -2*o(h) + z(h). Factor k(s).
s**2*(s - 4)*(s - 1)**2
Suppose -20 = 3*c + 4*k - 23, 5*c + 2*k - 5 = 0. Suppose 0 = -j + c, -4*x + 10*j + 6 = 8*j. Find u such that 24/7*u**x - 2/7 - 32/7*u**4 - 8/7*u**3 - 2/7*u = 0.
-1, -1/4, 1/2
Suppose 0 = -3*g + 5*c - 4, -g + 3*c = -2*c + 8. Suppose -5*t + 13 = -g*t - 5*f, -5*t = -f - 7. Let -3*u**2 + t + 12*u - 3 + 2 = 0. Calculate u.
0, 4
Let -1/4*n**2 + 31/2*n - 817/4 = 0. Calculate n.
19, 43
Let g(m) be the second derivative of -m**6/105 - 204*m**5/7 - 260100*m**4/7 - 176868000*m**3/7 - 67652010000*m**2/7 - 804*m. Factor g(j).
-2*(j + 510)**4/7
Let l(m) be the first derivative of -1/3*m**3 + 0*m**2 - 1/6*m**4 - 218 + 1/3*m. Suppose l(w) = 0. What is w?
-1, 1/2
Factor 3*o**2 - 3612 + 2864*o - 10642*o + 4169*o.
3*(o - 1204)*(o + 1)
Let n(l) be the first derivative of -5*l**4/12 + 5*l**3/3 + 75*l**2/2 - 43*l + 74. Let w(h) be the first derivative of n(h). Factor w(p).
-5*(p - 5)*(p + 3)
Let s be -12 - (17 + -54) - 88/4. Factor -93312/11 - 7776/11*c - 2/11*c**s - 216/11*c**2.
-2*(c + 36)**3/11
Let w(c) = 152*c - 11. Let a be w(1). Factor -144 + 467*x - 5181 + a - 4*x**2 - 179*x.
-4*(x - 36)**2
Suppose 2*v - 5*v = 0. Let x be 1/((-3)/(-36)) - (135/6 - 12). Solve x*j**4 + v - 3*j**3 + 3*j - 3/2*j**2 = 0 for j.
-1, 0, 1, 2
Let c(g) be the second derivative of 5*g**7/42 - g**6/2 - g**5/4 + 55*g**4/12 - 10*g**3 + 10*g**2 - 777*g. Factor c(r).
5*(r - 2)*(r - 1)**3*(r + 2)
Suppose -36 = -4*x + x. Suppose 4*h + 4 - x = 0. Factor 6*d + 9*d**2 + 7*d**2 - 10*d**h + 2 + 2*d**3.
2*(d + 1)**3
Let m be (336/(-105))/(1 + 12/(-10)). Factor m*h**2 - 3*h**5 + 12*h**5 + 4*h**5 + 72*h**3 - 2428*h**4 + 2488*h**4 + h**5.
2*h**2*(h + 2)**2*(7*h + 2)
Let l = 27557 + -468453/17. What is o in -4/17*o**3 + 2/17*o**5 + 6/17*o**4 - 24/17*o**2 + 0 - l*o = 0?
-2, -1, 0, 2
Suppose 0 = 19*i - 6*i - 26. Suppose -2*h = -t - 4 + i, 5*h - 5 = -2*t. Let 1/4*x**3 + x + t - x**2 = 0. Calculate x.
0, 2
Find m such that -2/11*m**3 + 170/11*m - 900/11 + 12/11*m**2 = 0.
-9, 5, 10
Let g(p) be the second derivative of -p**4/96 + p**3/48 + 21*p**2/8 + 23*p + 30. Determine m so that g(m) = 0.
-6, 7
Let h be ((-170)/4)/(30/(-12) + 2). Let d = h - 81. Solve r + 59*r**3 + 1 - 31*r**3 + r**d - 30*r**3 - 2*r**2 + r**5 = 0 for r.
-1, 1
Let -608*n + 10889*n**3 - 7372*n - 5443*n**3 - 2015*n**2 - 5451*n**3 = 0. What is n?
-399, -4, 0
Let u = -253076 - -253079. Factor 0 - 3/4*k**u + 9/4*k**2 + 3*k.
-3*k*(k - 4)*(k + 1)/4
Let b(d) be the second derivative of -d**7/28 - 11*d**6/60 + 5*d**5/8 + 23*d**4/24 - 5*d**3/6 + 906*d + 1. Let b(u) = 0. Calculate u.
-5, -1, 0, 1/3, 2
Let l be (-1 + 0)*-23 - 2062379/90497. Find n, given that 2/19*n**4 - 2/19*n**5 + l*n + 0 - 10/19*n**2 + 6/19*n**3 = 0.
-2, 0, 1
What is j in 70575104/17 + 1968/17*j**2 - 2/17*j**3 - 645504/17*j = 0?
328
Let h(o) be the third derivative of -5/21*o**7 - 18*o**2 + 0*o + 0*o**4 + 13/24*o**6 - 1/4*o**5 + 0*o**3 + 0. Factor h(t).
-5*t**2*(t - 1)*(10*t - 3)
Factor -86/5*l**2 + 8/5*l**3 - 96/5 - 188/5*l + 2/5*l**4.
2*(l - 6)*(l + 1)**2*(l + 8)/5
Let d(a) be the third derivative of -a**8/672 + 37*a**7/210 - 59*a**6/40 + 157*a**5/30 - 485*a**4/48 + 23*a**3/2 + 448*a**2. Determine f so that d(f) = 0.
1, 2, 69
Let x(f) be the third derivative of -f**9/332640 - f**8/110880 + f**7/13860 + 37*f**5/60 - f**2 - 1. Let g(k) be the third derivative of x(k). Factor g(t).
-2*t*(t - 1)*(t + 2)/11
Let f = -3165/2 + 9511/6. Factor 2/3*h**3 + f*h + 8/3*h**2 + 0.
2*h*(h + 2)**2/3
Let q = -12674 + 12674. Let g(t) be the second derivative of -34/7*t**3 - 1/7*t**5 + q + 2*t**4 + 4*t**2 + 48*t. Factor g(r).
-4*(r - 7)*(r - 1)*(5*r - 2)/7
Let x = 792 - 789. Let r(a) = -a**3 + 5*a**2 - 5*a + 6. Let i be r(x). Let -3/8*t**3 - i*t + 3/2 - 135/8*t**4 + 75/8*t**5 + 123/8*t**2 = 0. What is t?
-1, 2/5, 1
Let v(x) be the third derivative of x**8/504 - x**6/180 + 434*x**2 - x - 5. Factor v(g).
2*g**3*(g - 1)*(g + 1)/3
Let p = 24 + -15. Suppose 0 = 2*s + 5*k + 21, -k - 11 = -5*s + 2*s. Factor -206 + 206 + 3*b**s + p*b.
3*b*(b + 3)
Let c = 35 + -137/4. Let a = 45437 - 45435. Find b, given that -3/4 - 3/2*b - c*b**a = 0.
-1
Let n(y) be the third derivative of 21*y**6/80 + y**5/80 - 21*y**4/16 - y**3/8 - y**2 - 769. What is b in n(b) = 0?
-1, -1/42, 1
Let n be ((-4)/(-9))/(4/18). Factor 12*h - 9 - 30*h**2 + 16*h**2 + 0*h + 11*h**n.
-3*(h - 3)*(h - 1)
Let f be (48/84 + (-734)/1260)*(-3)/2. Let k(x) be the second derivative of 16/3*x**2 + 0 + 5/18*x**4 - 16/9*x**3 - x - f*x**5. Find h such that k(h) = 0.
2, 4
Let a(r) = 28*r**2 + 24*r - 160. Let u be a(2). Factor 2/3*y**3 - 1/6*y**2 + u - 1/6*y**4 - y.
-y*(y - 3)*(y - 2)*(y + 1)/6
Solve -45/4*v**2 + 3/4*v**3 + 0 + 81/4*v + 1/4*v**4 = 0 for v.
-9, 0, 3
Let j = -1 + 3. Let f = 263245/41 - 3414641/533. Factor f*k**j + 900/13 + 1470/13*k + 6/13*k**3.
2*(k + 15)**2*(3*k + 2)/13
Let g(y) = -y - 8. Let t be g(-4). Let p(z) = 4*z**2 - 4. Let h(u) = -u**3 + 5*u**2 + u - 5. Suppose 0 = -5*a - 2 + 32. Let f(k) = a*p(k) + t*h(k). Factor f(c).
4*(c - 1)*(c + 1)**2
Let j(o) be the third derivative of o**8/1512 + o**7/945 - 17*o**6/540 + 19*o**5/270 + 4*o**4/27 - 20*o**3/27 + 2*o**2 + 17*o - 4. Find k such that j(k) = 0.
-5, -1, 1, 2
Let o = 18 - 13. Suppose 32 = o*t + 22. Factor 1/8*h**t + 0 - 1/4*h.
h*(h - 2)/8
Let f(u) = 2*u. Let m(q) = -57*q**2 + 49*q. Let k(o) = -4*f(o) + m(o). Let y(p) = -2*p**2 + p. Let i(z) = k(z) - 6*y(z). Let i(t) = 0. What is t?
0, 7/9
Let -201*j + 9*j**3 - 14*j**2 - 210 + 147*j**2 - 163*j**2 = 0. Calculate j.
-2, -5/3, 7
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