
v*(v + 1)*(v + 3)/2
Solve 26*a + 91 + 85 + a**2 - a**2 - 206*a + 4*a**2 = 0.
1, 44
Let i be (-33)/(-9) + 637/(-147) - 196/(-6). What is b in -24*b + 9/2*b**2 + i = 0?
8/3
Suppose 0*a + 2*m - 103 = 3*a, 3*a - 4*m = -101. Let k be 1/(-5) - 147/a. Factor 13*p**2 + 7*p + 4*p + 4 + 8*p - 6*p**3 + p**k - 31*p.
(p - 2)**2*(p - 1)**2
Let i(a) be the first derivative of -a**6/810 - a**5/45 + a**3/3 - 17*a + 64. Let p(j) be the third derivative of i(j). Factor p(l).
-4*l*(l + 6)/9
Let p = -2/134653 + 30835543/403959. Find s, given that 130/3*s**4 - 46*s**2 + 4/3*s - p*s**3 + 75*s**5 + 8/3 = 0.
-1, -2/5, 2/9, 1
Suppose 76*t - 219*t + 160 = -63*t. Determine x, given that -25/6*x**t + 35/6*x + 5/6*x**3 - 5/2 = 0.
1, 3
Let n(y) be the second derivative of 5*y**7/42 - 25*y**6/3 + 777*y**5/4 - 1470*y**4 + 2511*y. Determine z, given that n(z) = 0.
0, 8, 21
Solve -28239 - 28*r**4 + 68*r**2 - 76*r**3 - 64*r - 4*r**5 + 28223 - 168*r**2 = 0 for r.
-2, -1
Let p(x) be the first derivative of 0*x**2 + 0*x + 8/15*x**5 - 1/9*x**6 + 0*x**3 + 23 + 0*x**4. Suppose p(y) = 0. Calculate y.
0, 4
Let v be 160/60 + (3/3)/(4/(-8)). Factor 0 - v*r**2 - 28/3*r.
-2*r*(r + 14)/3
Let z = -1 + -9. Let q be z/(-6) + -4*3/(-36). Factor 6*x + 34*x**q + 36*x**2 - 68*x**2.
2*x*(x + 3)
Let t = -4021 + 8047/2. Let m(f) be the first derivative of 0*f - 14 - f**5 - t*f**2 + 5/3*f**3 + 5/4*f**4. Factor m(a).
-5*a*(a - 1)**2*(a + 1)
Let n = 74081/592840 - -3/74105. Suppose -n*y**3 - 1/8*y**5 - 3/8*y**4 + 0 + 1/4*y + 3/8*y**2 = 0. Calculate y.
-2, -1, 0, 1
Suppose 0 = -7*z - 8*z + 19*z - 13*l + 148, -24 = -2*l. Find i such that 54/5*i + 36/5*i**2 + z*i**3 + 27/5 + 1/5*i**4 = 0.
-3, -1
Suppose -42*o - 30 = -2*k - 43*o, -40 = 5*o. Let b(u) be the first derivative of 1/4*u**2 - k - 1/6*u**3 + 0*u. Factor b(f).
-f*(f - 1)/2
Factor 17/3*o**2 + 8/3 + 98/9*o + 7/9*o**3.
(o + 3)*(o + 4)*(7*o + 2)/9
Suppose 0 = 6*l + 678 - 750. What is r in 4 + 2*r**3 + 4*r**5 - 4*r - 10*r**3 + 6 + 8*r + 2 + l*r**4 - 24*r**2 = 0?
-3, -1, 1
Let i(b) = b**3 - 22*b**2 + 1461*b - 23389. Let z be i(17). Factor 52/5 + 2/5*c**z + 48/5*c**2 - 102/5*c.
2*(c - 1)**2*(c + 26)/5
Let k(h) be the second derivative of h**7/2240 + h**6/120 + h**5/64 + 23*h**4/12 + h**3/3 + 4*h + 8. Let c(j) be the third derivative of k(j). Factor c(b).
3*(b + 5)*(3*b + 1)/8
Let p = -210269/2 - -105135. Determine u so that -19/2*u**3 + 0*u**4 + 6*u + 2*u**5 - p*u**2 + 2 = 0.
-2, -1/2, 1, 2
What is w in 23*w**2 - 80*w**2 - 144*w - 980 + 29*w**2 + 24*w**2 - 24*w = 0?
-35, -7
Suppose 3*y + 3*v - 7*v = 17, -v + 4 = 2*y. Solve -2*i**4 - 11*i**2 + 5*i**2 + 3*i**3 + 8 + 11*i**3 - 4*i**y - 10*i = 0 for i.
-1, 1, 4
Let y(x) be the third derivative of -x**5/90 + 89*x**4/36 - 1168*x**3/9 + 4*x**2 + 2*x - 89. What is a in y(a) = 0?
16, 73
Let p be ((-432)/924)/((-42)/462). Solve -p + 38/7*d - 2/7*d**2 = 0 for d.
1, 18
Let c(r) be the second derivative of -4*r**7/189 - 34*r**6/135 - 7*r**5/15 + r**4/27 + 14*r**3/27 - 129*r - 6. Let c(h) = 0. Calculate h.
-7, -1, 0, 1/2
Suppose 0 = -22*n - 47*n - 4*n. Let h(l) be the third derivative of -1/120*l**6 + 0*l**3 - 21*l**2 + n*l + 1/30*l**5 + 0*l**4 + 0. Factor h(v).
-v**2*(v - 2)
Let n(w) be the second derivative of -45/8*w**4 - 35*w + 0 - 1/96*w**6 - 45*w**3 + 7*w**2 - 3/8*w**5. Let o(k) be the first derivative of n(k). Factor o(p).
-5*(p + 6)**3/4
Let c be ((-114)/(-456) + (-14)/(-8))*(-1 - -2). Factor -17/3*v**c + 7/3*v**4 + 0 - 2*v + 16/3*v**3.
v*(v - 1)*(v + 3)*(7*v + 2)/3
Let m(j) be the first derivative of 8 - 1/8*j**4 + 2*j**3 + 9*j - 12*j**2. Let r(p) be the first derivative of m(p). Factor r(k).
-3*(k - 4)**2/2
Determine o, given that -4/7*o**2 - 4712/7*o - 1387684/7 = 0.
-589
Let l(z) be the second derivative of -z**7/14 - 19*z**6/10 - 81*z**5/10 + 191*z**4/2 + 55*z**3/2 - 1089*z**2/2 - 1050*z. Suppose l(b) = 0. What is b?
-11, -1, 1, 3
Let b(j) = -4*j**4 + 35*j**3 + 57*j**2 - 145*j - 274. Let q(v) = -v**4 - v**2 - v - 2. Let u(c) = -b(c) + 5*q(c). Factor u(n).
-(n - 2)*(n + 2)**2*(n + 33)
Factor -19*l**2 - 12*l**2 + 13*l**2 + 60 + 4*l - 36 - 4*l**3 - 6*l**2.
-4*(l - 1)*(l + 1)*(l + 6)
Let z(d) be the second derivative of -d**4/48 + 97*d**3/3 - 18818*d**2 + 1089*d. Suppose z(m) = 0. Calculate m.
388
Let t(m) be the third derivative of -5*m**4 - 1/60*m**6 - 200/3*m**3 + 0*m + 0 + 3/5*m**5 + 15*m**2. Factor t(u).
-2*(u - 10)**2*(u + 2)
Let z = 10614 + -10609. Let c(h) be the third derivative of 4/315*h**6 + 0*h + 0 + 0*h**4 + 0*h**3 + 1/735*h**7 + 1/126*h**z + 16*h**2. Let c(n) = 0. What is n?
-5, -1/3, 0
What is s in 5160/7*s - 3328200/7 - 2/7*s**2 = 0?
1290
Let o = 94 + -91. Let h be 6 + (-1)/(1/3). What is p in -110*p - 111*p + 224*p - h*p**o = 0?
-1, 0, 1
Suppose -5*w = 5*d - 155, -5*w = -d + 18 + 7. What is y in 28*y + 10 - 25*y**2 - d*y + 17*y = 0?
-2/5, 1
Let s(n) be the second derivative of n**4/9 - 67*n**3/36 - 25*n**2/4 - 5*n + 71. Solve s(j) = 0 for j.
-1, 75/8
Let b(a) be the third derivative of a**8/672 + 11*a**7/420 + 2*a**6/15 + 7*a**5/30 + a**2 + 9*a + 126. What is r in b(r) = 0?
-7, -2, 0
Let j be 61/(5490/(-27)) + 7269/30. What is o in 1/6*o**3 + j*o + 11*o**2 + 5324/3 = 0?
-22
Let w = 172613 - 517711/3. Factor 16/3*a - 1/6*a**2 - w.
-(a - 16)**2/6
Let r(i) = 8*i**2 + 4876*i + 1473804. Let m(y) = 7*y**2 + 4871*y + 1473802. Let f(j) = 4*m(j) - 3*r(j). Find o such that f(o) = 0.
-607
Let y(g) = -g**3 + 11*g**2 + 3*g + 18. Suppose -3*k = 4*s - 33, 2*s + 70 - 15 = 5*k. Let d be y(k). Factor -3*b**3 + 2*b**3 - d*b - 4*b**2 + 51*b.
-b**2*(b + 4)
Let b be (-6)/(4 - 152/32). Let n be 147/126*(b - -1). Let 0 + 0*u + n*u**3 - 3*u**2 = 0. What is u?
0, 2/7
Let j(f) be the first derivative of -f**5/40 + 7*f**4/24 - 2*f**3/3 - f**2/2 + 11*f - 2. Let y(g) be the second derivative of j(g). Factor y(t).
-(t - 4)*(3*t - 2)/2
Let u(v) be the second derivative of v**5/70 - 2*v**4/7 - 127*v**3/21 - 114*v**2/7 + 783*v. Factor u(b).
2*(b - 19)*(b + 1)*(b + 6)/7
Let g(f) be the second derivative of f**6/75 - f**5/2 + 47*f**4/30 - 23*f**3/15 + 4*f + 6. Factor g(j).
2*j*(j - 23)*(j - 1)**2/5
Let y(p) be the second derivative of 11*p**6/180 + 371*p**5/40 + 160*p**4/9 - 167*p**3/3 - 100*p**2/3 + 6726*p. Let y(b) = 0. What is b?
-100, -2, -2/11, 1
Suppose 0 = 19*v - 14*v - u, 4*v = -u + 9. Let c be v/3*(-210)/(-490). Find y, given that -c*y**2 + 2/7*y + 0 = 0.
0, 2
Let d(i) = -11*i**3 - 11*i**2 - 38*i - 36. Let l(s) = 9*s**3 + 10*s**2 + 37*s + 36. Let q(v) = -5*d(v) - 6*l(v). Factor q(a).
(a - 9)*(a + 2)**2
Let a(v) be the first derivative of -v**9/12096 - v**8/3360 + v**6/720 + v**5/480 + 14*v**3/3 + 5*v + 17. Let f(s) be the third derivative of a(s). Factor f(g).
-g*(g - 1)*(g + 1)**3/4
Factor -31*i**2 - 29*i**2 - i**4 + 10185*i**3 + 10164*i**3 - 20365*i**3.
-i**2*(i + 6)*(i + 10)
Suppose -27*a + 26*a = 0, 0 = 2*k + 2*a + 70. Let u be (-2)/(-2) - (-5)/(k/(-14)). Factor 2/3 + 2/9*h - 2/3*h**2 - 2/9*h**u.
-2*(h - 1)*(h + 1)*(h + 3)/9
Let p(i) be the second derivative of -5*i**7/21 + 181*i**6/5 + 223*i**5/10 - 181*i**4/2 - 218*i**3/3 + i + 3754. Suppose p(h) = 0. What is h?
-1, -2/5, 0, 1, 109
Let p(n) be the second derivative of -n**6/270 - n**5/135 + n**4/27 - 29*n**2/2 - 36*n - 2. Let u(g) be the first derivative of p(g). Factor u(x).
-4*x*(x - 1)*(x + 2)/9
Let h = 5537/24930 - -1/8310. Let p(t) be the first derivative of -2 - h*t + 1/27*t**6 - 2/45*t**5 + 1/9*t**2 + 4/27*t**3 - 1/9*t**4. Factor p(k).
2*(k - 1)**3*(k + 1)**2/9
Let n(s) = 5*s**2 - 2*s + 12. Let i(u) = -9*u**2 + 5*u - 24. Let q(g) = -6*i(g) - 11*n(g). Let a be q(-9). Factor 4*d**a + 0 + 4*d**3 + 4*d**2 - 4 - 8*d.
4*(d - 1)*(d + 1)*(2*d + 1)
Let k(q) = 5*q**2 + 90*q + 1946. Let l(z) = 17*z**2 + 271*z + 5843. Let d(s) = -28*k(s) + 8*l(s). Suppose d(x) = 0. What is x?
-44
Determine k, given that 910*k**3 - 926*k**3 - k**2 - k**2 + 11*k + 5*k + 2*k**4 = 0.
-1, 0, 1, 8
Let y(a) = -5*a**2 - a + 2. Let c(k) = 2*k**2 - 1. Let b(o) = 2*c(o) + y(o). Let w(f) = 86*f**2. Let i(x) = 4*b(x) - w(x). Factor i(p).
-2*p*(45*p + 2)
Let g = 1874 - 1864. Let j be 986/(-203) + 6/(12/g). Let -j*p**5 + 4/7*p**2 - 2/7*p**4 - 1/7*p - 2/7 + 2/7*p**3 = 0. What is p?
-2, -1, 1
Let g(p) = -p + 3. Let j be g(1). Suppose 4*z - a = 57, -j*a = -z - 3*a + 18. Solve -6*o + 257 - 257 - 12