1
Suppose -136*i + 189 = -73*i. Find n, given that 9/2*n + 1/6*n**i + 3/2*n**2 + 9/2 = 0.
-3
Suppose 0 = -r + 5, -3*n - 2*n - 3*r = -40. Factor -36*s - 10*s**4 + 36*s - 5*s**n - 5*s**3.
-5*s**3*(s + 1)**2
Let p(n) = n**2 - n + 1. Let q(j) = -16 - 5*j - 12*j + 3*j. Suppose -21*i + 26*i - 5 = 0. Let b(y) = i*q(y) - 2*p(y). What is x in b(x) = 0?
-3
Let f be (2/4 + 35/(-14))/(-399). Let b = 1066/399 - f. Let -2/3*k**2 - 2*k + b = 0. Calculate k.
-4, 1
Let k = 287/130 + 5/26. Let -3/5*n**2 + 12/5*n - k = 0. Calculate n.
2
Let t(m) be the second derivative of 2*m**6/15 - 6*m**5/5 + 4*m**4 - 20*m**3/3 + 6*m**2 + 3*m + 11. Determine p so that t(p) = 0.
1, 3
Suppose -2*d - 5*t = 40, 2*d - 2*t + 26 = -0*t. Let z = -44/3 - d. Suppose -2/3*p + 1/3*p**3 + 0 - z*p**2 = 0. What is p?
-1, 0, 2
Determine p, given that -16 + 128/3*p - 20/3*p**3 - 4*p**2 = 0.
-3, 2/5, 2
Let t(h) = -h**2 + 2*h - 2. Let s(q) = -8*q**2 + 64*q - 204. Let m(b) = s(b) - 4*t(b). What is j in m(j) = 0?
7
Let i(s) be the third derivative of -5*s**6/72 + s**5/12 - s**4/24 + s**3/2 - 13*s**2. Let y(q) be the first derivative of i(q). Factor y(o).
-(5*o - 1)**2
Let -13456/5 - 1/5*h**2 + 232/5*h = 0. Calculate h.
116
Factor 242/7 + 2/7*p**2 - 44/7*p.
2*(p - 11)**2/7
Let j(l) = 3*l**2 + 14*l - 26. Let p be j(6). Let i = -164 + p. Let -k**i - 1/2*k + 0 - 1/2*k**3 = 0. What is k?
-1, 0
Factor -4/5*u**4 - 556/5*u**3 - 1636/5*u - 1644/5*u**2 - 544/5.
-4*(u + 1)**3*(u + 136)/5
Let m be 6/(-2) - 36/(-6) - 0. Let b(s) be the first derivative of 9/4*s**4 - 9/2*s**2 + 2*s**m - 6*s - 6. Factor b(f).
3*(f - 1)*(f + 1)*(3*f + 2)
Let z(k) be the second derivative of -2/147*k**7 + 0*k**2 + 3/140*k**5 - k + 0 - 5/84*k**4 + 1/42*k**6 + 1/42*k**3. Solve z(j) = 0 for j.
-1, 0, 1/4, 1
Factor -320/7*n - 2/7*n**3 - 46/7*n**2 - 600/7.
-2*(n + 3)*(n + 10)**2/7
Factor -4/5 - 1/5*j**2 + j.
-(j - 4)*(j - 1)/5
Let q = 97 - 152. Let r be (1 + q/30)*27/(-3). Factor 0*u + 6*u**5 + r*u**3 - 12*u**4 + 0 - 3/2*u**2.
3*u**2*(u - 1)*(2*u - 1)**2/2
Factor 4/5 + 2/5*m**2 - 6/5*m.
2*(m - 2)*(m - 1)/5
Let n(g) be the third derivative of -1/84*g**8 + 1/2*g**4 + 11*g**2 - 2/35*g**7 - 1/15*g**6 + 2/15*g**5 + 0*g + 0 + 2/3*g**3. Suppose n(i) = 0. Calculate i.
-1, 1
Let h(z) be the first derivative of -z**4/3 - 4*z**3/3 - 10*z + 6. Let i(b) be the first derivative of h(b). Factor i(s).
-4*s*(s + 2)
Factor -1/3*g**4 - 4*g + 0 + 23/3*g**2 - 10/3*g**3.
-g*(g - 1)**2*(g + 12)/3
Let m(h) = -h**2 - 15*h - 10. Let s be m(-14). Solve -3*y**2 + y**s + 6*y**3 + 0*y + 2*y**4 - 6*y = 0.
-2, -1, 0, 1
Let u(v) be the second derivative of -v**6/240 - 7*v**5/160 - 11*v**4/96 - 5*v**3/48 + 217*v. Solve u(r) = 0 for r.
-5, -1, 0
Let z(x) = x**3 + 14*x**2 + 11*x - 20. Let b(u) = 2*u**3 + 26*u**2 + 22*u - 40. Let r(q) = 3*b(q) - 5*z(q). Factor r(f).
(f - 1)*(f + 4)*(f + 5)
Let t(b) be the second derivative of -b**7/2880 + b**6/2880 + 5*b**4/6 - 16*b. Let k(o) be the third derivative of t(o). Factor k(l).
-l*(7*l - 2)/8
Let m = 16 + -12. Let a be 2/8 - (-35)/m. Suppose -4*j**2 - 4 + a*j + 0 - j = 0. Calculate j.
1
Suppose -2*b = -3*f + 9, 4*b + 13 = 2*f + 3*f. Let q(o) = -2*o**2 - 17*o - 18. Let u be q(-7). Let 23/3*y**u - b*y**2 - y + 1/3 - 4*y**4 = 0. What is y?
-1/3, 1/4, 1
Let x(h) be the third derivative of 0 + 0*h + 4/15*h**4 + 4/15*h**3 + 11*h**2 - 3/50*h**5. Factor x(c).
-2*(c - 2)*(9*c + 2)/5
Let t = -14 + 17. Determine a so that -12*a**t - 18*a**2 - 12*a**3 - 8*a**3 + 5*a**3 - 3*a = 0.
-1/3, 0
Let p be -6 - (((-96)/20)/4)/(14/70). Factor p + 2/5*w**2 - 4/5*w.
2*w*(w - 2)/5
Let y(o) be the first derivative of -4/3*o**3 + 0*o + 1 - 2*o**2. Determine n so that y(n) = 0.
-1, 0
Suppose 14*i - 115 = -59. Factor -349/6*x**2 + 161*x**3 - 529/6*x**i - 2/3 - 14*x.
-(x - 1)**2*(23*x + 2)**2/6
Let s(c) be the third derivative of c**6/6 - 23*c**5/12 + 65*c**4/8 - 15*c**3 + 422*c**2. Suppose s(f) = 0. What is f?
3/4, 2, 3
Let o(x) be the first derivative of -26 + 9/5*x**5 + 0*x + 1/2*x**2 + 15/4*x**4 + 7/3*x**3. Factor o(p).
p*(p + 1)*(3*p + 1)**2
Find j, given that -260*j**3 - 30*j - 9*j**4 - 38 + 110 + 45*j**4 - 77*j + 596*j**2 - 337*j = 0.
2/9, 1, 3
Let b = -4/29 - -70/87. Suppose -3*d + 8 = -2*s, -28*s + 26*s + d = 0. Factor -2/3*n**s + 0*n + b.
-2*(n - 1)*(n + 1)/3
Find f, given that f**3 - 2*f**2 - 22 + 3*f**3 - 5*f**3 + 27*f - 14*f + 12*f**2 = 0.
-2, 1, 11
Let v(o) be the third derivative of 0*o**3 - 1/112*o**8 + 24*o**2 + 0 + 0*o + 1/10*o**7 - 4/5*o**5 + 0*o**4 - 1/5*o**6. Factor v(s).
-3*s**2*(s - 4)**2*(s + 1)
Let i(z) be the first derivative of -2*z**5/5 - z**4 + 18*z**3 - 52*z**2 + 56*z - 162. Factor i(j).
-2*(j - 2)**2*(j - 1)*(j + 7)
Let d be 1 + 213*3/12. Let k = d + -54. What is u in 0 + k*u - 1/2*u**2 = 0?
0, 1/2
Factor -14 + 2/3*o**2 + 122/9*o - 2/9*o**3.
-2*(o - 9)*(o - 1)*(o + 7)/9
Solve 1/5*c**3 + 0 + 18/5*c - 19/5*c**2 = 0 for c.
0, 1, 18
Let z = 249 + 176. Let j = -1259/3 + z. Determine m so that 4/3*m**3 - j*m + 32/3 - 8/3*m**2 = 0.
-2, 2
Let h = -13 - -15. Suppose -3*m + 2*p = 2*m - h, 0 = 3*m + 4*p - 22. Factor g**m + 8*g**3 + 3*g**2 + 8*g**4 - 4*g**4.
4*g**2*(g + 1)**2
Suppose -6*x = 5*s - x - 35, x = -2*s + 13. Suppose 5*q = 3*f + s, -5*q = -f - 0*f - 12. Suppose -5*a + 4 - 7 + 8*a - q + 3*a**2 = 0. Calculate a.
-2, 1
Determine f, given that 0 + 1/4*f**5 + 0*f**2 + 0*f + 4*f**3 + 2*f**4 = 0.
-4, 0
Let 2/7*w**3 + 264/7*w - 72/7*w**2 - 256/7 = 0. What is w?
2, 32
Suppose 0 = s - 3*v, -154*v = 2*s - 157*v - 3. Factor 0*q - 4/11*q**s + 0 - 2/11*q**4 - 2/11*q**2.
-2*q**2*(q + 1)**2/11
Let g(a) be the first derivative of 2*a**3/21 - 6*a**2/7 + 18*a/7 - 80. Let g(c) = 0. Calculate c.
3
Let q be (-114)/(-56) + 1134/(-648). Solve 4/7*o - 6/7*o**2 + q*o**3 + 0 = 0.
0, 1, 2
Let w(p) be the third derivative of p**5/420 - 202*p**2. Find y, given that w(y) = 0.
0
Let q(s) be the second derivative of s**7/168 - s**6/120 - s**5/16 - s**4/16 - 75*s. Factor q(y).
y**2*(y - 3)*(y + 1)**2/4
Let j(k) be the second derivative of -5*k**7/42 - 9*k**6/2 - 115*k**5/2 - 1445*k**4/6 + 385*k**3/2 + 3025*k**2/2 - 120*k + 2. Find h such that j(h) = 0.
-11, -5, -1, 1
Let z be (-24)/(-15) + 1 + 9/(-15). Factor -2*h**5 + 15*h**3 - 9*h**2 - 5*h**2 - 3*h**5 + 24*h**z.
-5*h**2*(h - 2)*(h + 1)**2
Let q(t) be the third derivative of t**7/1995 - t**6/30 + 397*t**5/570 - 3*t**4 + 108*t**3/19 + 2*t**2 + 48. Solve q(k) = 0.
1, 18
Let w(a) be the first derivative of -7*a**3/3 + 6*a**2 - 11*a + 2. Let v(n) = 13*n**2 - 24*n + 21. Let c(j) = -3*v(j) - 5*w(j). Determine m so that c(m) = 0.
1, 2
Let u(q) be the first derivative of 5*q**9/4032 - 11*q**8/6720 + q**7/1680 - 7*q**3/3 + 17. Let j(v) be the third derivative of u(v). Factor j(p).
p**3*(3*p - 1)*(5*p - 2)/4
Let q(h) = 9*h**3 + 6*h**2 + 13*h - 3. Let x be q(-3). Let b = -231 - x. Solve 3/4*z**2 + 0*z - 9/8*z**4 - 3/8*z**3 + b = 0.
-1, 0, 2/3
Suppose 42 = 2*c + 4*h - 0*h, -3*h = 5*c - 77. Factor -5*j**2 + 19 + 5*j + 24 - 46 + c.
-5*(j - 2)*(j + 1)
Let t(p) be the first derivative of 0*p - 5/3*p**3 - 40 + 0*p**2 + 5/4*p**4. Factor t(z).
5*z**2*(z - 1)
Suppose 50 = 2*i - 46. Let l be 3/6*5*i/540. Factor 0 - 2/9*v**3 - l*v**2 + 0*v.
-2*v**2*(v + 1)/9
Let d(i) be the third derivative of 2*i**7/21 - 58*i**6/5 + 1124*i**5/3 + 2544*i**4 + 3456*i**3 + 30*i**2 + 3*i. Suppose d(h) = 0. Calculate h.
-2, -2/5, 36
Let x(p) be the third derivative of -1/10*p**5 - 1/40*p**6 + 1/35*p**7 + 0*p + 0*p**3 + 0*p**4 + 0 + 1/112*p**8 + 3*p**2. Find b, given that x(b) = 0.
-2, -1, 0, 1
Let m(y) be the first derivative of y**4/12 + 2*y**3/3 + 3*y**2/2 - 99. Factor m(z).
z*(z + 3)**2/3
Let w(j) be the second derivative of -j**7/21 - 8*j**6/15 + 9*j**5/5 + 46*j**4/3 + 103*j**3/3 + 36*j**2 + 582*j. Factor w(f).
-2*(f - 4)*(f + 1)**3*(f + 9)
Suppose 20*o**4 - 280/3*o**2 + 124/3*o**3 - 32 - 368/3*o = 0. What is o?
-3, -2/3, -2/5, 2
Let l(o) be the second derivative of -o**5/70 + o**4/2 - 24*o**3/7 - 432*o**2/7 + 888*o. Factor l(f).
-2*(f - 12)**2*(f + 3)/7
Suppose 5*q - r = 3 + 3, -4 = -4*q + r. Factor 12*h**3 + 8*h**2 - 6*h**3 - q*h**3 - 24*h - 8*h.
4*h*(h - 2)*(h + 4)
Let f(u) = 10*u**4 - 6*u**3 - 58*u**2 - 50*u - 12. Let i(j) = -30*j**4 + 18*j**3 + 175*j**2 + 150*j + 36. Let s(y) = -13*f(y) - 4*i(y). Let s(d) = 0. What is d?
-1, -2/5, 3
Let j b