**3 + 206*r**4 = 0. Calculate r.
-4, -1, 2/37, 1
Let b be (-6)/(-10) + (-369)/(-410) + 4/64*8. What is x in 424/3*x**b - 4/3*x**5 + 28*x**4 - 296/3*x**3 - 92*x + 68/3 = 0?
1, 17
Let q be -3 + 20 + (-2 - (1 - -2)). Suppose -2*u + 6 = 2. Factor -q - 1 + 14*n - 4*n**u - 7 + 10*n.
-4*(n - 5)*(n - 1)
Determine w, given that 2/7*w**3 + 142/7*w + 148/7*w**2 - 292/7 = 0.
-73, -2, 1
Let y(r) be the first derivative of 35*r**4/12 - 550*r**3/9 + 365*r**2/6 + 50*r - 1819. Factor y(p).
5*(p - 15)*(p - 1)*(7*p + 2)/3
Let l = 4926/17 + -219494/765. Let h(k) be the first derivative of -8 + 8/15*k**4 + 0*k + l*k**3 + 2/75*k**5 + 0*k**2. Factor h(d).
2*d**2*(d + 8)**2/15
Let j(l) be the third derivative of l**8/448 + l**7/10 + l**6 + 27*l**5/8 - 81*l**4/32 - 189*l**3/4 + 4319*l**2. Find x, given that j(x) = 0.
-21, -3, -2, 1
Let g(d) be the third derivative of -d**5/420 + 3023*d**4/84 - 9138529*d**3/42 - 38*d**2 + 20*d. Factor g(n).
-(n - 3023)**2/7
Let d(j) = -j**2 + 45*j - 235. Let l be d(25). Let x = -263 + l. Factor -2*y - 2/3*y**3 - x*y**2 - 2/3.
-2*(y + 1)**3/3
Let t(g) be the first derivative of 0*g - 2/3*g**6 - 16/3*g**3 + 0*g**2 + 124 - 8*g**4 - 4*g**5. What is f in t(f) = 0?
-2, -1, 0
Let t(l) be the first derivative of -l**3/4 + 201*l**2/8 - 855*l/2 - 232. Factor t(f).
-3*(f - 57)*(f - 10)/4
Suppose 95 = 5*d - 5*u, -270886*d + 270889*d = 5*u + 87. Solve 4/9*n**2 + d*n + 80/9 = 0 for n.
-5, -4
Let x = -86 - -81. Let z(n) = 2*n**2 + n + 1. Let t(h) = -15*h**2 - 23*h - 22. Let j(i) = x*t(i) - 35*z(i). Factor j(b).
5*(b + 1)*(b + 15)
Let n(x) be the second derivative of 0*x**2 + 113*x - 1/40*x**5 - 1/4*x**4 - 2/3*x**3 + 0. Factor n(z).
-z*(z + 2)*(z + 4)/2
Let w(z) = -35*z**3 - 1650*z**2 + 4675*z - 3130. Let x(d) = -5*d**3 - 237*d**2 + 668*d - 447. Let m(f) = -3*w(f) + 20*x(f). Determine l, given that m(l) = 0.
-45, 1, 2
Suppose 85 = 3*f - 32. Let g = f - 28. Let 32*s**4 - g*s**5 - 6*s**3 + 2*s - 18*s**3 - s**5 + 2*s = 0. What is s?
-1/3, 0, 1
Let r(t) = 6*t**3 + 320*t**2 - 350*t. Let z(x) = 14*x**3 + 627*x**2 - 701*x. Let g(q) = 5*r(q) - 2*z(q). Factor g(p).
2*p*(p - 1)*(p + 174)
Let r(u) = 262*u - 1822. Let f be r(7). Suppose -3*z + 19 = -2*i, -z + 34 = 2*z - 5*i. Factor 49 - 9*k - 107*k + 22*k**2 + k**4 + 32*k + f*k**z.
(k - 1)**2*(k + 7)**2
Find r, given that -40 + 347*r - 45*r**4 - 17*r**3 + 5*r**5 - 215*r**2 + 162*r**3 + 348*r - 545*r = 0.
1, 2, 4
Let c(d) be the first derivative of 2/17*d**3 - 132 + 4/17*d**2 - 24/17*d - 1/34*d**4. Factor c(s).
-2*(s - 3)*(s - 2)*(s + 2)/17
Let q(x) = 4*x**3 + 8*x**2 + 16*x. Let d(b) = -2*b**3 - 8*b**2 - 14*b. Let s(o) = -3*d(o) - 2*q(o). Factor s(c).
-2*c*(c - 5)*(c + 1)
Let t(v) be the first derivative of 0*v**2 - 4/3*v**3 + 0*v + 3/8*v**4 - 83 + 1/20*v**5. Factor t(b).
b**2*(b - 2)*(b + 8)/4
Let x(g) = 32*g**2 + 2850*g + 135392. Let t(c) = -11*c**2 - 950*c - 45131. Let i = 56 + -50. Let n(d) = i*x(d) + 17*t(d). Factor n(p).
5*(p + 95)**2
Let m(w) be the first derivative of -20/9*w**5 - 5/9*w**4 - 8/9*w**2 + 64/27*w**3 + 0*w - 27. Factor m(o).
-4*o*(o + 1)*(5*o - 2)**2/9
Let j(u) = -103*u**2 - 6812*u - 3878297. Let m(t) = -93*t**2 - 6813*t - 3878298. Let f(y) = -9*j(y) + 10*m(y). Suppose f(i) = 0. Calculate i.
-1137
Suppose q = -d + 14, -5*d + 91 = -0*d - 2*q. Find y, given that 6*y**2 + 3*y**2 - 24*y**2 + 40*y - d*y**2 + 2*y**4 + 2*y**3 = 0.
-5, 0, 2
Let y(p) be the first derivative of 11/2*p**2 + 1/4*p**4 + 6*p - 11 + 2*p**3. Solve y(a) = 0 for a.
-3, -2, -1
Suppose -g - 575 - 254 = 0. Let n = g - -831. Factor 0 - 2/3*s**n + 0*s**3 + 2/3*s**4 + 0*s.
2*s**2*(s - 1)*(s + 1)/3
Factor -2 - 4*w**3 + 24*w**2 + 3295*w + 2*w**5 - 3311*w - 6*w**4 + 4 - 2.
2*w*(w - 2)**2*(w - 1)*(w + 2)
Let t(l) = -l**3 + l**2 + 1. Let w = -22 + 18. Let o = -3 - w. Let q(x) = 15*x**3 - 15*x**2 - 15*x - 21. Let j(y) = o*q(y) + 12*t(y). Factor j(z).
3*(z - 3)*(z + 1)**2
Let 1/4*h**2 + 0 + 37/2*h = 0. Calculate h.
-74, 0
Solve -522 - 7*w**2 - 65*w**2 + w**3 + 61*w - 4*w**3 - 19*w + 375*w = 0 for w.
-29, 2, 3
Let t = -70 - -98. Suppose -t*j**3 - 42*j**2 - 32*j - 4*j**4 - 141 + 141 - 14*j**2 = 0. What is j?
-4, -2, -1, 0
Let q(z) be the third derivative of 5*z**5/12 - 105*z**4/2 + 250*z**3/3 - z**2 - 302. What is g in q(g) = 0?
2/5, 50
What is g in 3 - 113/2*g + 55/2*g**2 = 0?
3/55, 2
Let a(u) be the first derivative of -u**6/15 + 12*u**5/25 + 7*u**4/5 - 56*u**3/5 - 17*u**2 + 60*u - 1920. Suppose a(b) = 0. What is b?
-3, -2, 1, 5
Let a(t) be the third derivative of 0*t**3 + 0 + 4/27*t**4 - 57*t**2 + 4/135*t**5 + 0*t + 1/540*t**6. Factor a(f).
2*f*(f + 4)**2/9
Suppose 0 = -2343*h + 2215*h + 384. Solve 2*l**h + 14/5*l**4 - 12/5*l + 0 - 14/5*l**2 + 2/5*l**5 = 0 for l.
-6, -1, 0, 1
Let z(r) = -4*r**2 - 5*r + 3. Suppose -3*p - 2*o - 58 = 0, 0 = p - 3*p - o - 37. Let v(i) = -20*i**2 - 24*i + 16. Let w(a) = p*z(a) + 3*v(a). Factor w(s).
4*s*(s + 2)
Let a(t) be the second derivative of -t**5/150 + 4*t**4/45 + 4*t**3/45 - 32*t**2/15 - 5*t + 37. Factor a(f).
-2*(f - 8)*(f - 2)*(f + 2)/15
Let y = 16650101/127 + -99294061789/757428. Let h = 1/852 + y. Let 363/7 + h*f + 3/7*f**2 = 0. Calculate f.
-11
Let i(p) be the first derivative of 25*p + 26 + 5/3*p**3 - 15*p**2. Factor i(k).
5*(k - 5)*(k - 1)
Suppose a - 24 = -14*b + 19*b, -2*a + 2*b = -8. Let k be (a/(-1))/(-10 + 217/21). Determine f so that 2*f**5 - 8*f**2 + 0 - 15/2*f**k - 2*f + 2*f**4 = 0.
-2, -1/2, 0, 2
Let g(c) be the third derivative of 0 + 2/33*c**4 - 4*c**2 + 0*c - 1/330*c**5 - 7/33*c**3. Find i such that g(i) = 0.
1, 7
Let d = 384 - 368. Let x(w) be the second derivative of -5/12*w**4 + 0*w**5 + 0 + 0*w**3 - d*w + 0*w**2 + 1/6*w**6. What is u in x(u) = 0?
-1, 0, 1
Let q(v) be the second derivative of -v**6/10 - 3*v**5/10 + 3*v**4 + 4*v**3 - 48*v**2 - v + 231. Determine z, given that q(z) = 0.
-4, -2, 2
Let c be (-1)/(-2)*1 + 126/84. Factor -16*o + 0 - 1/2*o**4 + 2*o**c + 4*o**3.
-o*(o - 8)*(o - 2)*(o + 2)/2
Suppose -11*q = -115 - 6. Find t such that 11*t**2 - q*t**3 + 8*t**2 + 92*t + t**4 - 101*t = 0.
0, 1, 9
Let y = 352 + -346. Let s be y/1 - (-117)/(-65). Factor -27/5*o**2 + s*o - 6/5 + 3*o**3 - 3/5*o**4.
-3*(o - 2)*(o - 1)**3/5
Solve 161*q - 4*q**2 - 75*q**3 + 71*q**3 - 153*q = 0.
-2, 0, 1
Let 58/5*u**2 + 14/5*u**4 + 104/5*u + 4/5*u**5 - 56/5 - 92/5*u**3 = 0. What is u?
-7, -1, 1/2, 2
Let y(t) = t**3 + 7833*t**2 + 7834*t. Let s(d) = 15665*d**2 + 15670*d. Let r(x) = 2*s(x) - 5*y(x). Solve r(b) = 0 for b.
-1566, -1, 0
Let u(c) = 11*c**3 - 7397*c**2 - 14807*c - 7403. Let z(y) = -69*y**3 + 44383*y**2 + 88843*y + 44417. Let k(p) = -13*u(p) - 2*z(p). Factor k(b).
-5*(b - 1481)*(b + 1)**2
Suppose -2898 = -12*l - 378. Suppose 3*t - 46 = -40. Factor -424 - 3*f**t + l - 72*f - 218.
-3*(f + 12)**2
Find v, given that -695*v**3 - 359*v**3 - 289*v**4 + 0*v**3 - 352*v**2 - 409*v**4 + 4*v**5 = 0.
-1, -1/2, 0, 176
Let v(t) = t**3 + 7*t**2 + 5*t + 6. Let k be v(-5). Suppose 4*i - 3*i = 5*f - 13, 2*f - 5*i = -4. Let 1 + 3*l**f + 3 + 2 - 16*l + 12*l**2 + k*l = 0. What is l?
-2, -1
Let i(s) be the third derivative of s**5/60 + 2*s**4/3 + 35*s**3/6 + 4*s**2. Let a be i(-14). Let a*u - 6*u**2 + 8*u - 4 + 11*u**2 + 14 = 0. Calculate u.
-2, -1
Let g(x) = x**2 + 5*x + 0*x**2 - 15*x - 14 + 17. Let f be g(10). Solve f*n - 13 + 5*n**2 - 3*n**2 - 17*n - 3 = 0.
-1, 8
Let y(v) be the second derivative of 3*v + 31 + 1/90*v**6 + 2/3*v**4 - 25/6*v**2 - 1/6*v**5 + 5/9*v**3. Solve y(q) = 0.
-1, 1, 5
Let l be ((-309063)/99 - (-6)/33)/(-3). Let b = 1041 - l. Solve 0 - b*o**4 + 0*o - 2/9*o**5 + 2/9*o**3 + 4/9*o**2 = 0 for o.
-2, -1, 0, 1
Let v(w) be the second derivative of -w**4/3 - 26*w**3/3 + 3196*w**2 + 2646*w. Factor v(l).
-4*(l - 34)*(l + 47)
Find g such that 50/3*g**2 - 280/3 - 100*g + 5/3*g**4 + 25*g**3 = 0.
-14, -2, -1, 2
Let b(q) be the third derivative of q**8/4032 - 5*q**7/504 + q**6/16 - 26*q**5/15 - 5*q**2. Let z(w) be the third derivative of b(w). Factor z(x).
5*(x - 9)*(x - 1)
Suppose 410 + 1235/3*k + 5/3*k**2 = 0. What is k?
-246, -1
Suppose 0 = 134*i - 150*i + 32. Factor -2*n**i - 547*n + 2*n**2 + 553*n - 24 + 3*n**2.
3*(n - 2)*(n + 4)
Suppose 7*d = -190 + 232. Let q be 33/d*31/341. Factor 0 + l**2 - l**4 + 0*l**3 - 1/2*l**5 + q*l.
-l*(l - 1)*(l + 1)**3/2
Suppose 0 = 186*q - 24*q - 324. Factor 0 - 2/13*