
Let k = 2/13189 + 39563/26378. Determine p, given that 0 + p - k*p**2 + 1/2*p**4 + 0*p**3 = 0.
-2, 0, 1
Suppose -2*q + 12 = t, 2*q + 29*t - 4 = 32*t. Factor -5/2*n + 1 + 1/2*n**q - 2*n**4 + 2*n**3 + n**2.
(n - 2)*(n - 1)**3*(n + 1)/2
Let r(v) be the first derivative of v**6/3 + 18*v**5/5 + 13*v**4 + 68*v**3/3 + 21*v**2 + 10*v - 34. Suppose r(u) = 0. Calculate u.
-5, -1
Let x(j) be the third derivative of j**5/5 + j**4/6 - 8*j**3/3 - 59*j**2. What is s in x(s) = 0?
-4/3, 1
Let c be -4 - (32 + (3 + 1 - 7)). Let i be (-77)/c*2/7. Factor 1/3*l**3 - i*l - 1/3*l**2 + 0.
l*(l - 2)*(l + 1)/3
Let s(u) be the first derivative of 5*u**6/4 - 12*u**5/5 - 3*u**4/2 + 5*u**3 - 3*u**2/4 - 3*u - 67. Solve s(n) = 0.
-1, -2/5, 1
Let g(x) be the first derivative of -49*x**4 + 252*x**3 - 480*x**2 + 400*x + 510. Find f such that g(f) = 0.
1, 10/7
Let i(d) be the second derivative of -40*d + 0 + 0*d**2 - 2/3*d**3 - 1/3*d**4. Factor i(r).
-4*r*(r + 1)
Suppose 0 = -3*y + 3*h + 12, -y + 412*h = 415*h - 8. Suppose -4/13*n**y + 2/13*n - 4/13 - 10/13*n**4 + 14/13*n**2 + 2/13*n**3 = 0. What is n?
-2, -1, 1/2, 1
Let l be (-3)/3*2 + 2/2. Let d be (((-2)/6)/l)/(45/405). Factor 4/3*r - 5/3*r**2 - 1/3 + 2/3*r**d.
(r - 1)**2*(2*r - 1)/3
Suppose -8 = 3*x + 46. Let c = -12 - x. Find p such that 2 + 1 - p**2 - c*p + 4*p**2 = 0.
1
Let i be ((-27)/(-18) + -1)*11 + -5. Suppose -i*y**2 + 0*y + 1/2 = 0. What is y?
-1, 1
Let r(m) = -3*m**4 - 11*m**3 + 76*m**2 - 136*m + 104. Let z(i) = 7*i**4 + 21*i**3 - 153*i**2 + 271*i - 210. Let y(k) = 9*r(k) + 4*z(k). What is l in y(l) = 0?
2, 3, 8
Let p = 3917 + -15661/4. Factor 17/4*w**2 + 3/2*w + p*w**3 + 0.
w*(w + 2)*(7*w + 3)/4
Let t(s) be the second derivative of 2/15*s**6 - 4/3*s**4 + 1/5*s**5 - 9*s + 0 + 0*s**2 - 8/3*s**3. Let t(y) = 0. What is y?
-2, -1, 0, 2
Let z = 58/845 + 956/845. Solve -z + 14/5*a**2 - 14/5*a + 6/5*a**3 = 0 for a.
-3, -1/3, 1
Let l(k) = -k**2 - 63*k - 147. Let h(s) = 64*s + 148. Let w(o) = 5*h(o) + 4*l(o). Factor w(r).
-4*(r - 19)*(r + 2)
Let m = -181 - -2177/12. Let s(t) be the first derivative of 2/9*t**3 - 5 + 1/3*t - 1/24*t**4 - m*t**2. Factor s(x).
-(x - 2)*(x - 1)**2/6
Let x be -3*3/(-4 - -1). Determine l so that 3*l**2 + 3597*l**3 - 3*l - 3*l - 3594*l**x = 0.
-2, 0, 1
Let o(i) be the third derivative of -11/60*i**6 - 13/30*i**5 - 1/3*i**4 - 2/105*i**7 + 0 + 0*i - 4*i**2 + 0*i**3. Let o(y) = 0. Calculate y.
-4, -1, -1/2, 0
Let w(y) be the third derivative of 2*y**2 - 1/60*y**6 + 0*y**3 + 0 + 0*y**4 - 1/45*y**5 - 1/315*y**7 + 0*y. Solve w(b) = 0 for b.
-2, -1, 0
Let w(a) = 2*a**3 - 47*a**2 - 8*a + 44. Let t(g) = 15*g**3 - 330*g**2 - 55*g + 310. Let i(s) = -3*t(s) + 20*w(s). Factor i(p).
-5*(p - 10)*(p - 1)*(p + 1)
Let s(a) be the third derivative of a**5/12 - 115*a**4/12 + 2645*a**3/6 + 76*a**2. Let s(x) = 0. What is x?
23
Let d be 2 + (3 - 6 - 9). Let x be ((-2)/4)/(1/d). Factor -3*s**4 + s**3 + 2*s**2 + x*s**4 + 3*s**3.
2*s**2*(s + 1)**2
What is k in 2/9*k**5 + 0*k - 2*k**3 + 0 + 10/9*k**2 + 2/3*k**4 = 0?
-5, 0, 1
Factor 1/3*m**3 + 46/3*m - 13/3*m**2 - 16.
(m - 8)*(m - 3)*(m - 2)/3
Let g be ((-50)/(-15))/((-4)/(-6)). Suppose -4*k = 3*w - 21, -g*w + 24 = 4*k - w. Factor -3*c**k + 9*c**5 + 2*c**2 - 4*c**5 - 4*c**5.
c**2*(c - 1)**2*(c + 2)
Let s(c) be the second derivative of -c**7/84 - 7*c**6/60 - 9*c**5/40 + 7*c**4/24 + 5*c**3/6 + 28*c. Solve s(n) = 0 for n.
-5, -2, -1, 0, 1
Let d(r) = 2*r**3 - 91*r**2 + 1440*r - 3456. Let j(n) = -n**2. Let t(q) = -2*d(q) - 22*j(q). Solve t(p) = 0.
3, 24
Let g(v) be the first derivative of 5*v**6/12 + 3*v**5 - 5*v**4 - 5*v**3 + 35*v**2/4 + 609. Let g(k) = 0. What is k?
-7, -1, 0, 1
Let u = 6/523 + 2062/2615. Factor 2/5*z**3 - u - 2/5*z + 4/5*z**2.
2*(z - 1)*(z + 1)*(z + 2)/5
Let t(s) be the second derivative of -s**6/6 + 3*s**5 - 175*s**4/12 + 7*s + 10. Factor t(x).
-5*x**2*(x - 7)*(x - 5)
Let p = 18 + 91. Suppose 0 = p*v - 111*v + 4. Suppose -1/4*n**v + 0 - 1/2*n = 0. Calculate n.
-2, 0
Let v(c) be the second derivative of -3*c**4/7 + 40*c**3/21 - 8*c**2/7 - 6*c - 5. Factor v(k).
-4*(k - 2)*(9*k - 2)/7
Let z = -369/26 - -1949/130. Factor 0 + 0*c**4 + 0*c**2 + 2/5*c**5 + 2/5*c - z*c**3.
2*c*(c - 1)**2*(c + 1)**2/5
What is k in 66*k + 1200*k**2 - 59 + 36*k + 62 + 18*k = 0?
-1/20
Factor 14/17*r + 0 - 12/17*r**2 - 2/17*r**3.
-2*r*(r - 1)*(r + 7)/17
Let g(j) be the third derivative of -j**7/210 + 11*j**6/120 - 17*j**5/60 - 11*j**4/24 + 3*j**3 + 3*j**2 - 7*j. Let g(w) = 0. What is w?
-1, 1, 2, 9
Find n such that 2909 - 832*n - 6056 - 1655 + 4*n**2 + 27160 + 20906 = 0.
104
Let w(r) = 6*r**2 - 19*r + 8. Let k be w(5). Let s be (-8)/28 + 39/k. Factor s*x**2 - 1/3*x + 0.
x*(x - 1)/3
Let m = 97 + -93. Solve -96*c**2 - m*c**2 - 16 + 38*c + 42*c = 0 for c.
2/5
Let w = -4184 + 29291/7. Find z such that 0*z**4 + 0*z + 3/7*z**3 - w*z**5 + 0 + 0*z**2 = 0.
-1, 0, 1
Let f(g) be the first derivative of -2*g**3/15 - 3*g**2/5 + 108*g/5 + 391. Factor f(o).
-2*(o - 6)*(o + 9)/5
Let l be 3 + 3/(-1) + 4. Suppose -6*t + 20 = -3*t - l*o, 0 = 2*t - 2*o - 14. Solve 0*p**3 + t + 2*p**3 + 6*p**4 - 3*p**3 - 14*p**2 + 3*p**3 - 2*p**5 = 0.
-1, 1, 2
Let l be 21/(-126)*2/(-1). Factor -1/3*i**3 - l + 1/3*i**2 + 1/3*i.
-(i - 1)**2*(i + 1)/3
Let l(x) be the first derivative of -x**6/12 - 3*x**5/5 - 11*x**4/8 - x**3 + 36. Let l(q) = 0. What is q?
-3, -2, -1, 0
Let j(c) = 6*c - 5. Let o be j(2). Factor -2 + 12*i + o - 2 - 15 - 3*i**2.
-3*(i - 2)**2
Let z(k) = -74*k - 20. Let q be z(4). Let o = -310 - q. Let -51/2*g**3 + 45/2*g**5 + 0 + 39*g**4 - 30*g**2 - o*g = 0. What is g?
-2, -2/5, -1/3, 0, 1
Let n = -4/857 - -937/17140. Let c(m) be the second derivative of m + 2*m**3 - 1/2*m**4 - 4*m**2 + n*m**5 + 0. Let c(y) = 0. Calculate y.
2
Suppose -3 = -4*b + 5. Suppose -10 = -4*l + 2*y, -b*l - 2*y = l - 4. Solve 0*s**2 + l*s**2 + s**2 = 0.
0
Let b = 191576870 + -634119433737/3310. Let a = b - 1/662. Factor -6/5 - a*r - 3/5*r**2.
-3*(r + 1)*(r + 2)/5
Let u(a) be the third derivative of 1/21*a**3 + 1/42*a**5 - 1/14*a**4 - 8*a**2 + 0 + 0*a. Find r such that u(r) = 0.
1/5, 1
Let w(d) be the second derivative of d**8/10080 - d**7/3780 - d**6/1080 + d**5/180 - d**4/12 - 5*d. Let g(k) be the third derivative of w(k). Factor g(o).
2*(o - 1)**2*(o + 1)/3
Let v(x) be the first derivative of -x**5/35 + 4*x**4/7 - 24*x**3/7 + 17*x - 5. Let j(u) be the first derivative of v(u). Find d, given that j(d) = 0.
0, 6
Suppose 7*y = 3*y + 20, 0 = 4*t + 5*y - 41. Let j be 1/((6/t)/(3/1)). Solve -1/5*d**3 + 0*d + 2/5*d**j + 0 = 0.
0, 2
Let t(j) be the third derivative of -1/3*j**3 - 11/120*j**6 - 2/5*j**5 + 0*j + 0 - 5/8*j**4 + 24*j**2. Factor t(m).
-(m + 1)**2*(11*m + 2)
Let p be (0/(-1))/(-4 - -6). Let r(f) be the third derivative of -2*f**2 + p*f + 0 + 3/2*f**4 - 2*f**3 - 1/4*f**5. Suppose r(a) = 0. Calculate a.
2/5, 2
Let p(f) be the first derivative of 1/120*f**4 - 5 + 0*f**3 + 2*f**2 + 0*f - 1/300*f**5. Let v(d) be the second derivative of p(d). Factor v(z).
-z*(z - 1)/5
Let o = 236 - 230. Let x be -6*27/36*(-4)/o. Factor 0 - 9/4*b**4 + 0*b - 1/4*b**2 + b**5 + 3/2*b**x.
b**2*(b - 1)**2*(4*b - 1)/4
What is l in -2/11*l**2 + 106/11 + 104/11*l = 0?
-1, 53
Let u(i) be the first derivative of -i**4/7 + 40*i**3/21 + 46*i**2/7 + 48*i/7 + 166. Factor u(h).
-4*(h - 12)*(h + 1)**2/7
Let s(m) be the third derivative of 1/40*m**6 - 1/10*m**5 + 0*m**3 + 1/70*m**7 + 0*m**4 + 3*m - 5*m**2 + 0. Factor s(x).
3*x**2*(x - 1)*(x + 2)
Suppose -28/5*b**2 + 4/5*b + 0 + 13/5*b**3 = 0. Calculate b.
0, 2/13, 2
Let a(q) be the second derivative of -q**6/45 + 11*q**5/15 + 8*q**4/3 + 362*q. Factor a(z).
-2*z**2*(z - 24)*(z + 2)/3
Let y = -10 + 10. Let w(t) be the third derivative of 0 - 3*t**2 + 0*t + 0*t**4 - 1/150*t**5 + y*t**3. Factor w(f).
-2*f**2/5
Let i(s) be the first derivative of s**6/180 + s**5/30 + 19*s**3/3 - 6. Let n(q) be the third derivative of i(q). Let n(k) = 0. Calculate k.
-2, 0
Let v(q) be the second derivative of q**7/105 + q**6/75 - 3*q**5/50 - q**4/6 - 2*q**3/15 + 4*q. Find t, given that v(t) = 0.
-1, 0, 2
Let j(n) be the second derivative of 0*n**2 + 1/20*n**5 + 1/42*n**7 - 1/3*n**3 + 0 + 1/10*n**6 - 6*n - 1/4*n**4. Determine a so that j(a) = 0.
-2, -1, 0, 1
Let t(c) be the first derivative of -c**4/2 + 4*c**3 + 71. Determine v, given that t(v)