439 - -12442. Let -8/7*j**f - 16/7*j**4 + 12/7*j**5 - 4/7*j + 0 + 16/7*j**2 = 0. Calculate j.
-1, 0, 1/3, 1
Let s(o) be the third derivative of 5/6*o**4 + 8*o**2 + 0*o - 1/12*o**5 + 0*o**3 + 0. Find n, given that s(n) = 0.
0, 4
Factor 10*b + 26*b - 215*b**3 - 27*b**2 + 3*b**4 + 218*b**3 - 3*b - 12.
3*(b - 1)**3*(b + 4)
Let h = -2/7981 - -39917/47886. Factor -h*i - 1/6*i**5 + 1/6 + 5/6*i**4 - 5/3*i**3 + 5/3*i**2.
-(i - 1)**5/6
Let o = -5867 + 5869. Factor 2/11*s - 4/11 + 2/11*s**o.
2*(s - 1)*(s + 2)/11
Let t(h) = -h**2 + h + 3. Let a = 30 + -22. Let v(r) = -7*r - a + 4*r**2 + 3*r + 0*r - 6. Let f(d) = 28*t(d) + 6*v(d). Factor f(z).
-4*z*(z - 1)
Suppose -2*b + 6 = b. Find l such that -35*l - 8 - 36*l - b*l**2 + 79*l = 0.
2
Let u = -78 + 60. Let a = u + 37/2. Suppose 3/2*w**2 - 5/2*w + 1 + a*w**3 - 1/2*w**4 = 0. What is w?
-2, 1
Let l(j) be the first derivative of -2*j**3 - 4*j**2 + 6*j + 7. Let v(c) = -24*c**2 - 31*c + 25. Let w(k) = -9*l(k) + 2*v(k). Factor w(g).
2*(g + 2)*(3*g - 1)
Solve 3/8*j**2 + 723/8 - 363/4*j = 0.
1, 241
Let t be (-3)/(6/(-40))*(-90)/(-24). Factor -14*l - 4*l + 48 - t*l**2 + 78*l**2 - 6*l.
3*(l - 4)**2
Let u(k) be the third derivative of -k**5/75 - 3*k**4/10 + 4*k**3/3 + 3*k**2 + 6. Find m, given that u(m) = 0.
-10, 1
Let d = 35 + -30. Let 128*c**3 - 14*c**d - 160*c - 32 + 166*c**4 + 36*c**5 + 20*c**5 - 144*c**2 = 0. What is c?
-2, -2/3, -2/7, 1
Let b(y) = y**2 + 6*y - 5. Let u be b(-7). Let g(t) = 491*t + 984. Let q be g(-2). Let 2/3*m**u - 8/3*m**3 + q*m + 0 = 0. Calculate m.
-3/4, 0, 1
Let d(u) be the third derivative of -u**5/300 - u**4/40 + 14*u**3/15 + 2*u**2 + 218*u. Find g, given that d(g) = 0.
-7, 4
Let x(b) be the second derivative of -b**5/15 + b**4/6 + 9*b**2/2 + 2*b. Let q(l) be the first derivative of x(l). Find d such that q(d) = 0.
0, 1
Let n(d) = -d**3 - 27*d**2 + 2*d + 30. Let y be n(-27). Let v be (6/(-16))/(y/112). Suppose -9/4*z**2 + 0 + 1/2*z + v*z**3 = 0. Calculate z.
0, 2/7, 1
Let d(b) = -2*b**2 + 410*b - 1606. Let w be d(201). Factor -2/11*k**3 + 0 + 2*k**w + 0*k.
-2*k**2*(k - 11)/11
Let h(g) = g**2. Suppose 3*o = o + 54. Let q = o - 15. Let i(t) = -5*t**2 - 3*t - 2. Let c(j) = q*h(j) + 3*i(j). Determine r, given that c(r) = 0.
-2, -1
Factor 5/2*w**4 + 7/2*w**2 - w - 9/2*w**3 - 1/2*w**5 + 0.
-w*(w - 2)*(w - 1)**3/2
Let h(q) be the second derivative of 0*q**3 + 1/60*q**4 + 0 - q + 1/300*q**5 + 3*q**2. Let l(n) be the first derivative of h(n). Factor l(f).
f*(f + 2)/5
Let n(v) be the second derivative of 16*v - 2/165*v**6 + 1/231*v**7 + 1/110*v**5 + 0*v**3 + 0*v**4 + 0 + 0*v**2. Factor n(k).
2*k**3*(k - 1)**2/11
Suppose 3*v + 38 - 11 = 0. Let t be v/(-2) - (-6)/(-2). Find d, given that d**4 - t*d**2 + 1/2*d**3 + 1/2 - 1/2*d = 0.
-1, 1/2, 1
Let b(f) be the third derivative of 0*f**3 + 0*f + 0 - 1/60*f**5 + 16*f**2 + 1/10*f**6 + 0*f**4. Factor b(z).
z**2*(12*z - 1)
Determine v, given that 16/7 - 26/7*v**4 + 18/7*v**5 + 114/7*v**2 - 46/7*v**3 - 76/7*v = 0.
-2, 4/9, 1
Let m = 420036786457/2051 + -204796100. Let n = 1/293 - m. Factor 38/7*c**3 - 8/7 - n*c**2 + 2/7*c**5 - 2*c**4 + 32/7*c.
2*(c - 2)**2*(c - 1)**3/7
Let k = 6514 + -6512. Factor -24/5*d**k - 12/5*d**4 - 2/5*d**5 - 26/5*d**3 + 0 - 8/5*d.
-2*d*(d + 1)**2*(d + 2)**2/5
Let w(l) = -l + 1. Let a(s) = 6*s - 7. Let r(c) = 2*a(c) + 14*w(c). Let d be r(-1). Let -4*p**3 - 26*p**2 - 20*p + 8 + d*p**3 - 5*p**3 = 0. What is p?
-2, 2/7
Let p(t) = 5*t**4 - 8*t**3 - 16*t**2 + 22*t + 4. Let y(u) = -2*u**4 + 3*u**3 + 5*u**2 - 7*u - 1. Let j = -60 - -67. Let c(q) = j*y(q) + 2*p(q). Factor c(l).
-(l - 1)**2*(l + 1)*(4*l - 1)
Let l(q) = -11*q + 4. Let m be l(-4). Let r be ((-32)/m)/(-1 + (-10)/6). Factor -r*g + 0*g**2 + 0*g**4 + 0 - 1/4*g**5 + 1/2*g**3.
-g*(g - 1)**2*(g + 1)**2/4
Let n(s) be the third derivative of 0*s - 11*s**2 - 1/20*s**5 + 0*s**3 + 0 - 1/40*s**6 + 3/4*s**4. Let n(x) = 0. Calculate x.
-3, 0, 2
Let g(u) be the first derivative of 5*u**3/6 + 55*u**2/2 + 605*u/2 + 28. Factor g(v).
5*(v + 11)**2/2
Let d(p) be the first derivative of -3/2*p**2 + p**4 + 7 - 1/6*p**6 - 2*p + 0*p**5 + 2/3*p**3. Factor d(l).
-(l - 2)*(l - 1)*(l + 1)**3
Let i(r) be the second derivative of -r**7/21 - r**6/15 + r**5/10 + r**4/6 - 89*r. Factor i(m).
-2*m**2*(m - 1)*(m + 1)**2
Let w(y) = -9*y - 2*y**3 + 3 - 2 - 8*y**2 + 1 + 14*y**2. Let i(m) = -m**3 + m**2 - 1. Let p(b) = -3*i(b) + w(b). Factor p(z).
(z - 1)**2*(z + 5)
Let j = 1049/1665 + -10/333. Suppose 0 = -0*s + s. Factor s + 0*r + j*r**2.
3*r**2/5
Suppose -o + 4*n = -0*n, -3*o = -n - 33. Find g such that -o*g + 2*g**2 + 0*g + 2*g = 0.
0, 5
Let l = 5569/4 + -1392. Factor 0*r + 0 - l*r**2.
-r**2/4
Let l(o) = o**3 + 25*o**2 - o + 20. Let r be l(-25). Determine d, given that -100*d**2 - r + 200*d + 15*d**3 + 10*d + 5*d**3 - 25*d**2 = 0.
1/4, 3
Suppose 2*q - 13 = -3*l, -4*l - q + 3 + 6 = 0. Suppose 9 = 5*o + 5*y - l, 5*o - 16 = y. Let -4/11*p + 2/11*p**4 + 4/11*p**o + 0 - 2/11*p**2 = 0. What is p?
-2, -1, 0, 1
Let z(w) be the third derivative of -2*w**7/315 + w**6/40 - w**5/90 + 60*w**2. Determine v, given that z(v) = 0.
0, 1/4, 2
Let z be 3 + ((-40)/(-15) - (-2)/6). Find d such that -8*d**3 + 64 + 12*d**2 - z*d**3 - 48*d + 13*d**3 = 0.
4
Let y(o) be the first derivative of 1/18*o**3 - 1/12*o**2 - o - 6. Let y(m) = 0. Calculate m.
-2, 3
Factor -3/2*d**3 + 4*d - 5*d**2 + 0.
-d*(d + 4)*(3*d - 2)/2
Let q(y) be the first derivative of -5*y**4/4 - 20*y**3/3 - 15*y**2/2 + 101. Factor q(c).
-5*c*(c + 1)*(c + 3)
Let n(z) be the first derivative of -2 - 12*z - 2*z**3 - 27/2*z**2. Factor n(t).
-3*(t + 4)*(2*t + 1)
Let c(q) be the first derivative of q**4/36 - 28*q**3/27 - 59*q**2/18 - 10*q/3 - 715. Factor c(m).
(m - 30)*(m + 1)**2/9
Let d(i) be the first derivative of 4*i**3 + 39*i**2/2 - 36*i - 183. Solve d(o) = 0 for o.
-4, 3/4
Let g(r) = -6*r - 31. Let p be g(-5). Let q be (-8)/56 + (75/(-84))/p. Suppose q + 1/4*j**2 + j = 0. What is j?
-3, -1
Let b(k) be the first derivative of -k**4/8 - 43*k**3/6 + 90. Factor b(h).
-h**2*(h + 43)/2
Suppose 2*o - h - 5 = 0, -3*o = -4*h + 8 - 13. Factor 1/3*i**4 + 0 + 0*i - 2/3*i**2 - 1/3*i**o.
i**2*(i - 2)*(i + 1)/3
Factor 7/4*b**3 + 3*b - 4*b**2 + 0 - 1/4*b**4.
-b*(b - 3)*(b - 2)**2/4
Let m = 32 - -3. Let i be (-1)/(-3) - (m/(-165) + 0). Factor 8/11*g**2 + i - 14/11*g.
2*(g - 1)*(4*g - 3)/11
Let j(i) = i**2 + 6. Let h(o) = 5. Let g(z) = -7*h(z) + 5*j(z). Factor g(s).
5*(s - 1)*(s + 1)
Let m(g) be the first derivative of -3/25*g**5 - 12/5*g**2 + 9/5*g + 0*g**4 + 6/5*g**3 - 17. Factor m(a).
-3*(a - 1)**3*(a + 3)/5
Find l, given that -3/5*l**3 + 0 - 72/5*l**2 + 0*l = 0.
-24, 0
Suppose 4/7*u - 4/7*u**4 + 0 - 4/7*u**3 + 4/7*u**2 = 0. What is u?
-1, 0, 1
Let f(k) be the first derivative of -k**9/4536 + 8*k**3/3 - 7. Let c(l) be the third derivative of f(l). Solve c(m) = 0 for m.
0
Suppose m + 10 = -0*m. Let k(t) = t**3 + 10*t**2 - t - 3. Let j be k(m). Determine q, given that j*q - 2*q**2 + 8*q - 6 - 10*q**2 + 4*q**3 - q**3 = 0.
1, 2
Let r(b) be the first derivative of 0*b**2 + 2/3*b**3 + 1/2*b**4 + 0*b - 2/5*b**5 + 2 - 1/3*b**6. Suppose r(l) = 0. What is l?
-1, 0, 1
Let i(o) = 5*o**4 - 90*o**2 - 60*o. Let m(b) = b**3 + 2*b**2. Let c(x) = -i(x) - 25*m(x). Factor c(p).
-5*p*(p - 2)*(p + 1)*(p + 6)
Suppose -121*l = -125*l + 20. Let j(x) be the third derivative of -3*x**2 + 0 + 1/8*x**3 - 1/80*x**l + 0*x + 1/160*x**6 - 1/32*x**4. Factor j(i).
3*(i - 1)**2*(i + 1)/4
Let u = 24878 + -49755/2. Factor 3/4*j**2 - u*j**3 + 1 - 1/4*j**4 + 2*j.
-(j - 2)*(j + 1)**2*(j + 2)/4
Let v be 2*(-2)/(-10) - (-39420)/20075. Factor -24/11*t - 12/11*t**3 - 2/11*t**4 - 8/11 - v*t**2.
-2*(t + 1)**2*(t + 2)**2/11
Suppose 0 + 8/5*n + 2*n**3 - 2/5*n**4 - 16/5*n**2 = 0. What is n?
0, 1, 2
Let f(n) = -3*n**3 + 16*n**2 + 32*n + 24. Let q be f(7). Factor q*k - 1 - 3/4*k**2 - 5/4*k**3.
-(k - 1)*(k + 2)*(5*k - 2)/4
Let a(c) be the third derivative of 0*c + 0 - 8*c**2 - 1/6*c**4 + 4/3*c**3 - 1/15*c**5. Find f such that a(f) = 0.
-2, 1
Let i(g) = -g + 1. Let d(u) = 4*u + 18. Let o(l) = d(l) + 3*i(l). Let m be o(-15). Factor 4*y**3 + 12 + 9*y**2 - m*y - 12 + 11*y**3.
3*y*(y + 1)*(5*y - 2)
Let o = -6229 + 6233. Factor 0*n**3 - n**o + 0*n**2 - 1/4*n**5 + 0*n + 0.
-n**4*(n + 4)/4
Let q(f) = f**2 + 14*f + 18. Let b be q(-13). Let i = 9/1