Let c(v) be the second derivative of v**10/25200 + v**9/18900 + v**4 - 25*v. Let l(o) be the third derivative of c(o). Factor l(h).
2*h**4*(3*h + 2)/5
Factor 49*t - 343/10 - 1/10*t**4 + 11/5*t**3 - 84/5*t**2.
-(t - 7)**3*(t - 1)/10
Let -19*l - 89*l**4 + 5*l - 12*l**2 + 6*l**3 + 91*l**4 + l - 3*l = 0. Calculate l.
-4, -1, 0, 2
Let x(f) be the third derivative of 1/3*f**5 - 17*f**2 + 0*f - 1/4*f**4 + 0 + 0*f**3 - 1/5*f**6 + 2/35*f**7 - 1/168*f**8. Factor x(r).
-2*r*(r - 3)*(r - 1)**3
Let h be (-34)/(-10) - (-2)/(-5). Let x be 0 - (12/h)/(-2). Factor 7*u**x - u**3 + 4*u**3 + 2*u**2 - 12.
3*(u - 1)*(u + 2)**2
Factor -68/5*m - 2*m**3 + 51/5*m**2 - 1/5*m**4 + 28/5.
-(m - 2)*(m - 1)**2*(m + 14)/5
Let y(x) be the first derivative of 2*x**6/3 + 76*x**5/5 - 42*x**4 + 318. What is j in y(j) = 0?
-21, 0, 2
Let h(o) be the third derivative of -o**5/330 + 4*o**4/33 - 49*o**2. Factor h(y).
-2*y*(y - 16)/11
Let r(l) be the third derivative of -1/210*l**5 + 1/21*l**3 + 0*l**4 + 0 + 0*l + 27*l**2. Factor r(w).
-2*(w - 1)*(w + 1)/7
Let n be 2 - 0/(-4 - -5). Let u(m) = -45*m - 2*m**3 - 7 + 26*m + 21*m + 10*m**n. Let r(s) = s**3 - s + 1. Let j(p) = 3*r(p) - u(p). Find z, given that j(z) = 0.
-1, 1, 2
Let v = -44 + 48. Determine d so that -6*d - 6*d**3 + v*d**2 + 3*d + 3*d + 2*d**5 = 0.
-2, 0, 1
Let r be (6 + 30/(-4))*-2. Let z(v) be the third derivative of 0*v - 1/50*v**5 + 0*v**4 - v**2 + 0 - 1/300*v**6 + 0*v**r. Determine i, given that z(i) = 0.
-3, 0
Let g(t) = 11*t**4 + 38*t**3 - 478*t**2 + 1086*t. Let j(c) = 15*c**4 + 37*c**3 - 479*c**2 + 1087*c. Let h(w) = 4*g(w) - 3*j(w). Determine b so that h(b) = 0.
0, 3, 19
Let g(r) be the third derivative of -r**6/60 + 11*r**5/30 - 19*r**4/12 + 3*r**3 - 109*r**2. Factor g(a).
-2*(a - 9)*(a - 1)**2
Let v be 8/10*(535/(-550) + 36/30). Solve 0 - 14/11*k**2 - v*k**3 - 12/11*k = 0.
-6, -1, 0
Let x be 3*(-2 + 1 + 2). Let o = 1994/3 + -664. Let 8/9*f**2 + 0 - o*f - 2/9*f**x = 0. What is f?
0, 1, 3
Determine q so that 40*q + 1421*q**2 - 2862*q**2 + 4*q**3 + 1413*q**2 = 0.
0, 2, 5
Let m(h) be the first derivative of -h**6/288 - h**5/16 - 25*h**4/96 + 3*h**3 + 17. Let t(s) be the third derivative of m(s). Factor t(p).
-5*(p + 1)*(p + 5)/4
Let r(i) = -4*i**2 + 10*i - 4. Let t(n) = 5*n**2 - 9*n + 6. Let u(w) = 3*r(w) + 2*t(w). Solve u(g) = 0.
0, 6
Let -98/3*v**2 - 94/3*v**3 + 32*v + 98/3*v**4 + 0 - 2/3*v**5 = 0. What is v?
-1, 0, 1, 48
Let x(p) be the third derivative of p**10/75600 - p**9/30240 - p**8/10080 + p**7/2520 - p**5/30 + 7*p**2. Let k(u) be the third derivative of x(u). Factor k(v).
2*v*(v - 1)**2*(v + 1)
Suppose 38*o = 41*o - 24. Suppose -4*v - 3*b - 1 = 0, 6*v + 4*b = o*v - 16. Determine q, given that -1/2 - 1/2*q**v + q = 0.
1
Let h(x) = -5*x**2 + 21*x - 28. Let v(a) = -5*a**2 + 20*a - 30. Let b(r) = -5*h(r) + 4*v(r). Factor b(n).
5*(n - 4)*(n - 1)
Let n = 7517888/565 + -13306. Let f = n + 136/113. Determine p, given that f*p**3 + 3/5 - 3/5*p**2 - 6/5*p = 0.
-1, 1/2, 1
Find z such that 0*z + 0 + 1/6*z**4 + 2*z**2 + 13/6*z**3 = 0.
-12, -1, 0
Let v(c) be the second derivative of -c**6/25 + c**5/75 + c**4/10 - 2*c**3/45 + 17*c - 8. Find a such that v(a) = 0.
-1, 0, 2/9, 1
Let w(f) be the second derivative of f**3 - 3*f. Let x be w(2). Suppose -s**2 + s**2 + 12*s + 0*s**2 + x + 3*s**2 = 0. What is s?
-2
Let l = -780/11 + 2450/33. Let -2/3*r**3 + 4/3 - l*r + 8/3*r**2 = 0. What is r?
1, 2
Suppose -4*w + 3*w = -5. Let h(m) = 11*m**3 - 13*m + 7. Let v(r) = -11 - 5*r + 17*r - 273*r**3 + 257*r**3 + 8*r. Let k(o) = w*v(o) + 7*h(o). Factor k(p).
-3*(p - 1)**2*(p + 2)
Determine b, given that 0 - b**2 + 0*b + b**3 + 5/4*b**5 + 13/4*b**4 = 0.
-2, -1, 0, 2/5
Let r be ((-80)/(-28))/(3/21). Factor -611*y - 12*y**2 - r*y**4 + 4*y**5 + 28*y**3 + 611*y.
4*y**2*(y - 3)*(y - 1)**2
Factor 4*i**3 + 0 - 4/9*i**4 + 32/3*i - 104/9*i**2.
-4*i*(i - 4)*(i - 3)*(i - 2)/9
Let g be 1/10 - 1712/33920. Let i = g - -4/53. Find l, given that -1/4*l - 3/8*l**2 + 3/8*l**4 + 0 + 1/8*l**5 + i*l**3 = 0.
-2, -1, 0, 1
Let h = -13 + 27/2. Suppose -4*k + 13 = -5*f, -3*f + 4 = 3*k - f. Solve -1/4*o**4 - h*o**3 + 0 - 1/4*o**k + 0*o = 0.
-1, 0
Let n(k) = 2*k + 21. Suppose 24 = -13*m + 10*m. Let c be n(m). Factor 0 + 0*p + p**2 + 21/4*p**4 + 49/4*p**c - 6*p**3.
p**2*(p + 1)*(7*p - 2)**2/4
Let n(x) be the third derivative of x**6/360 - x**5/90 - x**4/8 + x**3 - 115*x**2. Factor n(p).
(p - 3)*(p - 2)*(p + 3)/3
Let g be (-2 + 320/156)*48. Let v = -717 + 719. Factor 2/13*y**v + g + 16/13*y.
2*(y + 4)**2/13
Let w(b) be the first derivative of 3*b**5/20 + 15*b**4/16 - 3*b**3/2 + 93. Solve w(r) = 0.
-6, 0, 1
Let r be 88/33*(-6)/(-4) - -124. Let j = -122 + r. What is h in -j*h + 50/7*h**3 + 10/7*h**2 - 18/7 = 0?
-3/5, 1
Suppose -g = -2*i + 71, 2*i - g + 127 = 6*i. Determine m, given that 0 - 42*m**3 - 12*m**2 - 15/2*m**5 - i*m**4 + 0*m = 0.
-2, -2/5, 0
Suppose 0 = -2*j - 3*j + 20. Suppose -12 = u - j*u. Factor -36*q**u - q - q - 2*q - 28*q**2 - 60*q**3.
-4*q*(q + 1)*(3*q + 1)**2
Let x(n) be the first derivative of -n**6/33 + 90*n**5/11 - 10125*n**4/11 + 607500*n**3/11 - 20503125*n**2/11 + 369056250*n/11 - 374. Factor x(m).
-2*(m - 45)**5/11
Let y(g) be the second derivative of -g**4/4 + 5*g**3/2 - g + 23. Let y(o) = 0. Calculate o.
0, 5
Let s(u) be the first derivative of -6*u**3 + u**2 + 4*u - 13/2*u**4 - 2*u**5 + 7. Factor s(w).
-2*(w + 1)**3*(5*w - 2)
Let n(f) be the third derivative of 2*f**7/315 - f**6/30 - 51*f**2 + 2*f. Factor n(h).
4*h**3*(h - 3)/3
Let v(j) = -62*j**4 - 222*j**3 - 314*j**2 - 90*j. Let b(c) = -12*c**4 - 44*c**3 - 63*c**2 - 18*c. Let k(i) = -16*b(i) + 3*v(i). Solve k(w) = 0 for w.
-3, -1/3, 0
Let c(m) be the second derivative of m**6/30 - 29*m**5/20 + 45*m**4/2 - 350*m**3/3 - 500*m**2 + 17*m - 2. Factor c(j).
(j - 10)**3*(j + 1)
Let r(d) = 26*d**3 - 129*d**2 - 200*d - 96. Let o(a) = 3*a**3 - 16*a**2 - 25*a - 12. Let t(u) = 51*o(u) - 6*r(u). Find k such that t(k) = 0.
-12, -1
Let n be 3/(-8*(-10)/16). Let -3/5*a**3 - n*a + 0 + 6/5*a**2 = 0. What is a?
0, 1
Let b(v) be the second derivative of 0*v**2 + 0 - 6*v + 1/40*v**5 + 0*v**3 - 1/12*v**4. Find m, given that b(m) = 0.
0, 2
Let q be ((-1464)/(-54))/(7/(420/(-8))). Let c = -203 - q. Factor -c*u**2 + 0 + 1/3*u.
-u*(u - 1)/3
Let d(m) be the first derivative of -m**6/10 - 36*m**5/25 - 24*m**4/5 + 48*m**3/5 + 216*m**2/5 + 85. Solve d(b) = 0 for b.
-6, -2, 0, 2
Let w = 53 + -43. Let r(q) = -q**4 - q**3 + q**2 + q. Let g(l) = 15*l**4 + 5*l**3 - 10*l**2 - 10*l. Let a(y) = w*r(y) + g(y). Factor a(u).
5*u**3*(u - 1)
Let a(i) = -3*i**3 + 14*i**2 - 4*i + 47. Let l be a(5). Determine h so that -3/7*h**l + 15/7*h - 12/7 = 0.
1, 4
Let q(l) be the third derivative of -l**10/50400 + l**9/6720 - l**8/2240 + l**7/1680 - l**5/60 + 7*l**2. Let w(g) be the third derivative of q(g). Factor w(d).
-3*d*(d - 1)**3
Let d(t) be the first derivative of -t**4/18 - 52*t**3/27 - 209*t**2/9 - 968*t/9 + 44. Factor d(f).
-2*(f + 4)*(f + 11)**2/9
Let t(d) be the second derivative of -d**7/14 + 3*d**5/10 - d**3/2 - 82*d. Suppose t(u) = 0. Calculate u.
-1, 0, 1
Let s = 5754082 - 8671402440/1507. Let y = -4/137 - s. Factor 0*x - 4/11*x**2 + 0 - y*x**3.
-2*x**2*(3*x + 2)/11
Factor -147/2 - 105/2*h + 39/2*h**2 - 3/2*h**3.
-3*(h - 7)**2*(h + 1)/2
Let a(d) = 42*d**3 + 12*d**2 - 28*d + 8. Let r(h) = 83*h**3 + 1 + 1 + 15 - 66*h + 9*h + 23*h**2. Let f(y) = 7*a(y) - 3*r(y). Factor f(u).
5*(u + 1)*(3*u - 1)**2
Let b(m) be the first derivative of -m**3/6 + 61*m**2/2 - 3721*m/2 - 155. Factor b(h).
-(h - 61)**2/2
Let p(n) be the second derivative of -n**5/15 + n**4/3 + 8*n**3/9 + 23*n. Let p(f) = 0. What is f?
-1, 0, 4
Let b be -3*(-1 + 4/12). Suppose 3*d + s = 11, 28 = 4*d + 6*s - b*s. Let 2 + 12*a + a**2 - d + 1 - 10*a = 0. What is a?
-1
Let p(x) be the first derivative of 1/18*x**3 + 0*x - 4 + 1/3*x**2. Find l such that p(l) = 0.
-4, 0
Suppose -3*j - 4 = -2*b - 1, 5*j - 14 = -3*b. Let i(f) be the third derivative of 0 + 0*f - 1/210*f**5 + 1/84*f**4 - 7*f**2 + 2/21*f**b. Solve i(v) = 0.
-1, 2
Suppose 10*z - 16*z + 18 = 0. Let v be 1*2/2*7. Factor -3*k**3 - v*k**4 - 9*k**z + 3*k**2 + k**2.
-k**2*(k + 2)*(7*k - 2)
Let f = 163634281/417 + -392407. Let u = f - 2/139. Suppose 0*o - 8/3*o**4 + 2/3*o**5 + 10/3*o**3 - u*o**2 + 0 = 0. What is o?
0, 1, 2
