/21 - 176*m**5/7 + 3337*m**4/14 - 1226*m**3/3 + 221*m**2 - 338*m/7 - 1237. Find s, given that k(s) = 0.
1/4, 1, 13
Let s(q) be the first derivative of -21*q + 9 + 1/8*q**5 + 20/3*q**3 - 5/3*q**4 + 0*q**2. Let i(r) be the first derivative of s(r). Factor i(n).
5*n*(n - 4)**2/2
Let c(z) = 6*z + 50. Let v be c(-8). Factor -461*u**2 - 32 + 44*u + 228*u**2 + 223*u**2 - v*u**3.
-2*(u - 2)*(u - 1)*(u + 8)
Let l(g) be the second derivative of -g**6/360 + 13*g**5/120 - 239*g**3/6 - 2*g + 83. Let t(z) be the second derivative of l(z). Factor t(v).
-v*(v - 13)
Let k(l) be the second derivative of -l**4/15 + 10796*l**3/15 - 14569202*l**2/5 - 6*l - 230. Factor k(g).
-4*(g - 2699)**2/5
Let a be 448/(-80)*(-20)/14. Let j(l) be the first derivative of -a - 5/3*l**2 - 4/3*l - 2/3*l**3. Factor j(r).
-2*(r + 1)*(3*r + 2)/3
Let q = -12/6667 - -213500/86671. Let 10/13 - q*c + 6/13*c**2 = 0. What is c?
1/3, 5
Let m(b) = 23*b**2 - 24*b - 24. Let w be m(-18). Factor -7860*s**2 - 2*s**3 + w*s**2 - 2*s**4.
-2*s**3*(s + 1)
Factor 1400 + 5*h**2 + 593 - 474 - 310*h + 0*h**2 + 161.
5*(h - 56)*(h - 6)
Let b(d) = 3*d + 7. Let t(z) = -13*z - 27. Let l(w) = 9*b(w) + 2*t(w). Let n be l(-7). Factor 22 - 440*r**n - 32 - 205*r - 15 - 80*r**3.
-5*(r + 5)*(4*r + 1)**2
Suppose -20*n - 63*z = -64*z - 88, 5*n = -4*z - 12. Solve 0*s**n + 19/2*s**3 - 6*s + 20 - 17*s**2 - 1/2*s**5 = 0 for s.
-5, -1, 2
Let j(t) = -7*t**3 - 3098*t**2 + t + 3095. Let r(a) = 6*a**3 + 3100*a**2 - 2*a - 3098. Let w(p) = 2*j(p) + 3*r(p). Let w(f) = 0. What is f?
-776, -1, 1
Let h(d) be the first derivative of 50/3*d + 5/2*d**2 - 5/9*d**3 + 21. Factor h(g).
-5*(g - 5)*(g + 2)/3
Solve 0 - r - 72 - 2*r**2 + 25*r = 0 for r.
6
Let o(q) = -q**3 - 14*q**2 - 19*q + 3. Let t(b) = 4*b**3 + 70*b**2 + 94*b - 14. Suppose -159 = 20*a + 121. Let z(r) = a*o(r) - 3*t(r). Factor z(d).
2*d*(d - 8)*(d + 1)
Factor -1760/9*a - 58/9*a**3 - 56*a**2 - 2/9*a**4 - 2176/9.
-2*(a + 4)**3*(a + 17)/9
Let a be ((-2)/30*4)/(332/(-3320)). Let a*b**2 + 46/9*b**3 + 0 - 8/9*b + 70/9*b**5 - 44/3*b**4 = 0. Calculate b.
-2/5, 0, 2/7, 1
What is p in -57868*p**3 + 0*p**4 - 267*p**2 - 64*p + 57799*p**3 - 6*p**4 - 135 - 16*p - 307*p = 0?
-5, -3, -1/2
Suppose -7328/13 - 10/13*b**2 - 18324/13*b = 0. Calculate b.
-1832, -2/5
Factor -158/5 + 472/5*z + 6/5*z**2.
2*(z + 79)*(3*z - 1)/5
Let c(x) = -x**3 + x**2 - 31*x + 1. Let d(j) = -241*j**3 - 38574*j**2 + 22224*j - 3164. Let h(s) = 4*c(s) + d(s). Factor h(l).
-5*(l + 158)*(7*l - 2)**2
Suppose -c + 5 = 4*t, -25 = -3*t + 4*c - 7. Factor -12*n**3 + 226*n + 226*n + 32*n**t - 468*n + 4*n**5 - 8*n**4.
4*n*(n - 2)*(n - 1)**2*(n + 2)
Suppose 0 = 79*n - 69*n. Let z(b) be the third derivative of 1/420*b**7 + 0*b**5 + 0*b**6 + 9*b**2 + 0*b**3 + 0*b**4 + n*b + 0 + 1/224*b**8. Factor z(m).
m**4*(3*m + 1)/2
Suppose -15/8*n**2 - 3/8*n**5 + 9/8*n**3 + 3/8*n**4 + 0 + 3/4*n = 0. Calculate n.
-2, 0, 1
Suppose 89*a**2 - 203*a**2 + 117*a**2 + 757*a + 398*a = 0. Calculate a.
-385, 0
Let d = -12947/5 + 2588. Let a = 83/20 + d. Solve -1/4*u**3 - 1 + 1/4*u**4 - 9/4*u**2 - a*u = 0.
-1, 4
Determine m, given that 30/11 + 32/11*m + 2/11*m**2 = 0.
-15, -1
Factor -100*k**2 - 18*k - 3*k + 5*k + 17*k**4 - 98*k**3 - 53*k**4 - 70*k**3.
-4*k*(k + 4)*(3*k + 1)**2
Suppose n - 16 = -9*w, 77*n = 74*n - 6. Suppose 2/9*q**4 + 0*q - 2/9*q**3 + 0*q**w + 0 = 0. What is q?
0, 1
Factor -192*z + 12*z**3 - 71*z**2 - 113*z**2 - 402*z**4 + 406*z**4.
4*z*(z - 6)*(z + 1)*(z + 8)
Find l such that 30/7*l - 22/7 - 8/7*l**2 = 0.
1, 11/4
Let s(i) be the first derivative of -1/28*i**4 + 0*i - 4/7*i**2 + 51 - 2/7*i**3. Suppose s(j) = 0. Calculate j.
-4, -2, 0
Let i(x) be the second derivative of -x**7/42 + 9*x**5/20 + x**4/3 - 2*x**3 + 709*x. Factor i(h).
-h*(h - 3)*(h - 1)*(h + 2)**2
Let p(g) be the first derivative of -2/7*g**5 - 20/21*g**3 + 0*g + 40 - 1/42*g**6 - 29/28*g**4 + 0*g**2. Let p(o) = 0. Calculate o.
-5, -4, -1, 0
Suppose 27*y - 1496 = -7*y. Find b, given that 2 + 3 - 13 - 10*b**2 - y*b - 10*b**2 = 0.
-2, -1/5
Let u = 928931/19660 - -1/4915. Determine k so that u*k**3 + 15*k**4 + 9/2 + 105/4*k + 54*k**2 = 0.
-1, -3/4, -2/5
Let z = 15520/63 - 2212/9. Let g = 4531/2639 - 1/377. Determine j, given that 0 + 8/7*j + z*j**3 + g*j**2 = 0.
-2, -1, 0
Suppose -t = 2*p - 4*t - 6, -10 = 5*p + 5*t. Let f(y) be the first derivative of p*y - 1/5*y**4 - 4/15*y**3 + 0*y**2 + 1. Factor f(n).
-4*n**2*(n + 1)/5
Suppose -4/7*j**4 + 32/7*j**3 + 31/7*j - 6/7 - 53/7*j**2 = 0. What is j?
1/2, 1, 6
Let n(m) be the first derivative of 13/5*m**5 + 12*m**3 + 0*m + 0*m**2 - 12*m**4 + 198 - 1/6*m**6. Determine q so that n(q) = 0.
0, 1, 6
Suppose -13 = -11*d + 31. Find x, given that -8*x**2 + 32*x + 13*x + d*x**2 - x**2 = 0.
0, 9
Let p = 92057 + -92054. Factor 19/3*n**2 + 8/3*n**p + 0 + 1/3*n**4 + 4*n.
n*(n + 1)*(n + 3)*(n + 4)/3
Let y(b) be the second derivative of -b**4/3 + 36*b**3 + 342*b**2 + 2*b - 448. Factor y(p).
-4*(p - 57)*(p + 3)
Let a = -193620 + 193620. Determine g, given that 3/2*g**4 + a - 9/4*g - 3/2*g**2 - 3/4*g**5 + 3*g**3 = 0.
-1, 0, 1, 3
Factor 1134 + 1198 + 2290*f - 226 + 108*f - 2*f**2 + 294.
-2*(f - 1200)*(f + 1)
Let r(y) be the second derivative of y**6/25 + 3*y**5/25 - 14*y**4/5 - 10*y**3 + 45*y**2 + y - 426. Find z such that r(z) = 0.
-5, -3, 1, 5
Suppose 48/7 + 225/7*s**2 + 39*s = 0. Calculate s.
-1, -16/75
Suppose 6*b = -2*m + 2*b + 14, 30 = 3*m - 3*b. What is c in c**4 - m*c + 7*c**4 + 9*c**3 + 3*c**4 - 8*c**4 - 3*c**2 = 0?
-3, -1, 0, 1
Determine p, given that -153*p**3 - 3*p**4 + 75*p**3 + 7*p**4 + 1800*p + 28*p**2 - 924*p**2 + 70*p**3 - 900 = 0.
-15, 1, 15
Let j be -8 + (-14)/(-5 + 12). Let b be 1776/3515 - (-4)/j. Solve 2/19*c**2 - 2/19*c - 2/19*c**4 + 0 + b*c**3 = 0.
-1, 0, 1
Let d = 20701/1985 - 329/397. Determine y, given that 4/5*y + d - 2/5*y**2 = 0.
-4, 6
Let g(a) be the third derivative of 1/3*a**3 + 1/90*a**6 + 0 - 1/18*a**4 - 1/945*a**7 - 4/135*a**5 + 0*a + 95*a**2. Find y such that g(y) = 0.
-1, 1, 3
Let v(x) = -83*x**3 - 173*x**2 - 410*x + 11. Let h(n) = 15*n**3 + 35*n**2 + 82*n - 2. Let k(j) = 11*h(j) + 2*v(j). Determine i so that k(i) = 0.
-2, 0, 41
Determine a so that 0*a**3 + 48/5*a**2 + 48/5*a + 0 - 12/5*a**4 - 3/5*a**5 = 0.
-2, 0, 2
Let h(l) be the third derivative of -l**5/270 + 25*l**4/3 - 7500*l**3 + 5*l**2 + 3. Suppose h(r) = 0. Calculate r.
450
Let t be ((-24)/(-20))/(2 + (438/60 - 9)). What is u in -u**5 + 3/2*u**3 - 1/2*u**t - 1/2*u + 1/2*u**2 + 0 = 0?
-1, 0, 1/2, 1
Let i(h) be the first derivative of 53*h**2 + 20*h - 9*h**6 + 348/5*h**5 - 262 - 97*h**4 - 32/3*h**3. Find q, given that i(q) = 0.
-1/3, -2/9, 1, 5
Let b(j) = 8*j**2 - 225*j + 1306. Let i(r) = -4*r**2 + 112*r - 656. Let z(d) = -4*b(d) - 9*i(d). Solve z(v) = 0 for v.
10, 17
Let n(r) be the second derivative of r**7/630 - 13*r**6/45 + 338*r**5/15 - 103*r**4/12 - 128*r. Let p(c) be the third derivative of n(c). Factor p(k).
4*(k - 26)**2
Let b(l) = -18*l - 9. Let i be b(-4). Let q = i - 55. Find m such that q*m + m - 8*m + 3*m**2 + m + m**3 = 0.
-2, -1, 0
Solve -342/7*x**2 - 159/7*x + 90/7*x**4 + 36 + 3/7*x**5 + 156/7*x**3 = 0.
-28, -3, -1, 1
Let f(c) be the first derivative of -4/5*c**5 + 0*c + 0*c**2 - 5/4*c**4 + 2/3*c**3 + 1/2*c**6 + 57. Suppose f(x) = 0. What is x?
-1, 0, 1/3, 2
Let p(u) be the second derivative of 3*u**5/20 - u**4/2 - 74*u**3 - 420*u**2 - 3*u - 103. Factor p(g).
3*(g - 14)*(g + 2)*(g + 10)
Let m be (-13)/1625*4*-5. Let s(u) be the first derivative of 0*u**2 + 7 + 4/15*u**3 + m*u**5 - 2/5*u**4 + 0*u. Factor s(h).
4*h**2*(h - 1)**2/5
Suppose 4*w + 15 = 3*z + 8*w, z = -2*w + 5. Factor -65*x**5 + 3*x**3 + 35*x**5 - 2*x**4 + 29*x**5 + z*x**4 - 7*x**2 - 6*x.
-x*(x - 3)*(x - 2)*(x + 1)**2
Determine d so that 666/7*d - 20*d**3 - 268/7 - 56*d**2 + 132/7*d**4 + 2/7*d**5 = 0.
-67, -2, 1
Let 0 + 2042/19*x**3 - 14/19*x**5 + 256/19*x**4 - 2956/19*x**2 + 672/19*x = 0. What is x?
-7, 0, 2/7, 1, 24
Solve -44/3 + 16/3*v**2 - 82/9*v - 2/9*v**3 = 0 for v.
-1, 3, 22
Determine t so that -459 + 241 - 2070*t**2 + 5*t**3 + 218 = 0.
0, 414
Let m(z) = 25*z**2 - 12*z + 11. Let k be 18*(-4)/(-72)*6. Let c(u) = -46*u**2 + 25*u - 23. Let l(v) = k*c(v) + 11*m(v). Factor l(i).
-(i - 17)*(i - 1)
Let q(b) be the third derivative of -b**7/315 - 41*b**6/180 - 94*b**5/45 - 73*b**4/9 -