
Find u, given that -138*u**4 + 60*u + 143*u**4 + 125*u**2 + 93*u**3 - 23*u**3 = 0.
-12, -1, 0
Let o(q) be the first derivative of -5*q**6/6 + 14*q**5 - 125*q**4/4 + 20*q**3 - 248. Determine l, given that o(l) = 0.
0, 1, 12
Let x(b) be the second derivative of b**5/35 + 2*b**4/21 - 2*b**3/7 - 24*b. Factor x(d).
4*d*(d - 1)*(d + 3)/7
Let a(d) be the second derivative of -d**6/45 - d**5/10 + 4*d**3/9 + 16*d. Factor a(u).
-2*u*(u - 1)*(u + 2)**2/3
Factor -191*t**2 - 778*t - 554*t**2 - 183*t**3 - 2560 - 335*t**2 - 2742*t - 5*t**4 + 58*t**3.
-5*(t + 1)*(t + 8)**3
Let d(a) = -5*a**2 - 8*a + 7. Let y be 18/(-3) + (-6)/(-2) + 0. Let s(n) = 5*n**2 + 7*n - 8. Let v(j) = y*s(j) - 2*d(j). Factor v(b).
-5*(b - 1)*(b + 2)
Let o(h) be the second derivative of -35*h**4/12 - 60*h**3 - 50*h**2 - 161*h. Suppose o(b) = 0. What is b?
-10, -2/7
Let q(d) be the third derivative of 29*d**6/24 + 22*d**5/3 + 5*d**4/8 + 600*d**2. What is b in q(b) = 0?
-3, -1/29, 0
Factor 103 + 24*z - 49 - 54 + z**2.
z*(z + 24)
Let l(y) = -1564*y - 1562. Let g be l(-1). Factor -2/9*q + 2/9*q**3 + 4/9 - 4/9*q**g.
2*(q - 2)*(q - 1)*(q + 1)/9
Let y(w) be the second derivative of -w**5/20 - 5*w**4/36 + 8*w**3/9 + 2*w**2 - 78*w + 4. Solve y(o) = 0 for o.
-3, -2/3, 2
Let r = -17444/5 + 3510. Let t = r + -21. Find c such that t*c**2 + 2/5 - 3/5*c = 0.
1, 2
Suppose -9 + 59 = 10*v. Suppose -j - 3 = -v*s + s, -s - 8 = -2*j. Factor -1/2*q**s + 1/4*q**5 + 1/4 + 1/4*q - 1/2*q**3 + 1/4*q**4.
(q - 1)**2*(q + 1)**3/4
Let c = -19 + 21. Solve 18 + 17 + 30*l + 5*l**c - 10 = 0 for l.
-5, -1
Let o(k) be the second derivative of -5*k**4/6 - 32*k**3/9 - 4*k**2/3 + 4*k + 4. Determine l, given that o(l) = 0.
-2, -2/15
Let v(q) = 19*q**2 + 30*q + 29. Suppose -3*s + 2*y = 29, 2 = 5*s - y + 48. Let b(r) = 9*r**2 + 15*r + 14. Let a(u) = s*b(u) + 4*v(u). Factor a(h).
-5*(h + 1)*(h + 2)
Let h = 655/63 + -72/7. Let o(x) be the third derivative of 0*x - 6*x**2 + h*x**4 + 1/90*x**5 + 0 + 4/9*x**3. Factor o(v).
2*(v + 2)**2/3
Let w(g) be the second derivative of g**7/672 - g**6/720 - g**3/3 - 9*g. Let q(j) be the second derivative of w(j). Suppose q(c) = 0. What is c?
0, 2/5
Let h(k) = 15*k**5 + k**4 - 71*k**3 - 89*k**2 - 7*k + 7. Let j(x) = -7*x**5 - x**4 + 35*x**3 + 45*x**2 + 3*x - 3. Let i(v) = -3*h(v) - 7*j(v). Factor i(m).
4*m**2*(m - 3)*(m + 2)**2
Factor 3937*w - 2104*w**2 + 870*w**3 - 2448*w**2 - 948 - 672 + 1283*w - 45*w**4 - 193*w**2.
-5*(w - 9)**2*(3*w - 2)**2
Suppose -12 = -9*g + 33. Determine j so that 15*j**2 - 14*j - g*j**3 - 15 + 14*j - 5 = 0.
-1, 2
Let i = 12 + 0. Suppose h + i = 14. Determine k, given that -49*k**2 - 5*k + 5*k**3 + 3 - 5*k**4 - 3 + 54*k**h = 0.
-1, 0, 1
Let g(h) be the first derivative of -2/9*h - 1/3*h**2 - 1/9*h**6 - 2/45*h**5 + 4/27*h**3 - 5 + 1/3*h**4. Solve g(a) = 0.
-1, -1/3, 1
Let m(n) be the first derivative of 4*n**3/15 + 24*n**2 - 244*n/5 + 249. Factor m(f).
4*(f - 1)*(f + 61)/5
Let j = 13/278 + 4305/3058. Factor -j*p - 2/11*p**2 - 32/11.
-2*(p + 4)**2/11
Let v(m) be the third derivative of -169*m**6/1140 - 364*m**5/285 - 53*m**4/57 - 16*m**3/57 - 119*m**2. Factor v(x).
-2*(x + 4)*(13*x + 2)**2/19
Let l(s) be the third derivative of s**5/240 + 7*s**4/12 + 98*s**3/3 + 80*s**2. Solve l(a) = 0 for a.
-28
Let h(i) = -3*i**2 - 62*i - 157. Let l be h(-3). Factor 0*v - 1/3*v**4 + 1/3*v**l - 1/3*v**3 + 1/3*v**5 + 0.
v**2*(v - 1)**2*(v + 1)/3
Let l be (-4)/(-26) + -4 + 4. Let v be 8/5 + (-6)/(-15). Suppose 0 + 2/13*a**4 - 2/13*a**v + l*a**3 - 2/13*a = 0. Calculate a.
-1, 0, 1
Let m(g) be the second derivative of -30*g**3 - 7/4*g**5 - 20*g**2 - 12*g + 0 - 25/2*g**4. Suppose m(r) = 0. What is r?
-2, -2/7
Find n such that 1568/17 - 112/17*n + 2/17*n**2 = 0.
28
Let f(u) be the third derivative of -u**7/105 + 13*u**6/60 - 2*u**5/5 + 186*u**2. Factor f(z).
-2*z**2*(z - 12)*(z - 1)
Factor -44 - 48*o**2 - 60*o - 93 + 4*o**3 - 96 + 337.
4*(o - 13)*(o - 1)*(o + 2)
Suppose 0 = 2*o - 2*t - 0*t - 6, 5*t - 9 = -3*o. Factor -47 - o*z**2 + 0*z**2 + 50.
-3*(z - 1)*(z + 1)
Let g(m) = m**5 + m**3 + m**2 + m + 1. Let v(b) = 10*b**5 + 5*b**4 - 10*b**3 + 15*b + 5. Let z(k) = 5*g(k) - v(k). Determine w, given that z(w) = 0.
-2, -1, 0, 1
Let h be (-2 - (-252)/27)*2/22. Find a such that 0*a**2 + 4 + 14/3*a - h*a**3 = 0.
-2, -1, 3
Suppose 5*s + 5*s = 50. Suppose 98 = s*o + 83. Factor 0*t - 2/5*t**o + 0 + 2/5*t**2.
-2*t**2*(t - 1)/5
Suppose -6*d + 2*d = -4*b - 28, 4*b + 19 = d. Let n = 6 - d. Suppose -1 + n*m**2 - 8*m + 1 + 5*m = 0. What is m?
0, 1
Let k(o) = 2*o**2 - 55*o + 105. Let u be k(2). Let t be (3/2)/((-45)/(-4)). Determine z, given that -2/15*z**u - 2/5*z - 2/5*z**2 - t = 0.
-1
Let u = 54931 + -54929. Determine j, given that 2 - 1/4*j**u - 7/4*j = 0.
-8, 1
Let n(s) be the second derivative of s**5/25 - s**4/5 - 8*s**3/15 + 24*s**2/5 - 165*s - 1. Find k such that n(k) = 0.
-2, 2, 3
Let w(n) be the second derivative of n**4/72 - 17*n**3/36 + 2*n - 335. Factor w(b).
b*(b - 17)/6
Let v(r) be the first derivative of -r**3/12 + 11*r**2/4 + 11. Factor v(g).
-g*(g - 22)/4
Let 41*c - 34*c + 6 - 697*c**2 + 698*c**2 = 0. What is c?
-6, -1
Let i be -7 + 376/56 - 46/(-63). Let c(u) be the first derivative of 1/3*u**2 - 5 - i*u - 2/27*u**3. What is m in c(m) = 0?
1, 2
Let a be 70/(-15)*(-66)/(-4). Let l be a/(-35) + (-1)/5. What is b in -b**2 - 2 + 1 - l*b + 0*b = 0?
-1
Let s be (-2)/(-6) - (-234)/27. Factor s*u**2 + 3*u + 2*u - 7*u.
u*(9*u - 2)
Suppose -5*f = -4*y + 7, -3*f = -9*y + 13*y - 15. Factor 3/2*q**y + 0*q + 3/2*q**2 - 3/2*q**4 - 3/2*q**5 + 0.
-3*q**2*(q - 1)*(q + 1)**2/2
Let y be 1 + ((-720)/50)/(-12) - 2. Factor 0 - y*i**3 - 1/5*i**2 + 0*i.
-i**2*(i + 1)/5
Suppose 50*q - 194*q + 184*q**2 - 44*q**3 - 48*q**4 - 5825 + 5857 + 20*q**5 = 0. Calculate q.
-2, 2/5, 1, 2
Let a(m) be the third derivative of m**8/336 + m**7/70 + m**6/120 - m**5/20 - m**4/12 + 36*m**2. Factor a(b).
b*(b - 1)*(b + 1)**2*(b + 2)
Let u(m) be the third derivative of m**6/60 + 13*m**5/30 + m**4 + 169*m**2. Factor u(d).
2*d*(d + 1)*(d + 12)
Solve 0*l - 22/9*l**4 + 0 + 16/3*l**3 + 2/9*l**5 + 8*l**2 = 0 for l.
-1, 0, 6
Let t be ((-2537)/18275 - 2/(-25))*-32. Let -96/17 - 48/17*d**3 + 2/17*d**4 + 2/17*d**5 + t*d + 80/17*d**2 = 0. What is d?
-6, -1, 2
Let g(c) be the first derivative of 9 - 6/65*c**5 - 3/13*c**2 + 1/39*c**6 + 1/13*c**4 + 4/39*c**3 + 2/13*c. Solve g(a) = 0.
-1, 1
Let h(p) be the first derivative of -5*p**4/12 - 5*p**3 - 25*p**2/2 + 53*p - 44. Let l(a) be the first derivative of h(a). Solve l(v) = 0.
-5, -1
Determine f so that 2/3*f**3 - 2/3*f + 2/9*f**4 + 8/9 - 10/9*f**2 = 0.
-4, -1, 1
Determine i, given that -286/7*i - 188/7 - 100/7*i**2 - 2/7*i**3 = 0.
-47, -2, -1
Factor 3/4*q**3 - 51/4*q + 0 + 12*q**2.
3*q*(q - 1)*(q + 17)/4
Suppose -24 = -2*n - 2*n. Suppose 0 = -4*g - n - 2, 5*k = -3*g + 14. Factor 0 + 2/5*x**2 + 0*x**3 + 0*x - 2/5*x**k.
-2*x**2*(x - 1)*(x + 1)/5
Let t be ((-9)/(-21))/((-6)/(-42)). Find m, given that 216*m - 223*m**3 + 274*m**t - 149*m**3 - 336*m**2 - 32 = 0.
-4, 2/7
Let v(z) be the third derivative of 1/105*z**7 + 1/1008*z**8 + 1/45*z**6 - 1/30*z**5 + 0*z - 1/8*z**4 + 0*z**3 - 21*z**2 + 0. Solve v(r) = 0 for r.
-3, -1, 0, 1
Let l be ((-54)/(-24))/(6/16). Factor -22 - l*k + 4*k + 2*k**2 + 6*k**3 - 4*k**3 + 20.
2*(k - 1)*(k + 1)**2
Let a(w) = -w**3 + 2*w**2 + 3*w + 2. Let l be a(3). Let f = -69945/7 + 10023. Factor 128/7*h**4 + 4/7 + f*h**l + 50/7*h + 352/7*h**3.
2*(h + 2)*(4*h + 1)**3/7
Suppose 193*n - 259*n + 264 = 0. Suppose 3/4 - 3*f**n + 9/4*f**2 + 21/8*f - 9/8*f**5 - 3/2*f**3 = 0. What is f?
-1, -2/3, 1
Let d(v) be the first derivative of -4*v**5/5 + 19*v**4 + 28*v**3 - 38*v**2 - 80*v - 146. Factor d(i).
-4*(i - 20)*(i - 1)*(i + 1)**2
Let d(s) = -s**4 + s**3 - 2*s**2 - s - 1. Let m(u) = u**5 + 22*u**3 - u**2 - 3*u - 7. Let i(b) = -35*d(b) + 5*m(b). Factor i(h).
5*h*(h + 1)**3*(h + 4)
Let i(c) be the first derivative of -3*c + 3 + 27*c**3 + 4 - 13*c**3 - 15*c**3 + 3*c**2. Factor i(o).
-3*(o - 1)**2
Let a = 743/2 - 1114/3. Let v(w) be the second derivative of 0 + 10*w + w**3 - a*w**4 - 2*w**2. Determine u so that v(u) = 0.
1, 2
Let z**3 - 482*z**2 + 239*z**2 + 247*z**2 = 0. Calculate z.
-4, 0
Let q be 5 + 235/(-80) + 4/(-2). Let w(d) be the third derivative of -2*d**2 + 0*d + 0 + 1/80*d**5 + 1/8*d**