ctor b(d).
4*d**2
Suppose -20 = -4*h + 4*o, -6*h - 6 = -3*h + 4*o. Let m(t) be the third derivative of 1/9*t**4 - 2*t**h + 0 + 1/90*t**5 + 0*t + 4/9*t**3. Solve m(z) = 0.
-2
Let t(o) be the first derivative of 24*o**2 - 4*o**3 - 12 - 7*o + 1/4*o**4. Let l(b) be the first derivative of t(b). Find m such that l(m) = 0.
4
Let b(j) be the first derivative of j**4/28 + j**3/14 - 9*j**2/7 + 10*j + 28. Let g(t) be the first derivative of b(t). Let g(z) = 0. Calculate z.
-3, 2
Let m be 3 + (0 - 0)*10/(-20). Solve -12*w**4 - 4*w**2 + 0*w**5 - 12*w**m - 2*w**5 - 2*w**5 = 0.
-1, 0
Let h be (2/(-5))/((3/(-20))/3). Let c be -7 + h - (-3)/(-6). Factor 0 + 0*u**3 + c*u**4 + 0*u - 1/2*u**2.
u**2*(u - 1)*(u + 1)/2
Let n(a) be the second derivative of -1/90*a**5 + 1/135*a**6 + 0*a**2 + 0*a**4 + 0 + a + 0*a**3. Let n(b) = 0. What is b?
0, 1
Let u(y) be the first derivative of y**4/16 + y**3/2 + 5*y**2/8 - 83. Determine p, given that u(p) = 0.
-5, -1, 0
Let y = 300 - 295. Let g(c) = -21*c - 1. Let t be g(-1). What is o in 32 - 3*o**y + t*o**3 + 80*o**2 + 4*o**5 + 20*o**3 + 10*o**4 + 80*o = 0?
-2
Suppose 8*j - 8 = 8. Let 11*h**j - 7*h**2 + 10*h + 4*h + 6 = 0. Calculate h.
-3, -1/2
Let x be (-6)/(-1 - 597/(-606)). Let t = -1202/3 + x. Determine u, given that 10/3*u**4 - 2/3*u**5 - 20/3*u**3 + 2/3 - t*u + 20/3*u**2 = 0.
1
Let u(g) be the third derivative of 1/240*g**6 + 0*g**7 + 0 - 1/1344*g**8 + 0*g + 0*g**3 + 0*g**5 - 1/96*g**4 + 4*g**2. Suppose u(r) = 0. Calculate r.
-1, 0, 1
Let d(k) be the first derivative of -k**7/315 + 12*k**2 + 39. Let v(w) be the second derivative of d(w). Suppose v(j) = 0. Calculate j.
0
Let m = 248/189 - 20/27. Factor 0*f**2 - m*f**5 - 4/7*f**3 - 8/7*f**4 + 0*f + 0.
-4*f**3*(f + 1)**2/7
Let i be ((-69)/(-8))/(357/34). Let h = i + -4/7. Let h*r**2 + 0 + 1/4*r**3 + 0*r = 0. What is r?
-1, 0
Let k = -14 + 5. Let l = -6 - k. Factor b - 2*b**2 + l*b - b**3 - 4*b.
-b**2*(b + 2)
Let b(l) = -l**2 + 6*l - 1. Let t be b(3). Let r be (1 + 215/(-55))*(-2)/t. Factor -2/11*x**5 + 8/11*x**4 + 0 - 2/11*x + r*x**2 - 12/11*x**3.
-2*x*(x - 1)**4/11
Let p be (-1 - -3)*((-90)/6)/(-15). Factor 2/9*w**4 + 0 + 0*w - 2/9*w**5 - 2/9*w**p + 2/9*w**3.
-2*w**2*(w - 1)**2*(w + 1)/9
Let j = -26 - -66. Factor -5*u**2 + j*u + u**2 + 2*u**3 - 38*u.
2*u*(u - 1)**2
Let q = -1/85 - -93/680. Let f(n) be the third derivative of -1/80*n**5 + 1/16*n**4 - q*n**3 + 0*n + 0 + 2*n**2. Factor f(c).
-3*(c - 1)**2/4
Let b(c) be the third derivative of -14*c**2 + 1/48*c**5 + 245/24*c**3 + 0*c - 35/48*c**4 + 0. Determine j, given that b(j) = 0.
7
Let i = 4898/239679 - 16/891. Let v = i - -358/269. Determine w, given that -2/3*w**4 - 2/3*w**5 + 0 - v*w + 2/3*w**2 + 2*w**3 = 0.
-2, -1, 0, 1
Let w(v) = -16*v**2 + 38*v - 14. Let h(t) = 11*t**2 - 25*t + 10. Let y(f) = 7*h(f) + 5*w(f). Factor y(x).
-3*x*(x - 5)
Let a(c) = 3*c**2 + 15*c - 30. Let p = 13 + -10. Suppose -w = -p - 2. Let g(q) = q**2 + 6*q - 12. Let x(f) = w*a(f) - 12*g(f). Suppose x(o) = 0. Calculate o.
-2, 1
Factor 0 + 22/9*v**2 - 2/9*v**3 - 20/9*v.
-2*v*(v - 10)*(v - 1)/9
Let m(t) = 4*t - t**3 + 11 + 5*t**2 - 7 - 5*t**2. Let u be m(0). Determine x, given that 2/5*x - 2/5*x**3 + 2/5*x**2 + 0 - 2/5*x**u = 0.
-1, 0, 1
Let r be (-3)/(-6) + 21/6. Suppose -u = 1 - r. Factor -3*k + k**3 + 5*k**3 - u*k**3 + 0*k.
3*k*(k - 1)*(k + 1)
Suppose -24 = -2*f - 3*k - 1, -4*f - 5*k + 41 = 0. Determine b so that -225*b**3 - f*b**2 + 231*b**3 - 9*b**4 + 13*b**2 - 6*b = 0.
-1, 0, 2/3, 1
Suppose 0 = -5*r + 10. Factor -4*i + 5*i**2 - i**2 - 2*i**2 - 4*i**r.
-2*i*(i + 2)
Let b = -5 + 4. Let r be b/(-3)*-3*-2. Factor q**2 - 3*q**2 + 0*q**2 - r*q.
-2*q*(q + 1)
Let w be 4 + (14/(-819))/((-24)/(-6326)). Let n = -2/351 - w. Solve n*s**3 - 1/2*s + 1/2*s**4 + 0 - 1/2*s**2 = 0 for s.
-1, 0, 1
Let m(z) = -5*z**2 + 154*z - 600. Let p(t) = -55*t**2 + 1700*t - 6600. Let s(l) = 45*m(l) - 4*p(l). Determine h, given that s(h) = 0.
6, 20
Let d(u) be the third derivative of u**6/180 - 2*u**5/15 - 3*u**4/4 - 14*u**3/9 - 34*u**2. Factor d(f).
2*(f - 14)*(f + 1)**2/3
Suppose -19*w + 45 = -4*w. Factor 17*m**4 - 11*m**w - 35*m**4 - 29*m**3 - 8*m**2.
-2*m**2*(m + 2)*(9*m + 2)
Factor 5/6*t**3 + 5/2*t**2 + 5/3*t + 0.
5*t*(t + 1)*(t + 2)/6
Let z(r) be the third derivative of 0*r**3 + 1/2352*r**8 + 0*r + 0*r**5 + 0 + 0*r**7 - 1/420*r**6 + 7*r**2 + 1/168*r**4. Factor z(y).
y*(y - 1)**2*(y + 1)**2/7
Let l = -729 - -732. Let t(r) be the third derivative of -4*r**2 + 5/16*r**6 - 2*r**l + 0 - 2/35*r**7 + 1/224*r**8 - 19/20*r**5 + 7/4*r**4 + 0*r. Factor t(o).
3*(o - 2)**3*(o - 1)**2/2
Suppose -3*f + 106 = -2*p, -5*p - 4*f - 261 = -42. Let w = p + 142/3. Suppose 0*k - 1/3*k**2 + 0 - w*k**3 = 0. What is k?
-1, 0
Factor -14/13*z + 20/13 + 2/13*z**2.
2*(z - 5)*(z - 2)/13
Let i(p) be the second derivative of 1/21*p**4 + 2/21*p**3 + 0*p**2 + 0 + 10*p. Factor i(m).
4*m*(m + 1)/7
Let i(t) = -t**3 + 8*t**2 - 16*t. Let h be 6*(4/(-3) - -2). Let c be i(h). Solve 4/7*s - 2/7*s**3 + c + 2/7*s**2 = 0.
-1, 0, 2
Factor 2*h**3 + 5*h + 25310*h**2 - 25312*h**2 - 15*h - 6.
2*(h - 3)*(h + 1)**2
Let j be 5 - (10959/3042 - 2/(-12)). Factor -90/13*n**4 + 0 + j*n - 84/13*n**3 + 8/13*n**2.
-2*n*(3*n + 2)**2*(5*n - 2)/13
Let c(t) be the first derivative of 0*t**3 + 4/3*t**2 + 4/15*t**5 + 6 - 2/3*t**4 - 4/3*t. Factor c(p).
4*(p - 1)**3*(p + 1)/3
Let v(o) be the first derivative of 2*o**5/25 - 3*o**4/5 - 2*o**3/5 + 4*o**2 - 24*o/5 - 64. What is b in v(b) = 0?
-2, 1, 6
Let p(w) be the first derivative of -8*w**5/15 - 325*w**4/6 - 4534*w**3/3 - 8080*w**2/3 - 3200*w/3 + 39. Solve p(x) = 0 for x.
-40, -1, -1/4
Suppose 23*j - 28*j = 3*z - 19, 2*j + 11 = 5*z. Factor 1/5*a**4 + 0*a + 2/5*a**z + 0 + 0*a**2.
a**3*(a + 2)/5
Let r be ((-567)/(-12))/9 - (-8)/(-2). Factor -25/4*u - r*u**3 + 5*u**2 + 5/2.
-5*(u - 2)*(u - 1)**2/4
Let n(f) be the second derivative of -1/25*f**5 - 1/5*f**2 + 0 - 13/60*f**4 - 11/30*f**3 + 6*f. Factor n(a).
-(a + 1)*(a + 2)*(4*a + 1)/5
Let n(w) = -w**4 - 6*w**3 - 2*w**2 - 6*w - 1. Let z(m) = -8*m**4 - 49*m**3 - 14*m**2 - 49*m - 8. Let s(b) = -51*n(b) + 6*z(b). Find c, given that s(c) = 0.
-1
Let p(k) be the second derivative of -k**6/75 - k**5/25 + 7*k**4/30 + 8*k**3/15 - 12*k**2/5 - 40*k - 10. Let p(j) = 0. Calculate j.
-3, -2, 1, 2
Let b(o) = 0*o + 124 + o**2 - o - 123. Let j(z) = -3*z**2 - 5*z - 1. Let g(d) = 2*b(d) + 2*j(d). Factor g(r).
-4*r*(r + 3)
Suppose -5*p + 14 = 2*c, -3 = -5*c - 5*p + 2. Let i be c + 2/2 - -4. Factor 2/3*z**2 + 4/3 + i*z.
2*(z + 1)*(z + 2)/3
Let h(t) = t + 17. Let r be h(-9). Factor -4*g**2 - 4*g - g - 12 - r - 19*g.
-4*(g + 1)*(g + 5)
Let z(l) be the first derivative of -l**4/2 - 76*l**3/3 + 79*l**2 - 80*l + 34. Factor z(p).
-2*(p - 1)**2*(p + 40)
Factor -16*w + 0 - 2/5*w**2.
-2*w*(w + 40)/5
Let g be (-244)/(-62) - (-82)/1271. Factor -3/7*f**2 + 3/7*f**g + 0 - 3/7*f**3 + 3/7*f.
3*f*(f - 1)**2*(f + 1)/7
Factor 18496*g**2 + 2515456/3*g + 544/3*g**3 + 2/3*g**4 + 42762752/3.
2*(g + 68)**4/3
Let m = 518 - 515. Let k(n) be the second derivative of 1/16*n**2 + 3/8*n**m + 0 + 27/32*n**4 - n. Factor k(v).
(9*v + 1)**2/8
Let q(s) = -25*s**2 - 1350*s - 6155. Let f(u) = 3*u**2 + 150*u + 684. Let n(d) = -35*f(d) - 4*q(d). Factor n(w).
-5*(w - 34)*(w + 4)
Let w be (580/(-592) - -1)/((-2)/8). Let d = 139/111 - w. Find u such that -10/3*u + 2/3*u**4 - 2 + d*u**2 - 2/3*u**5 + 4*u**3 = 0.
-1, 1, 3
Factor -647*h + h**2 + 328*h + 344*h.
h*(h + 25)
Let j = -13/138 - 5/598. Let s = j - -10/13. Factor -s*n**3 - 5/3*n**4 + 2*n**2 - 1/3*n - 1/3 + n**5.
(n - 1)**3*(n + 1)*(3*n + 1)/3
Suppose 12 = -2*x - 2*l, 2*x = -53*l + 50*l - 18. What is y in x*y + 1/7*y**3 + 0 - 1/7*y**2 = 0?
0, 1
Let m(g) = -g**2 + 3*g - 27. Let i be m(0). Let a = -25 - i. Factor -18*p**3 - p**2 + 19*p**3 + 0*p + 3*p - 1 - 2*p**a.
(p - 1)**3
Let m(t) be the second derivative of 3*t**5/110 + 43*t**4/66 - 10*t**3/11 + 395*t. Solve m(f) = 0.
-15, 0, 2/3
Suppose -22 = -3*n + 5*h, 3*n - 9*h - 20 = -5*h. Let s(z) = z**4 - 2*z**3 - 3*z. Let c(i) = i**4 - i**3 - 2*i. Let u(o) = n*s(o) - 6*c(o). Factor u(r).
-2*r**3*(r + 1)
Let v be (-7)/(-28) - 46/(-8). Suppose -4 = -v*l + 2. Solve l + 1/2*x**4 - 1/2*x**3 - 3/2*x**2 + 1/2*x = 0 for x.
-1, 1, 2
Let o(a) = -75*a**4 + 45*a**3 + 30*a**2 - 11*a. Let h(q) = 25*q**4 - 15*q**3 - 10*q