.
v*(v - 1)**2*(v + 1)/5
Suppose 0 = 2*n + 6*n - 40. Factor -3*t - t + t**2 + 0*t + n*t.
t*(t + 1)
Let q(a) be the second derivative of -a**5/60 - 7*a**4/24 + 4*a**3/3 + 3*a**2 - 15*a. Let u(k) be the first derivative of q(k). Let u(w) = 0. What is w?
-8, 1
Let n be 2/(-24) + (17 - (336/18 + -2)). Determine i, given that -n*i - 1/4*i**2 + 1/2 = 0.
-2, 1
Let u(v) be the first derivative of 1/44*v**4 + 11 + 1/55*v**5 - 2/11*v - 1/11*v**3 - 5/22*v**2. Suppose u(t) = 0. What is t?
-1, 2
Let p(l) be the third derivative of -1/270*l**5 - 6*l**2 - 25/27*l**3 + 5/54*l**4 + 0*l + 0. Let p(s) = 0. Calculate s.
5
Suppose 16875/4 + 3/4*k**2 - 225/2*k = 0. Calculate k.
75
Find q, given that 7/4*q**2 + 5 - 1/4*q**3 + 7*q = 0.
-2, -1, 10
Let n = 1546 - 1543. Factor 12/5*m**2 + 6/5 + 3/5*m**n + 3*m.
3*(m + 1)**2*(m + 2)/5
Let u(f) be the second derivative of f**7/1960 - 3*f**5/280 - f**4/28 - 4*f**3 - 31*f. Let j(z) be the second derivative of u(z). Factor j(q).
3*(q - 2)*(q + 1)**2/7
Let s(t) = -t + 31. Let z be s(17). Suppose -z*f = -39 + 11. Solve -4/5 + 0*l**f + 4*l**4 - 4*l**3 - 6/5*l**5 + 2*l = 0.
-2/3, 1
Suppose 5*q = -3*j + 13, -13*q = -8*q + 4*j - 9. Let n(u) be the first derivative of -u - 1/12*u**3 - 1/2*u**2 + q. Find t such that n(t) = 0.
-2
Let f(v) be the third derivative of 7*v**5/54 + 11*v**4/36 - 2*v**3/27 + 31*v**2 - 2. Factor f(t).
2*(t + 1)*(35*t - 2)/9
Let u(q) be the first derivative of -4*q**5/35 + 33*q**4/14 - 32*q**3/21 + 168. Factor u(y).
-2*y**2*(y - 16)*(2*y - 1)/7
Let s(b) be the third derivative of 0*b - 1/60*b**5 - 1/3*b**4 - 10*b**2 + 0 - 8/3*b**3. Let s(w) = 0. Calculate w.
-4
Let z(o) = -o**2 - o - 1. Suppose 0*s = s + 3. Let j(m) = -3*m**2 - 4*m - 3. Let f(b) = s*j(b) + 6*z(b). Factor f(v).
3*(v + 1)**2
Let v be 56/(-128)*8/(-14). Let 0*s + v*s**2 - 1/4 = 0. Calculate s.
-1, 1
Let o(g) be the third derivative of -g**7/1764 + g**6/840 + g**5/210 - 7*g**4/24 - 5*g**2. Let s(z) be the second derivative of o(z). What is r in s(r) = 0?
-2/5, 1
Let f(w) be the third derivative of 0*w + 1/30*w**4 + 2/75*w**5 + 1/150*w**6 + 24*w**2 + 0*w**3 + 0. Factor f(u).
4*u*(u + 1)**2/5
Let w(m) = m**3 + 12*m**2 + 11*m + 2. Let s be w(-11). Factor -108/5 - 3/5*l**s + 36/5*l.
-3*(l - 6)**2/5
Factor 2/25*p**2 + 2/25*p + 0.
2*p*(p + 1)/25
Factor -74623*m**2 + 3 - 3 - 2*m**5 + 74647*m**2 - 2*m**4 + 16*m**3.
-2*m**2*(m - 3)*(m + 2)**2
Suppose 4*y - 48 = -32. Let j(i) be the second derivative of 0 + 4/5*i**6 - 2*i**y - 3/7*i**7 + 4/3*i**3 - 3*i + 0*i**2 + 1/2*i**5. Suppose j(q) = 0. What is q?
-1, 0, 2/3, 1
Let q be 3468/10 - ((0 - -1) + 1). Let k = -342 + q. Let 2/5 + k*r + 26/5*r**3 + 6*r**2 + 8/5*r**4 = 0. Calculate r.
-1, -1/4
Let m(j) be the third derivative of 0*j + 0*j**3 + 1/120*j**4 - 8*j**2 + 0 + 1/300*j**5. Factor m(c).
c*(c + 1)/5
Let f = -5/518 - -6353/777. Factor -4 - 161/3*k**2 - 86/3*k - f*k**3.
-(k + 6)*(7*k + 2)**2/6
Let y(q) be the second derivative of 0 + 1/6*q**3 + 13*q - 1/4*q**4 + 3/2*q**2 - 1/20*q**5. Suppose y(u) = 0. What is u?
-3, -1, 1
Factor -7/2*a - 5*a**2 + 0.
-a*(10*a + 7)/2
Let d(k) be the third derivative of 1/9*k**3 - 1/360*k**5 + 0*k + 0 + 1/48*k**4 + 4*k**2. Factor d(u).
-(u - 4)*(u + 1)/6
Let l be (-74)/(-10) - 2/5. Let s be 4 + l/(14/(-4)). Solve -4*r**3 + 7 - 7*r**2 + 23*r**s + 1 - 20*r = 0 for r.
1, 2
Let t be (-996)/1245*(2 - 1)/(-2). Factor -1/5*a**2 - 3/5*a - t.
-(a + 1)*(a + 2)/5
Suppose -15 - 21 = 9*t. Let u be (4 - (2 + -2)) + t. Determine y, given that -2/3*y**2 - 4/3*y + u = 0.
-2, 0
Let n = 324 + -322. Let c(l) be the first derivative of -1/5*l**5 - 3 - 1/16*l**4 + 0*l**3 + 0*l - 1/8*l**6 + 0*l**n. Factor c(s).
-s**3*(s + 1)*(3*s + 1)/4
Factor 147/5 + 15*w**2 + 42*w.
3*(5*w + 7)**2/5
Let p(y) be the third derivative of y**8/672 - y**7/42 - 11*y**6/240 - y**2 - 70. Factor p(m).
m**3*(m - 11)*(m + 1)/2
Let l = -2543/3 + 848. Let l*t + t**2 + 0 = 0. What is t?
-1/3, 0
Factor 9/4*v**3 + 0 - 1/4*v**2 + 1/4*v**4 - 9/4*v.
v*(v - 1)*(v + 1)*(v + 9)/4
Let y(u) be the first derivative of -u**5/15 - 11*u**4/3 - 242*u**3/3 - 17*u**2/2 - 9. Let f(r) be the second derivative of y(r). Solve f(l) = 0 for l.
-11
Let u(o) = o**3 - 96*o**2 - 4*o + 389. Let l be u(96). Factor -10/3*y**3 + 2/3*y**4 - 8/3 + 16/3*y + 2/3*y**l - 2/3*y**2.
2*(y - 1)**3*(y + 2)**2/3
Find a such that -3/2*a**4 - 15*a + 6*a**3 + 9/2*a**2 - 12 = 0.
-1, 2, 4
Suppose 3*x + 11 = 5*n - 16, -2*n + 14 = -2*x. Determine w so that -2*w**n + 11*w - 2*w**4 - 3*w + 3*w**2 + 7*w**2 - 2*w**2 = 0.
-2, -1, 0, 2
Let v(d) be the first derivative of -d**3 - 39*d**2 - 20. Factor v(c).
-3*c*(c + 26)
Factor -204*b**3 - 1117*b**2 + 1021*b**2 - 14*b**3 - 3*b - 139*b**3 - 411*b**3.
-3*b*(16*b + 1)**2
Let d = -93 - -96. Let o be (-92)/(-14) - (-4 + 10). Suppose 4/7*w**4 + 8/7*w**d + 0 - 8/7*w**5 + 0*w - o*w**2 = 0. What is w?
-1, 0, 1/2, 1
Let t be ((-14)/3)/(4/(-412)). Let g = t + -15658/33. Find w, given that -g*w**3 + 0 - 4/11*w + 30/11*w**2 + 42/11*w**4 = 0.
0, 2/7, 1/3, 1
Let j(w) be the first derivative of w**4/18 + 22*w**3/27 + 19*w**2/9 + 2*w - 7. Factor j(i).
2*(i + 1)**2*(i + 9)/9
Let o(i) be the second derivative of -3*i + 0 + 2/5*i**6 + 1/4*i**4 + 0*i**2 + 3/5*i**5 + 0*i**3. Determine q, given that o(q) = 0.
-1/2, 0
Let c = 111 + -111. Let p(a) be the third derivative of 3*a**2 - 1/6*a**4 - 1/10*a**5 + 0*a**6 + c + 1/105*a**7 + 0*a**3 + 0*a. Factor p(k).
2*k*(k - 2)*(k + 1)**2
Let a be 88/132*(-5)/((-10)/12). Let i(k) be the first derivative of -2*k**2 + 8/3*k + 2/3*k**3 - 1/12*k**a - 11. Factor i(u).
-(u - 2)**3/3
Let z(d) = -27*d**2 + 38*d - 13. Let b(x) = 12*x**2 - 18*x + 6. Let m(u) = -5*b(u) - 2*z(u). Let m(c) = 0. What is c?
1/3, 2
Let b(c) be the first derivative of -c**5 + 10*c**3 + 20*c**2 + 15*c + 97. Factor b(w).
-5*(w - 3)*(w + 1)**3
Suppose k - 2 = 5*d + 1, -4*k + 12 = 4*d. Let s(x) be the second derivative of -5*x + 0*x**2 + d + 1/12*x**4 + 1/18*x**3. Suppose s(y) = 0. Calculate y.
-1/3, 0
Let c(k) be the second derivative of k**4/12 - 19*k**3/3 + 361*k**2/2 + 136*k. Find h such that c(h) = 0.
19
Suppose 0*n - 27 = -3*n. Factor n - o - o - 7*o + 3*o + o**2.
(o - 3)**2
Let d(o) be the third derivative of -o**6/1260 - 5*o**5/126 + o**4/252 + 25*o**3/63 - 175*o**2. Find q, given that d(q) = 0.
-25, -1, 1
Let c be 0 - (54/24 - 3). Let o(q) be the first derivative of -3 + c*q**6 - 3/4*q**4 + 0*q + 6/5*q**5 - 3/4*q**2 - 2*q**3. Find m, given that o(m) = 0.
-1, -1/3, 0, 1
Suppose 19 = 4*d + 7. Factor 8*w + 31*w**3 + 4*w**4 - 4*w**2 - 25*w**d - 14*w**3.
4*w*(w - 2)*(w - 1)*(w + 1)
Let a(h) be the second derivative of -h**7/147 - h**6/35 + 3*h**5/35 + 5*h**4/21 - h**3 + 9*h**2/7 + 2*h - 42. Find n, given that a(n) = 0.
-3, 1
Let y(o) be the second derivative of -o**4/12 + 5*o**3/6 - 2*o**2 - 5*o - 4. Find n such that y(n) = 0.
1, 4
Let 2691*c - 1335*c - 1337*c + c**2 + 18 = 0. Calculate c.
-18, -1
Let w(p) be the first derivative of p**6/36 - 7*p**5/15 - 9*p**4/2 - 115*p**3/9 - 197*p**2/12 - 10*p - 457. Find j, given that w(j) = 0.
-3, -1, 20
Factor 1/4*m**2 + 0 - 3/4*m.
m*(m - 3)/4
Let x be (2 - 1)/((-1)/(-7)). Factor f - 16*f**2 + 20*f**2 + x*f - 4*f**3.
-4*f*(f - 2)*(f + 1)
Let o = 1143/2 + -12569/22. Find b such that -4/11*b**3 + 4/11*b + o - 2/11*b**4 + 0*b**2 = 0.
-1, 1
Suppose 53 = 39*z - 25. Let -1/2*p**4 + 0 + 3/2*p**3 + 0*p + 0*p**z = 0. Calculate p.
0, 3
Let d(q) be the third derivative of 0 + 0*q + 1/8*q**3 + 0*q**4 - 1/80*q**5 + 18*q**2. Factor d(b).
-3*(b - 1)*(b + 1)/4
What is h in 12*h**2 - 4 + 1237*h**3 + 3*h - 6*h**4 - 1243*h**3 + 3*h**5 - 2 = 0?
-1, 1, 2
Let q(x) = 2*x - 5. Let y be q(5). Suppose 3*v = -2*v + 4*d + 26, 0 = v + y*d + 18. Factor 3*k**2 - k**2 + 0*k**2 - k**2 - v*k.
k*(k - 2)
Let w(n) = n**2 + 3*n - 6. Let l be w(-5). Solve -7 - 27*i - 40*i**3 + 67*i + 27 - 45*i**2 + 25*i**l = 0 for i.
-1, -2/5, 1, 2
Let z(x) = 10*x**4 + 18*x**3 + 26*x**2 - 6*x. Let u(i) = -15*i**2 + i - 4*i**2 + 18*i**2 + i**3 - i**4. Let n(f) = -6*u(f) - z(f). Factor n(d).
-4*d**2*(d + 1)*(d + 5)
Suppose 97*f - 866 = -284. Factor -f*l + 3/2*l**3 + 3/2*l**2 - 6.
3*(l - 2)*(l + 1)*(l + 2)/2
Let t(g) be the second derivative of g**8/17920 - g**7/6720 - g**4/6 - 9*g. Let r(i) be the third derivative of t(i). Solve r(p) = 0 for p.
0, 1
Let n = -83 - -9