*w = 0. What is w?
0, 2/3, 1
Let a(t) be the third derivative of t**5/105 + 184*t**4/21 - 246*t**3/7 + 3*t**2 + 9. Determine u so that a(u) = 0.
-369, 1
Let 170*w + 316*w - 2*w**2 + 49*w - 10*w**2 + 7*w**2 = 0. What is w?
0, 107
Suppose -3*f + 10 = -2*m, f - 3*m - 1036 + 1021 = 0. Find v such that 0 + 3/2*v**2 + 3/2*v**4 - 3*v**3 + f*v = 0.
0, 1
Let o = -61552 + 61554. Factor -16/3*s - 160/3 - 2/15*s**o.
-2*(s + 20)**2/15
Let s = -20947/225 - -2333/25. Factor s*y + 0 + 2/9*y**2.
2*y*(y + 1)/9
Let s(g) = -4*g**2 + 88472*g + 97947392. Let c(i) = -2*i**2 + 35388*i + 39178957. Let t(r) = -12*c(r) + 5*s(r). Factor t(v).
4*(v + 2213)**2
Suppose 7 + 1 = 2*q, q = 2*o. Factor 11*g**o + 42*g + 20*g - 38*g + g**3 + 3*g**2.
g*(g + 2)*(g + 12)
Suppose 2*d + 8 = 3*l - 3, -3*l = -d - 13. Let s be 12/20*(0 + l). Let 20*g - 5*g**2 - 8*g - 7*g**2 + 3*g**s = 0. Calculate g.
0, 2
Suppose 5*x + 28 = -4*i + 33, 3*x + 4*i = -5. Let -4*s**4 + 0*s**4 - x*s**3 - 12 - 61*s + 69*s + 16*s**2 + s**3 - 4*s**3 = 0. What is s?
-3, -1, 1
Let g(d) be the second derivative of 64*d**4/9 + 92*d**3/27 - d**2/9 - 228*d. Suppose g(l) = 0. Calculate l.
-1/4, 1/96
Let w(p) = -17*p**2 - 341*p - 18. Let n be w(-20). Let d be 1 - (-27)/(-5) - (-1 + -4). Find k such that 18/5*k - 3 - d*k**n = 0.
1, 5
Factor 2/9*m**3 - 2*m**2 + 14/3 + 22/9*m.
2*(m - 7)*(m - 3)*(m + 1)/9
Determine t so that -9*t**3 + 33/2 - 42*t + 69/2*t**2 = 0.
1, 11/6
Let g be (90/(-4))/(250*(-58)/20880). Factor -g - 9*k - 1/5*k**3 + 16/5*k**2.
-(k - 9)**2*(k + 2)/5
Let m(n) be the first derivative of -n**6/6 - 51*n**5 - 251*n**4/4 + 763*n**3/3 + 126*n**2 - 508*n + 971. What is l in m(l) = 0?
-254, -2, -1, 1
Factor 0*z - 3/2*z**4 - 387*z**2 + 393/2*z**3 + 0.
-3*z**2*(z - 129)*(z - 2)/2
Let p(u) be the third derivative of -u**7/126 - 2*u**6/9 + u**5 - 2019*u**2. Suppose p(o) = 0. What is o?
-18, 0, 2
Let s(i) be the first derivative of i**5/5 - 7*i**3 - 10*i**2 + 7499. What is x in s(x) = 0?
-4, -1, 0, 5
Let d(z) = 13*z**3 + 3*z**2 - 32*z - 22. Let o(v) be the first derivative of -7*v**4/4 - v**3/3 + 8*v**2 + 10*v + 9. Let q(i) = -3*d(i) - 5*o(i). Factor q(n).
-4*(n - 2)*(n + 1)*(n + 2)
Let h(z) be the first derivative of 43*z**4/12 - 101*z**3/3 + 74*z**2 - 20*z/3 - 10422. Factor h(t).
(t - 5)*(t - 2)*(43*t - 2)/3
Let q(w) be the third derivative of w**7/210 - 3*w**6/20 - 83*w**5/60 - 9*w**4/2 - 22*w**3/3 - 307*w**2. Factor q(z).
(z - 22)*(z + 1)**2*(z + 2)
Find x such that 6*x + 189/4*x**3 - 75/2*x**2 + 0 = 0.
0, 2/9, 4/7
Let x be -1*2/((-4)/6). Suppose 0 = f - d - 1, -2*f + 2*d = f - 5. Determine o, given that 2*o + o + 2*o - 3*o**2 - 2*o - 3*o**f + x = 0.
-1, 1
Let n(j) be the second derivative of 0 - 191*j + 4*j**2 - 1/54*j**4 - 16/27*j**3. Factor n(p).
-2*(p - 2)*(p + 18)/9
Suppose -1446 = 320*q - 397*q - 405*q. Find g, given that -2*g**q + 1/2*g**4 + 0 + 0*g - 2*g**2 + 1/2*g**5 = 0.
-2, -1, 0, 2
Let g(r) = r**2 - 14*r - 312. Let n be g(28). Let a be n/(-10) + (-7 - -18). Factor 5/2*z**2 - 5/4*z**a + 0 + 0*z.
-5*z**2*(z - 2)/4
Suppose 38*b - 134*b = 92*b - 376. Solve 178/5*a**3 + 64/5*a**4 + 18/5 + 8/5*a**5 + 102/5*a + 206/5*a**b = 0 for a.
-3, -1, -1/2
Let x(t) be the third derivative of t**6/30 - 1537*t**5/15 + 98560*t**4 - 393216*t**3 + 2245*t**2. What is m in x(m) = 0?
1, 768
Factor -314*y - y**2 + 4*y - 9*y**2 + 8*y**2 - 70*y - 18050.
-2*(y + 95)**2
Let u be ((-587)/586 - -1)/(9/(-36)). Let l = 871/1172 + u. Factor -81/4 - 27/4*x**2 + 81/4*x + l*x**3.
3*(x - 3)**3/4
Let b(h) be the third derivative of -h**5/12 + 115*h**4 - 2*h**2 - 125*h. Let b(t) = 0. Calculate t.
0, 552
Let d = 9444/33005 + -2/4715. Let n(p) be the third derivative of -7*p**2 + 0 + 0*p + 3/56*p**4 + 1/140*p**5 - d*p**3. Find w, given that n(w) = 0.
-4, 1
Suppose -500*f**3 + 169 + 1645*f**2 - 133 + 35*f**4 + 264 - 1480*f = 0. Calculate f.
2/7, 1, 3, 10
Suppose 5*v + 148 - 163 = 0. Suppose -2*h - v*w = -7*w + 12, -w + 3 = 0. Factor -4/7*p**3 + h + 2/7*p**5 + 0*p + 2/7*p**4 + 0*p**2.
2*p**3*(p - 1)*(p + 2)/7
Let j = -4150 - -199201/48. Let o(a) be the third derivative of 0*a + 0 + 5/4*a**3 + 5/24*a**5 + j*a**6 + 35/48*a**4 + 5*a**2. Factor o(r).
5*(r + 1)**2*(r + 3)/2
Factor 841/3*p**2 - 177241/3 + 1/3*p**3 + 176399/3*p.
(p - 1)*(p + 421)**2/3
Suppose 3*g = -5*w + 32, -w = 3*g - 18 + 2. Let c be (-9 - 310/(-30))/((-14)/(-3)). Let -2/7*m + c*m**3 + 2/7*m**2 + 0 - 2/7*m**g = 0. What is m?
-1, 0, 1
Let y(d) be the third derivative of -d**8/1008 + d**7/10 - 119*d**6/360 - 187*d**5/180 + 10*d**4/3 + 122*d**3/9 - 522*d**2 + 3*d. Let y(w) = 0. What is w?
-1, 2, 61
Let n(u) be the second derivative of -u**4/24 + 127*u**3/12 - 741*u**2/2 - 21*u - 34. Factor n(t).
-(t - 114)*(t - 13)/2
Let -10*s**3 + 5*s**3 - 76*s + 30*s**2 - 2*s**3 + 9*s**3 + 4*s**2 = 0. Calculate s.
-19, 0, 2
Suppose 4*r = -6*x + 9*x - 24, -x = -4*r - 16. Let p(i) be the second derivative of -2/11*i**3 - 12*i + 20/33*i**x + 0 - 1/11*i**2. Solve p(v) = 0 for v.
-1/10, 1/4
Let b = -117/10 + 353/30. Let q(x) be the second derivative of -b*x**6 + 7/6*x**4 + 12*x**2 + 0 - 1/5*x**5 + 20/3*x**3 + 28*x. Find d, given that q(d) = 0.
-2, -1, 3
Suppose 309*j + 394*j - 2812 = 0. What is r in -4*r**2 + 0 - 25/2*r**5 - 35*r**j - 22*r**3 + 0*r = 0?
-2, -2/5, 0
Let h = 4501 + -13477/3. Suppose 2/3*x**3 + h*x**2 + 0 + 0*x = 0. What is x?
-13, 0
Suppose -3*u = -3*p + 33, 5*p - 73 + 3 = 2*u. Let j be -19 + p - (-39)/(-9)*-1. Determine o so that -o - j*o**2 + 0 = 0.
-3/4, 0
Let t = 5873/15 + -783/2. Let j(u) be the third derivative of 0*u**4 + 0*u**5 + 0 - 9*u**2 - t*u**6 + 0*u + 0*u**3 + 2/105*u**7. Let j(k) = 0. Calculate k.
0, 1
Let o(c) be the first derivative of 0*c - 4/3*c**3 - 1/120*c**4 - 1/400*c**5 + 0*c**2 - 1 - 1/3600*c**6. Let p(m) be the third derivative of o(m). Factor p(s).
-(s + 1)*(s + 2)/10
Suppose 4*p - p + 4*j - 164 = 0, 5*p - 304 = j. Determine u, given that 59 + 82 - 4*u**2 + 39 - p - 116*u = 0.
-30, 1
Let l(f) be the third derivative of -28/15*f**5 + 2 - 10/9*f**3 - 9/4*f**4 - 4/45*f**6 + 0*f + 33*f**2. Determine p, given that l(p) = 0.
-10, -1/4
Suppose -158 = -2*p + 2*z, -2*p - 2*z = 2*p - 298. Factor 2 + 2182*r - 2138*r + 23*r**3 + p*r**2 + 13*r**3 + 2.
4*(r + 1)**2*(9*r + 1)
Let m(u) be the first derivative of -u**3/6 + 5*u**2/2 - 8*u + 165. Factor m(x).
-(x - 8)*(x - 2)/2
Let w(y) be the second derivative of y**5/90 + 146*y**4/9 + 583*y**3/9 + 874*y**2/9 + 4*y - 230. Factor w(g).
2*(g + 1)**2*(g + 874)/9
Determine x, given that 103/3*x**3 - 3520/3 - 284*x**2 - 4/3*x**4 + 2896/3*x = 0.
4, 55/4
Let g(o) = 14*o**3 + o**2 + 2*o + 2. Let a be g(-1). Let v = a + 19. Find r such that -56*r - 12*r**2 + 6 + 29*r - 6*r**3 + 3*r**5 + v*r**4 + 30*r = 0.
-2, -1, 1
Let f(d) be the second derivative of d**6/10 - 291*d**5/20 + 792*d**4 - 17920*d**3 + 49152*d**2 + 3357*d. Determine s so that f(s) = 0.
1, 32
Let w(c) be the second derivative of c**4/66 + c**3/33 - 1190*c**2/11 - 6315*c. Factor w(j).
2*(j - 34)*(j + 35)/11
Let x(j) be the second derivative of 0 + 41/12*j**3 - 1/24*j**4 - 10*j**2 - 176*j. Factor x(p).
-(p - 40)*(p - 1)/2
Suppose 0 = -122*r + 125*r - 93. Factor r*a - 99*a + 48*a - 4*a**2.
-4*a*(a + 5)
Let x = -612385/9 + 68043. Let n = -96 + 866/9. What is a in -2/9*a**3 - 2/9*a**2 + x*a + n = 0?
-1, 1
Let n = 367 + -359. Let l be (-1)/n - 5735/(-1240). Factor l*o**3 - 21*o**2 + 9/4*o**4 - 3/4*o**5 + 18*o + 0.
-3*o*(o - 2)**3*(o + 3)/4
Determine o so that -1676/7*o**3 - 349448/7 + 176388/7*o**2 - 171380/7*o + 4/7*o**4 = 0.
-1, 2, 209
Let m(t) be the third derivative of -t**6/300 - 7*t**5/75 + 47*t**4/60 + 16*t**3 + t**2 + 22*t + 8. Find z, given that m(z) = 0.
-16, -3, 5
Let h be 5/14*3/(225/20). Let z = -809/3 - -1891/7. Factor -h*b**3 - 8/21 - 16/21*b - z*b**2.
-2*(b + 1)*(b + 2)**2/21
Let t(k) be the first derivative of k**6/42 + 9*k**5/35 + 29*k**4/28 + 43*k**3/21 + 15*k**2/7 + 8*k/7 - 2498. Solve t(b) = 0 for b.
-4, -2, -1
Suppose -21*o = -22*o + 59. Factor 341 - b**2 + 6*b**2 + o*b + 939 - 219*b.
5*(b - 16)**2
Let g(j) be the first derivative of -j**4/28 + 20*j**3/7 + 17*j - 101. Let l(r) be the first derivative of g(r). Factor l(x).
-3*x*(x - 40)/7
Let h(m) = m**2 - 210*m + 7801. Let t be h(48). Let u(a) be the third derivative of 0*a + 1/6*a**4 - t*a**2 + 1/6*a**3 + 1/12*a