 + h*y**3 = 0.
-1, 0, 5
Let l(r) be the second derivative of r**6/27 - 997*r**5/90 + 8233*r**4/9 + 30400*r**3/27 - 20000*r**2/9 + 362*r. Solve l(s) = 0 for s.
-1, 2/5, 100
Let j(s) be the first derivative of s**4/18 + 44*s**3/27 - 160*s**2/9 + 448*s/9 + 4759. Solve j(m) = 0.
-28, 2, 4
Suppose 0 = -4*j + 1 + 7. Suppose l + 2 = j*l. Factor 12*c**3 - 4*c**2 + 6*c**5 - 4*c - 8*c**5 - l*c**4 - 6*c + 6.
-2*(c - 1)**3*(c + 1)*(c + 3)
Let m(n) be the first derivative of n**6/420 - n**5/70 - 13*n**4/84 + 5*n**3/7 + 10*n**2 - 109. Let t(k) be the second derivative of m(k). Factor t(s).
2*(s - 5)*(s - 1)*(s + 3)/7
Suppose -4*r + 4*k = -116, k - 76 = -r - 37. Suppose -r*c + c - 13*c - 2*c**2 - 44 = 0. What is c?
-22, -1
Solve 660/7 + 2/7*p**2 + 662/7*p = 0 for p.
-330, -1
Let l = 301610 - 301607. Factor -12*c**l - 105/4*c**2 + 0 + 3/4*c**4 - 27/2*c.
3*c*(c - 18)*(c + 1)**2/4
Let h be (-40)/(-6)*63/42. Suppose -2*k + 2 = -3*x, -6*k - 3*x - 10 = -h*k. Determine i, given that -6/5*i**2 + 14/5*i**k + 0*i - 14/5*i**3 + 6/5*i**5 + 0 = 0.
-3, -1/3, 0, 1
Let m(k) be the first derivative of -k**3/3 + 7*k**2/2 - 10*k + 9008. Factor m(v).
-(v - 5)*(v - 2)
Let o(j) = -j**2 - 4*j + 2. Let f(g) = 42*g**2 + 2800*g - 508. Let u(z) = -f(z) + 2*o(z). Find s, given that u(s) = 0.
-64, 2/11
Factor -3*p**4 - 42*p**2 + 11095*p**3 + 11125*p**3 - 936*p - 22139*p**3.
-3*p*(p - 26)*(p - 4)*(p + 3)
Let q(p) be the first derivative of 4*p**3/9 - 250*p**2 - 3016*p/3 + 1184. Factor q(u).
4*(u - 377)*(u + 2)/3
Suppose 1605*z + 20 - 2*z**3 + 2*z**2 - 813*z - 766*z + 2*z**2 = 0. Calculate z.
-2, -1, 5
Let m(p) be the third derivative of -p**5/240 + 1311*p**4/16 - 5156163*p**3/8 + 14*p**2 + 46*p - 3. Find a such that m(a) = 0.
3933
Let r(w) = w**2 - w - 1. Let p be r(2). Suppose 8*z - 676*c + 661*c = 4*z + 192, 21 = 3*z - c. What is x in 0*x + 1/4*x**z + 3/4*x**2 - p = 0?
-2, 1
Let c = -6/11 - -1/22. Let r = 0 - c. Factor 0*p + r*p**2 + 0 + 1/2*p**4 - p**3.
p**2*(p - 1)**2/2
Let m(s) = s**3 + 10*s**2 + 9*s + 2. Let r be m(-9). Determine a, given that -1275 + 413 + 411 - 4*a**r + 40*a + 415 = 0.
1, 9
Let w(r) be the third derivative of 1/5*r**5 + 1/3*r**4 + 0*r**3 - 4/15*r**6 + 0*r - 45*r**2 + 0 + 2/35*r**7. Suppose w(t) = 0. Calculate t.
-1/3, 0, 1, 2
Let w(a) be the first derivative of -2/9*a**3 - 257 - 5/3*a**2 - 4*a. What is c in w(c) = 0?
-3, -2
Let c(n) = 3*n**2 - 60*n - 404. Let x(s) = -17*s**2 + 301*s + 2022. Let v(y) = -11*c(y) - 2*x(y). Factor v(w).
(w + 8)*(w + 50)
Suppose -2 = -4*b + 6*b - 4*g, -2*b + 12 = 3*g. Let t be (-8 - -14)*b/(30/4). Find o such that 16*o**4 + 92/5*o**2 - 14/5*o**5 - 144/5*o**3 - 2/5*o - t = 0.
-2/7, 1, 3
Let h(z) be the third derivative of -7/16*z**4 - 71*z**2 + 0*z + 0*z**3 + 13/40*z**5 - 1/140*z**7 - 1/16*z**6 + 0. Factor h(x).
-3*x*(x - 1)**2*(x + 7)/2
Let u(t) be the first derivative of 36*t**5/5 + 7482*t**4 + 6239956*t**3/3 + 4140040*t**2 + 2755600*t - 1587. Solve u(h) = 0 for h.
-415, -2/3
Let p(w) be the second derivative of w + 9/2*w**2 + 1/48*w**4 + 1/2*w**3 - 4. Let p(q) = 0. Calculate q.
-6
Solve 21/2*m**2 + 3/2*m**3 - 45/2 + 21/2*m = 0 for m.
-5, -3, 1
Let c be 18/63 + ((-14562)/(-630) - 21). Let -2/5*b**4 + 1/5*b**5 + 0 - c*b**3 - 14/5*b**2 - b = 0. Calculate b.
-1, 0, 5
Let k be -1*3/9*(-2 - 13). Suppose -k*g = 67 - 87. Solve 3*i**3 + 10*i**2 - 18*i**2 - g*i**2 = 0.
0, 4
Let i be 1520/(-144) + 10 - -1. Let k(t) be the first derivative of -i*t**3 - 1/12*t**4 - 2/3*t - 5/6*t**2 - 9. What is q in k(q) = 0?
-2, -1
Let 19145*s**2 - 712 + 859 + 2273 - 435*s**3 - 210760*s = 0. What is s?
1/87, 22
Suppose 0 = 3*i, -10 = -2*b + i - 2*i. Suppose -7*a**3 + 7*a - 5*a**4 + b*a**2 + 8*a - 8*a**3 = 0. Calculate a.
-3, -1, 0, 1
Let n = -788/25 + 1601/50. Let m(i) be the first derivative of 11/4*i**4 + 0*i + 0*i**2 - n*i**5 - 51 - 4/3*i**3. Factor m(z).
-z**2*(z - 4)*(5*z - 2)/2
Find f, given that -5/2*f**5 + 0 - 20*f + 15*f**3 + 10*f**2 - 5/2*f**4 = 0.
-2, 0, 1, 2
Factor -3*j**2 - 716*j - 19*j**2 - 49*j + 17*j**2.
-5*j*(j + 153)
Let h(z) be the first derivative of -3*z**5/5 - 21*z**4/2 + 239*z**3 + 3024*z**2 - 62208*z + 2880. Factor h(x).
-3*(x - 9)**2*(x + 16)**2
Factor 1245*f + 1012*f**2 - 697*f**2 + 20*f**3 - 775*f**2 - 900.
5*(f - 20)*(2*f - 3)**2
Let h be 3/(-12) - (-30)/(-40). Let n be (17/h - -16)*(0 - 3). Factor s**n - 4/3*s**2 + 3/2 - 1/6*s**4 - s.
-(s - 3)**2*(s - 1)*(s + 1)/6
Let i be 24 + 18020/(-748) + 67/11. Factor -3/2*u**2 + i*u - 6.
-3*(u - 2)**2/2
Factor 1792587/2 + 2319*f + 3/2*f**2.
3*(f + 773)**2/2
Let f = 10/781 + 581/15620. Let r(t) be the third derivative of 1/2*t**4 + 0*t - 5/2*t**3 + f*t**5 + 0 - 4*t**2. Factor r(m).
3*(m - 1)*(m + 5)
Factor -2/7*d**2 - 72/7 - 74/7*d.
-2*(d + 1)*(d + 36)/7
Find w such that 43/9*w**3 + 0 + 1/9*w**4 + 122/9*w**2 + 80/9*w = 0.
-40, -2, -1, 0
Factor 18*n**2 - 6*n**3 + 21*n**2 - 17*n**2 + 187 - 193 - 10*n.
-2*(n - 3)*(n - 1)*(3*n + 1)
Let u = 421 - 387. Factor -u*q**3 + 62*q**3 - 32*q**3 + 22*q**2 + 6*q**2 + 32*q.
-4*q*(q - 8)*(q + 1)
Let m = 518430/13 - 1555160/39. Suppose m*v**2 + 1/3*v**3 + 0 + 7*v = 0. Calculate v.
-7, -3, 0
Let m(j) be the third derivative of -25/24*j**4 + 0 - 1/12*j**5 + 5*j**3 - 243*j**2 + 0*j. Factor m(g).
-5*(g - 1)*(g + 6)
Let j(q) = -3*q**3 + 38*q**2 + 19*q - 514. Let a be j(12). Let w(s) be the first derivative of -1/14*s**4 - 16/7*s - 12/7*s**a - 4/7*s**3 + 30. Solve w(c) = 0.
-2
Determine f so that 38*f + 4 + 77/2*f**3 + 65*f**2 + 15/2*f**4 = 0.
-2, -1, -2/15
Let r(m) be the first derivative of -m**5/120 + 5*m**4/24 - 25*m**3/12 - 3*m**2/2 - 7*m - 37. Let p(s) be the second derivative of r(s). What is k in p(k) = 0?
5
Let w(h) be the first derivative of 8/9*h**2 + 2/9*h + 5/9*h**4 - 38/27*h**3 - 2. Factor w(b).
2*(b - 1)**2*(10*b + 1)/9
What is z in -45414/7 + 6/7*z**4 - 348/7*z**3 + 3132/7*z + 4992/7*z**2 = 0?
-3, 3, 29
Let u(s) be the second derivative of -1/30*s**5 + 0*s**2 + 0*s**3 + 1/9*s**4 - 51*s + 0. Find m such that u(m) = 0.
0, 2
Let i be (0/(-100 - -89))/(0 + 1). Factor 1/2*y**5 - y**4 + 0*y**2 + 1/2*y**3 + i*y + 0.
y**3*(y - 1)**2/2
Suppose 3*o = 6*o - 219. Let h = 77 - o. Factor 565*v**h - 560*v**4 + 8*v**3 + 15*v**2 + 12*v**3.
5*v**2*(v + 1)*(v + 3)
Let s(h) be the second derivative of h**5/25 - 876*h**4/5 - 701*h**3/2 - 2629*h**2/10 + 105*h - 38. Factor s(k).
(k - 2629)*(2*k + 1)**2/5
Let u(p) be the third derivative of p**7/420 + 17*p**6/240 + 19*p**5/40 - 63*p**4/16 - 81*p**3/2 + 4675*p**2. Factor u(v).
(v - 3)*(v + 2)*(v + 9)**2/2
Let w(t) be the second derivative of t**5/110 + 4*t**4/11 + 7*t**3/11 - 46*t**2/11 - 563*t + 2. Let w(z) = 0. Calculate z.
-23, -2, 1
Let w(v) = 18*v + 93. Let h be w(-4). Factor 19*x - 38*x - 9*x - 11 - h + 4*x**2.
4*(x - 8)*(x + 1)
Let l(o) be the first derivative of -o**3/8 - 195*o**2/4 - 777*o/8 - 3492. Factor l(z).
-3*(z + 1)*(z + 259)/8
Let k(y) = y + 1. Let u(v) = -v**3 - 212*v**2 + 425*v - 216. Let b(r) = 2*k(r) + u(r). Find l, given that b(l) = 0.
-214, 1
Let a be (3/(-1))/(11/(-66)*6). Let j(p) be the first derivative of -5/3*p + 1/6*p**2 + 4 - 1/12*p**4 + 5/9*p**a. Factor j(y).
-(y - 5)*(y - 1)*(y + 1)/3
Let m be 2/((40/(-110))/(2/(-220)*5)). Let 1/4*k**3 + 11/4*k + 1 - m*k**4 + 9/4*k**2 = 0. Calculate k.
-1, 4
Find k, given that 0 - 126*k - 2/5*k**3 + 216/5*k**2 = 0.
0, 3, 105
Let b(g) be the second derivative of 0*g**2 - 1/18*g**3 - 5/72*g**4 - 1/30*g**5 - 64*g - 1/180*g**6 + 0. Factor b(u).
-u*(u + 1)**2*(u + 2)/6
Let u(n) = 3*n**3 - 9*n**2 + n. Let a be u(3). Factor 4*f**4 - 25 + 25 - 3*f**3 - f**a.
4*f**3*(f - 1)
Let f = -78/3365 + 104549/10095. Factor -f*m**2 - 1/2*m**3 - 100/3 - 170/3*m.
-(m + 10)**2*(3*m + 2)/6
Let x = 77/4 + -19. Let j be -203 - -191 - (-51)/4. Factor 1/2 + j*w + x*w**2.
(w + 1)*(w + 2)/4
Let r be 30/(-15)*((-34)/(-4) + -1). Let k(u) = 2*u**2 + 29*u - 13. Let v be k(r). Solve 8 + l**2 + l**2 - 8*l**v + 7*l**2 + 6*l = 0 for l.
-4, -2
Suppose 10 = 5*k - 5*l, 1 = -3*k - l - 1. Suppose -1348 - 1294 = -737*g - 431. Let -2/3*y**4 + k*y - 12*y**2 - 16/3*y**g + 18 = 0. What is y?
-3, 1
Let j be (18 - 15) + (-54)/(-2)*2. Suppose 3*i + j = 2*h - 10, -2*h - i + 79 = 0. Let -34*x**3 - 2*x**2 + h*x**3 + x + 6*x**2 = 0. What is x?
-1/2, 0
Let l(k) = -k**2 + 18. Let t be l(4). Suppose -5*y = -t*n - 2