Factor 562*k + 1250 - 205*k**2 + 15*k**3 + 2*k**b + 1480*k**2 + 177*k**2 + 89*k**3 + 2038*k.
2*(k + 1)**2*(k + 25)**2
Solve 33/8*j**3 - 27/2 - 1/8*j**4 - 171/8*j**2 + 247/8*j = 0.
1, 4, 27
Solve 0 + 1/2*t**3 - 47/2*t**2 - 24*t = 0 for t.
-1, 0, 48
Let s(z) = z**2 - 5*z + 8. Let b(c) = -c + 4. Let v be b(2). Let k be s(v). Factor 2 + 3*w**5 - 2 - 12*w**k - 6*w**5 + 9*w**4.
-3*w**2*(w - 2)**2*(w + 1)
Let o(f) be the second derivative of -3*f**5/40 - 281*f**4/8 - 4526*f**3 + 175857*f**2 + 15304*f. Factor o(b).
-3*(b - 11)*(b + 146)**2/2
Let r(i) = -12*i**3 + 10479*i**2 - 700257*i - 162. Let f(u) = u**3 - 806*u**2 + 53866*u + 12. Let g(p) = 27*f(p) + 2*r(p). Suppose g(x) = 0. What is x?
0, 134
Let i(q) be the third derivative of -q**7/70 - 3*q**6/2 + 63*q**5/20 + 61*q**4/4 - 183*q**2 + 2*q - 1. Suppose i(n) = 0. Calculate n.
-61, -1, 0, 2
Let s(c) be the first derivative of -3*c**5/20 - 57*c**4/8 - 95*c**3 - 2175*c**2/4 - 5625*c/4 - 11679. Find l, given that s(l) = 0.
-25, -5, -3
Let d(c) be the first derivative of -6/7*c - 2/3*c**3 + 43 - 2/7*c**4 + 2*c**2. Factor d(z).
-2*(z - 1)*(z + 3)*(4*z - 1)/7
Suppose -23*n + 16*n = -42. Factor n*q - 7*q - 56*q**2 - q + 54*q**2.
-2*q*(q + 1)
Let n(u) = 1324*u**3 - 733*u**2 + 132*u - 8. Let f(t) = -13*t**3 + t**3 + 11*t**3 - t**2. Let b(i) = -14*f(i) + 2*n(i). Factor b(k).
2*(11*k - 2)**3
Let a = 2905765/2490666 - -2/415111. Solve 0 + 2/3*g + a*g**4 - 1/6*g**3 - 14/3*g**2 = 0.
-2, 0, 1/7, 2
Suppose 19122*i**3 - 350 - 137*i - 19117*i**3 + 17*i - 75*i = 0. Calculate i.
-5, -2, 7
Let y(f) be the second derivative of f**6/10 - 9*f**5/4 + 250*f**3 - 3958*f. Find a, given that y(a) = 0.
-5, 0, 10
Let 1/5*i**2 + 1/5*i**3 - 1/5*i**4 + 0 - 1/5*i = 0. What is i?
-1, 0, 1
Let d(z) be the first derivative of 3*z**4/8 - 4533*z**3/8 + 3399*z**2/16 + 3421. What is s in d(s) = 0?
0, 1/4, 1133
Let v = -20213 - -20215. Find x such that -7/3*x**v - 2 + 23/3*x = 0.
2/7, 3
Let z = -39755 + 39755. Let w(x) be the third derivative of 0*x**3 - 1/12*x**5 + z*x + 35/24*x**4 - 18*x**2 + 0. Factor w(q).
-5*q*(q - 7)
Let x(k) be the third derivative of -2*k**2 + 1/168*k**8 + 2/3*k**3 + 1/15*k**6 - 4/105*k**7 + 8*k - 5/12*k**4 + 1/15*k**5 + 0. Factor x(p).
2*(p - 2)*(p - 1)**3*(p + 1)
Let g(x) be the first derivative of -x**2/2 - 6*x + 6. Let m be g(-10). Determine r, given that 9*r**4 - 8*r**m - 2*r**3 - 2*r**2 + r**3 = 0.
-1, 0, 2
Suppose -j = 10*j - 22. Suppose -3*o - j*o = 5*b - 95, 3*b - 4*o = 36. Find z such that 4*z**5 + 8*z**2 - 28*z + 12 + 3*z**4 - 7*z**4 - b*z**4 + 24*z**3 = 0.
-1, 1, 3
Let i(s) be the first derivative of 2*s**5/5 - 6*s**3 + 1172. Let i(y) = 0. Calculate y.
-3, 0, 3
Suppose -3 + 3 = -52*b. Suppose b = 386*c - 376*c - 20. Solve -3*u**3 + 0 - 33/4*u**5 + 0*u**c + 0*u - 18*u**4 = 0.
-2, -2/11, 0
Let a(t) = t**2 - 5*t + 28. Let o be a(-14). Solve -o + 26*q**4 + 125*q + 54*q**2 + 449*q - 2*q**5 - 298*q**2 - 60*q**3 = 0.
-3, 1, 7
Let h be (5/(-15)*-9 + -19)/(-2). Suppose -h*k - 50 = -33*k. Factor -2/9*w**3 + 0 + 0*w**k + 0*w - 2/9*w**4.
-2*w**3*(w + 1)/9
Let n(u) = 2*u**3 - 2*u**2 - 14*u + 3. Let f be n(0). Factor 0 + 12/5*t**2 + 3/5*t**f + 9/5*t.
3*t*(t + 1)*(t + 3)/5
Let r(d) = -12*d + 4. Let n be r(0). Let 94*v - 454*v - 60*v**2 + 50*v**3 - 4*v**4 - v**n = 0. Calculate v.
-2, 0, 6
Solve 4/7*o**3 - 424/7*o - 320/7 + 2/7*o**4 - 102/7*o**2 = 0.
-5, -4, -1, 8
Factor -s**2 + 52*s + 217 - 309*s + 956 - 131*s.
-(s - 3)*(s + 391)
Find o, given that -12061/3*o**2 - 300 - 25/6*o**4 - 4070*o - 509/2*o**3 = 0.
-30, -1, -2/25
Let k(x) = -22*x - 86. Let i be k(-4). Factor 5*q**i + 77*q - 146*q + 59*q.
5*q*(q - 2)
Suppose 5*v = 18*v - 39. Factor -2*u**2 + u**3 + u**4 - 5*u**2 + v*u - u**2 + 3*u**2.
u*(u - 1)**2*(u + 3)
Let r(y) be the third derivative of -y**7/42 + 29*y**6/24 - 20*y**5/3 + 65*y**4/6 - 1044*y**2. Suppose r(t) = 0. What is t?
0, 1, 2, 26
Let l(h) = -h**3 - 169*h**2 - 892*h + 14022. Let b be l(-163). Solve -b - 18/7*u - 2/7*u**2 = 0.
-7, -2
Let j(t) be the third derivative of 1/30*t**5 + 2*t**2 + 0*t + 1/12*t**6 - 2/3*t**4 + 0 - 1/105*t**7 + 4/3*t**3 - 1/168*t**8. Find k, given that j(k) = 0.
-2, 1
Let g(k) = -4*k**3 - 35*k**2 - 76*k + 12. Let f be g(-6). Let 0 + 3/2*q**4 - 39/2*q**3 + f*q**2 - 54*q = 0. What is q?
0, 1, 6
Let r be (9 - 14)*(48/(-5) - 0). Factor -r - 99 - 19*y - 3*y**3 + 16*y + 39*y**2 - 102*y.
-3*(y - 7)**2*(y + 1)
Let u(r) = -r**2 + 9*r - 5. Let k be u(8). Let p be 0 - (-3 + k)*-1. Solve -48*d**3 - 2*d + p*d + 2*d + 12*d**2 + 21*d**4 = 0.
0, 2/7, 2
Let g(o) be the third derivative of -o**5/25 + 319*o**4/40 + 8*o**3 + 3*o**2 - 119. Factor g(c).
-3*(c - 80)*(4*c + 1)/5
Let s(t) = t**2 - 129*t - 2482. Let f be s(-17). Let g(k) be the third derivative of -1/42*k**4 - 1/210*k**5 - 2*k**2 + 0 + 0*k**3 + f*k. Factor g(v).
-2*v*(v + 2)/7
Factor 161*m**3 - 197*m**2 + 60*m - 60*m - 331*m**3 + 169*m**3.
-m**2*(m + 197)
Let g(m) be the first derivative of m**5/12 + 35*m**4/24 + 4*m**2 + 28. Let q(u) be the second derivative of g(u). Factor q(i).
5*i*(i + 7)
Suppose -646*k + 651*k = 4*s - 45, 0 = 4*s + 5*k + 45. Suppose 2/3*l**5 + 2/3*l**3 + 0 + 4/3*l**4 + s*l + 0*l**2 = 0. What is l?
-1, 0
Let s(l) be the second derivative of -16/3*l**3 - 10 - 4*l - 1/3*l**4 - 30*l**2. Factor s(j).
-4*(j + 3)*(j + 5)
Let p be ((-111)/(-333))/(4286*(-2)/(-2136) - 4). Factor -7921/7 - p*j - 1/7*j**2.
-(j + 89)**2/7
Suppose 6*j - 252 = 10*j. Let a = j + 68. What is p in 5*p**3 - p**4 + 3*p + 0*p**4 - 2*p**2 - a*p**2 = 0?
0, 1, 3
Let k = -194 - -196. Let v be (0 + k)*(539/(-110) - -5). Let -v*c + 2/5 - 1/5*c**2 = 0. What is c?
-2, 1
Let x(r) = -r**2 - r + 64. Let w be x(-7). Suppose w*i - 18 = 13*i. Factor 0*g + 0 + 4/5*g**i - 2/5*g**3.
-2*g**2*(g - 2)/5
Let c be -2*(-12)/(-8)*-1. Let k be 13/(-104) - 88/(-192). Factor 5/3*x**2 - 4/3*x**c - 2/3*x + k*x**4 + 0.
x*(x - 2)*(x - 1)**2/3
Suppose -5 = -72*d + 77*d. Let j be (-11)/(550/40)*d/4. Factor -j*q - 1/10*q**2 - 1/10.
-(q + 1)**2/10
Let i be (-1726)/(-88)*35/1960. Let w = i + 3/224. Factor w*h**4 + 0 - 4/11*h**2 + 0*h**3 + 2/11*h - 2/11*h**5.
-2*h*(h - 1)**3*(h + 1)/11
Suppose -3*v + d + 4 = 2, 8 = -4*v + 4*d. Let t(g) be the first derivative of -194*g + g**3 + 36*g**v + 4*g**3 - 3 - 238*g - 6*g**3. Factor t(k).
-3*(k - 12)**2
Let o(v) be the first derivative of v**3/12 + 12*v**2 - 49*v - 1523. Factor o(w).
(w - 2)*(w + 98)/4
Let d(x) = 44*x - 62. Let c be d(4). Let a = -109 + c. Factor 0*w - 9/2*w**4 - 3/2*w**2 + 9/2*w**3 + 3/2*w**a + 0.
3*w**2*(w - 1)**3/2
Let o(v) = 16*v**2 - 5223*v + 1497. Let y(z) = 43*z**2 - 13058*z + 3743. Let j(p) = 26*o(p) - 10*y(p). Suppose j(w) = 0. Calculate w.
-373, 2/7
Let p(c) be the first derivative of 31 + 0*c**2 + 0*c - 1/10*c**5 + 1/90*c**6 + 10/3*c**3 + 0*c**4. Let j(x) be the third derivative of p(x). Factor j(h).
4*h*(h - 3)
Let o(t) be the first derivative of 12*t - 15/2*t**2 + 2*t**3 + 267 - 3/16*t**4. Let o(d) = 0. Calculate d.
2, 4
Let b be (-396)/3036 - (-4850)/506. Factor 900/11*p**3 - 8/11 - b*p - 210/11*p**2.
2*(2*p - 1)*(15*p + 2)**2/11
Factor 19319*b - 60*b**2 - 9678*b - 36*b**3 - 9666*b.
-b*(6*b + 5)**2
Let j be 34/(-357) - (-938)/588. What is z in 6*z + j*z**2 + 0 = 0?
-4, 0
Let s(c) be the first derivative of -c**3/5 + 186*c**2/5 - 684*c + 12667. Factor s(k).
-3*(k - 114)*(k - 10)/5
Let d = 7801/2410 + -789/482. Suppose -24/5*v + 0 + 12/5*v**4 + 18/5*v**3 - d*v**2 + 2/5*v**5 = 0. Calculate v.
-3, -2, 0, 1
Let t(g) be the second derivative of g**4/60 + 7*g**3/10 + 34*g**2/5 + 187*g. Determine y so that t(y) = 0.
-17, -4
What is u in -624/7 - 1/7*u**2 + 64/7*u = 0?
12, 52
Let u(v) be the first derivative of v**4/12 - v**3/2 + v**2 + 62*v - 58. Let t(g) be the first derivative of u(g). Factor t(m).
(m - 2)*(m - 1)
Suppose -28*m + 65*m + 51 = 140*m - 52. Factor -1/2*w**2 + m + 1/2*w.
-(w - 2)*(w + 1)/2
Let y(h) be the second derivative of 1/30*h**6 - 24/7*h**2 + 6*h - 3/35*h**5 - 5 - 4/21*h**4 - 1/294*h**7 + 32/21*h**3. Solve y(n) = 0 for n.
-2, 2, 3
Let a(i) be the third derivative of 13*i + 0*i**3 - 1/1260*i**7 + 1/72*i**4 + 1/120*i**5 + 0 + 0*i**6 + 3*i**2. Find w such that a(w) = 0.
-1, 0, 2
Suppose -41 + 2*d**3 + 505*d - d**3 - 263*d**2 - 209 + 4*d**3 + 3*d**2 = 0. What is d?
1, 50
Let n be (-5)/25 + (-73)/45*7. Let i =