t**3/9 + 40*t**2/3 - 32*t/3 + 27. Let q(w) = 0. Calculate w.
4/5
What is x in -1064 - 226 - 415*x + 2412*x**2 - 2407*x**2 = 0?
-3, 86
Let l(s) = s**3 + 3*s**2 - 4*s + 3. Let j be l(0). Determine b so that 43*b**j - 25*b**4 + 14*b**5 - 35*b**3 + 3*b**4 = 0.
0, 4/7, 1
Let -34/13*p**3 - 48/13 + 164/13*p + 178/13*p**2 = 0. What is p?
-1, 4/17, 6
Let z(h) be the second derivative of h**7/84 + 7*h**6/6 + 133*h**5/20 + 16*h**4/3 - 89*h**3/4 - 99*h**2/2 + 5643*h. What is g in z(g) = 0?
-66, -3, -1, 1
Let i(j) be the first derivative of 5*j**4/8 - 20*j**3/3 + 85*j**2/4 - 25*j + 5371. Determine z, given that i(z) = 0.
1, 2, 5
Suppose -2812 = -1827*q + 1570 - 728. Factor -1/5*m**q - 12 + 61/5*m.
-(m - 60)*(m - 1)/5
Find f, given that 195/8*f**2 + 729/8*f - 183/8 - 3/2*f**4 - 729/8*f**3 = 0.
-61, -1, 1/4, 1
Let v = 1797/44 - 5347/132. Determine x so that -v*x**2 - 196/3 + 28/3*x = 0.
14
Let g(d) be the third derivative of -23*d**6/120 + 11*d**5/10 + d**4/2 - 127*d**3/6 + 75*d**2. Let f(c) be the first derivative of g(c). Factor f(k).
-3*(k - 2)*(23*k + 2)
Suppose 22*g = 27*g - 25. Suppose -g = -m - 3. Factor 9*v - 5*v - v**3 - 2*v**m + 6*v**2 + 2*v**3.
v*(v + 2)**2
Let w(l) be the second derivative of l**4/60 - 8*l**3/5 + 88*l**2/5 - 11*l - 15. Suppose w(h) = 0. Calculate h.
4, 44
Let g(c) = -c**2 + 4. Let v(n) = -5*n**2 - 126*n + 272. Let d(b) = 12*g(b) - 3*v(b). Factor d(l).
3*(l - 2)*(l + 128)
Let w(q) = q**3 + 2*q**2 + q + 116. Let d be w(0). Let z = 118 - d. Factor -2*v - 2/3 - 4/3*v**z.
-2*(v + 1)*(2*v + 1)/3
Let s(y) be the first derivative of -7/18*y**4 - 28/9*y**2 - 8/3*y + 94/27*y**3 + 49. Solve s(i) = 0.
-2/7, 1, 6
Factor -1/9*u**3 + 268/9*u - 64/9*u**2 - 272/9.
-(u - 2)**2*(u + 68)/9
Let b = -206697 + 206699. Determine k so that 3/2*k - 3/4*k**3 - 21/8*k**b + 0 = 0.
-4, 0, 1/2
Let u be (15 + (6 - 21))/(-2). Let x(i) be the second derivative of 0*i**3 + 0 + u*i**2 + 1/100*i**5 + 1/30*i**4 + 2*i. Factor x(h).
h**2*(h + 2)/5
Let p(g) be the third derivative of -7*g**6/24 + 3*g**5/4 + 25*g**4/4 - 80*g**3/3 - 2*g**2 + 363*g. Factor p(u).
-5*(u - 1)*(u + 2)*(7*u - 16)
Let n(d) be the first derivative of -d**6/27 - 4*d**5/15 - d**4/18 + 16*d**3/9 - 16*d**2/9 - 1672. Factor n(t).
-2*t*(t - 1)**2*(t + 4)**2/9
Find l such that 0 - 9/2*l + 47/4*l**2 - 41/4*l**3 + 13/4*l**4 - 1/4*l**5 = 0.
0, 1, 2, 9
Let r(x) be the first derivative of x**3 - 51*x**2 - 1320*x - 5416. Factor r(t).
3*(t - 44)*(t + 10)
Let r(w) be the third derivative of 0*w + 0 - 11*w**2 + 7/18*w**3 - 1/360*w**5 - 13/144*w**4. Suppose r(h) = 0. What is h?
-14, 1
Let p = 71 - 68. Suppose -134 - 43*b - 45*b**2 - p*b**4 + 4*b - 21*b**3 + 122 = 0. Calculate b.
-4, -1
Let y(b) be the first derivative of 8*b**3/3 - 6*b**2 + 4*b - 2. Let v(j) = -j**2 + j - 1. Let c = -1429 + 1430. Let g(f) = c*y(f) + 4*v(f). Factor g(n).
4*n*(n - 2)
Let q(c) be the second derivative of 93312*c**3 - 1/10*c**6 - 1944*c**4 + 15*c + 108/5*c**5 - 3 - 2519424*c**2. Suppose q(f) = 0. Calculate f.
36
Let a(c) = -4*c**4 - 18*c**3 + 216*c**2 - 218*c + 78. Let z(k) = -5*k**4 - 8*k**3 + 215*k**2 - 218*k + 79. Let t(q) = 7*a(q) - 6*z(q). Factor t(f).
2*(f - 36)*(f - 1)**3
Suppose 970/7*s + 26/7*s**2 + 300 = 0. Calculate s.
-35, -30/13
Let o = -1775/258 - -41/6. Let k = o + 133/86. Factor -3/2*t**3 - 1/2*t**4 - 1/2*t**2 + 1 + k*t.
-(t - 1)*(t + 1)**2*(t + 2)/2
Let h be (-130)/(-26) + (-3)/(9/57). Let a be (-14)/h - (0 + (-1)/7). Factor 1/7*p**2 - 9/7 - a*p.
(p - 9)*(p + 1)/7
Let 5/2*o**4 - 13/2*o**3 + 0 + 2*o + 2*o**2 = 0. What is o?
-2/5, 0, 1, 2
Let s = -921006 - -3684063/4. Factor -s*g - 3/4*g**2 - 45/2.
-3*(g + 3)*(g + 10)/4
Let v = 471 + -333. Let z(p) = 96*p**3 - v*p**3 - 6 + 7*p**2 + 6. Let f(w) = 5*w**3 - w**2. Let i(m) = -51*f(m) - 6*z(m). Factor i(y).
-3*y**2*(y - 3)
Let i be -11 + 1316/(-273) + 16 + -9*12/(-702). Suppose 3267 + 66*x + i*x**2 = 0. What is x?
-99
Let u(c) be the third derivative of -c**8/840 + 58*c**7/525 - 27*c**6/25 + 316*c**5/75 - 104*c**4/15 + 16*c**2 + 5*c + 2. Determine v, given that u(v) = 0.
0, 2, 52
Let s be (-1)/(-5) - (32 - 92568/360). Factor -s - 1/3*h**2 + 52/3*h.
-(h - 26)**2/3
Let m(f) be the third derivative of -f**5/420 + 31*f**4/12 - 6727*f**3/6 + 413*f**2. Let m(c) = 0. Calculate c.
217
Let v(i) = -12*i**2 - i + 5. Let h(n) = -n**2 + n + 1. Suppose 2*u + 438 = 448. Let m(o) = u*h(o) - v(o). Factor m(g).
g*(7*g + 6)
Let l(f) be the first derivative of 4/5*f**5 + 117 + 256*f + 224*f**2 + 13*f**4 + 80*f**3. Factor l(u).
4*(u + 1)*(u + 4)**3
Suppose -5*j + 340 = -90*j. Let s be (3784/396)/(j/(-3)) - 7. Factor 1/6 - s*g**2 + 0*g.
-(g - 1)*(g + 1)/6
Let a be 643/(-7) + (-2)/14. Let d = -274/3 - a. What is s in 0 - 1/3*s - d*s**2 = 0?
-1/2, 0
Let n(o) = -o**2 - 3*o + 18. Let c be n(-4). Let v be ((-2)/c)/((-102)/476). What is u in 2/3*u**2 + 0*u - v = 0?
-1, 1
Let c(d) be the first derivative of -157*d**6/24 - d**5/10 + 157*d**4/2 + 4*d**3/3 - 314*d**2 - 8*d + 2195. Suppose c(p) = 0. What is p?
-2, -2/157, 2
Suppose -240*k - 15*k**2 - 173 - 11*k**2 - 12*k**2 - 319 - 12 - 2*k**3 = 0. Calculate k.
-7, -6
Let w(d) be the third derivative of 7/60*d**6 - 2*d**3 + 0*d - 269*d**2 + 1/105*d**7 - 7/12*d**4 + 0 + 1/6*d**5. Factor w(u).
2*(u - 1)*(u + 1)**2*(u + 6)
Let x = -426658 + 426658. Determine a so that -15/11*a**5 + 0 - 61/11*a**4 - 2/11*a**3 + 8/11*a**2 + x*a = 0.
-4, -2/5, 0, 1/3
Solve -76*w - 20 + 76*w**3 + 37*w**2 - 16*w**4 + 38*w**2 - 104*w**2 + 44*w**2 + 21*w**2 = 0.
-1, -1/4, 1, 5
Let r(n) be the third derivative of 205*n**2 + 7/20*n**5 + 0*n**3 + 0 + 41/48*n**4 + 1/240*n**6 + 0*n. Suppose r(y) = 0. Calculate y.
-41, -1, 0
Suppose 3*w = 4*w - 5*t, -4*w = -4*t. Let x be -1 - 44/(-36) - (-3)/(-54). Solve x*i + i**2 + w = 0.
-1/6, 0
Let c be (-2266)/(-7725)*(-72)/(-22). Factor 6/25*q**3 + 16/25*q + 26/25*q**2 - c.
2*(q + 2)*(q + 3)*(3*q - 2)/25
Let d be ((-64)/(-12) + -5)/(1/(-3)). Let f be d/(8 + 200/(-24)). Factor 0*m - 4/5*m**4 - 4/5*m**2 - 8/5*m**f + 0.
-4*m**2*(m + 1)**2/5
Let p(q) be the third derivative of -q**7/105 + 49*q**6/60 + 71*q**5/30 - 335*q**4/4 - 750*q**3 + 33*q**2 + 12*q. What is b in p(b) = 0?
-3, 5, 50
Let x(w) = -w**2 + 6*w - 4. Let v be x(4). Suppose -10*r + 34 - v = 0. Suppose -64 + 12*h**2 - 82*h - 107*h - 3*h**r + 35*h**2 + 13*h = 0. Calculate h.
-1/3, 8
Let k(s) = 14*s**3 + 71*s**2 - 43*s + 15. Let b(n) = -n**3 - 4*n**2 + n - 1. Let q(z) = 30*b(z) + 2*k(z). Factor q(h).
-2*h*(h - 7)*(h - 4)
Suppose 4*i - 9*w = -14*w + 48, 2*i - 3*w = -20. Suppose 10 + 5/3*l**i + 35/3*l = 0. Calculate l.
-6, -1
Find n, given that 1952/11*n + 476288/11 + 2/11*n**2 = 0.
-488
Let k(m) = -55*m**5 + 265*m**3 - 230*m**2 + 140*m. Let x(v) = 8*v**5 - 38*v**3 + 33*v**2 - 21*v. Let d(o) = -3*k(o) - 20*x(o). Determine p, given that d(p) = 0.
-3, 0, 1, 2
Let p(w) be the second derivative of 17*w**4/12 - 11*w**3 + 2*w + 8. Let x(s) = -4*s**2 + 17*s. Let c(u) = 6*p(u) + 26*x(u). Find j such that c(j) = 0.
0, 23
Suppose 74*h = 168 - 20. Suppose 5*t = 3*y - 4, 2*t + 42 - 38 = h*y. Factor 28*v - 20 + 4/5*v**y - 44/5*v**2.
4*(v - 5)**2*(v - 1)/5
Solve 217/3*q - 5/3*q**2 - 1/3*q**3 + 221/3 = 0.
-17, -1, 13
Suppose -i = 11 + 89. Let k = i + 107. Find w, given that 3*w**3 - k*w**3 + 2*w**4 - 28*w - 14*w**2 + 20*w = 0.
-1, 0, 4
Factor 0*g + 52*g**2 + 2/3*g**3 + 0.
2*g**2*(g + 78)/3
Let m be ((-1464)/(-3172))/(168/104). Suppose -m*q**2 + 4/7*q - 4/7*q**3 + 0 + 2/7*q**4 = 0. What is q?
-1, 0, 1, 2
Let u(x) be the second derivative of 2*x**7/63 - 338*x**6/45 + 1411*x**5/3 + 7225*x**4/9 + 3403*x. Factor u(l).
4*l**2*(l - 85)**2*(l + 1)/3
Let g(h) = -32*h**2 + 191*h + 213. Let c(l) = -38*l**2 + 190*l + 216. Let v(x) = -5*c(x) + 6*g(x). Factor v(i).
-2*(i - 99)*(i + 1)
Let x(c) be the first derivative of -304 - c - 1/20*c**5 - 3/16*c**4 + 3/8*c**2 + 5/12*c**3. Factor x(g).
-(g - 1)**2*(g + 1)*(g + 4)/4
Suppose -l + 1007 = 5*h, 3*h + 0*l = -4*l + 594. Suppose -213*g = -h*g. What is y in 3/4*y**4 - 9/4 - 6*y - 9/2*y**2 + g*y**3 = 0?
-1, 3
Let b(k) be the third derivative of -k**6/480 - 79*k**5/240 - 13*k**2 - k - 97. Factor b(a).
-a**2*(a + 79)/4
Let r(a) be the third derivative of a**6/180 + 2*a**5/45 - 55*a**4/9 - 1600*a**3/9 + 3464*a**2. Let r(c) = 0. Calculate c.
-10, 16
Let f(o) be the second derivati