ose 0 = o + 1 - 8. Suppose -o*c**4 - 3*c + 0*c**3 + 8*c**2 - 2*c**3 - c**4 + 5*c = 0. What is c?
-1, -1/4, 0, 1
Solve 7*m**4 - 9*m**3 - 125*m**5 + 20*m**2 + 27*m**3 + 62*m**3 + 18*m**4 = 0 for m.
-2/5, 0, 1
Let r(p) = -p - 3. Suppose -24 = 2*b + b. Let t be r(b). Solve 0*f**2 + 3*f**3 + 7*f**3 - 5*f + 1 + 10*f**2 + 10*f + 5*f**4 + f**t = 0.
-1
Determine j so that 23*j - 529/2 - 1/2*j**2 = 0.
23
Let n = -6 - -8. Find s such that -s**3 - 2*s**3 + s**n + 6*s**3 - 3 + s**4 - 3*s + 1 = 0.
-2, -1, 1
Solve -60*s**2 - 4*s**3 - 487*s**4 - 70*s - 485*s**4 - 6*s**3 + 977*s**4 - 25 = 0 for s.
-1, 5
Let k(l) be the second derivative of l**4/30 + l**3/3 + 5*l - 1. What is c in k(c) = 0?
-5, 0
Let s(m) be the second derivative of -m**5/50 - 2*m**4/15 + m**3/5 + 18*m**2/5 - 312*m. Factor s(f).
-2*(f - 2)*(f + 3)**2/5
Factor -152/3*s - 2/9*s**3 + 128 + 56/9*s**2.
-2*(s - 16)*(s - 6)**2/9
Let l(d) = d + 14. Let b be l(-11). Suppose 9 = 3*p - 3. Factor p*g**2 - 4*g**b + 0*g**2 + 3*g - 3*g.
-4*g**2*(g - 1)
Suppose -k = -5*i + 72 + 57, 8 = -2*k. Let s = i - 21. Factor 24*d**s + 10*d**2 + 2*d**2 + 8*d - 28*d**4.
-4*d*(d - 2)*(d + 1)**2
Factor -10/3*z**3 - 14/3*z + 4/3 + 2/3*z**4 + 6*z**2.
2*(z - 2)*(z - 1)**3/3
Let u = -663 - -670. Let q(j) be the first derivative of 1/12*j**3 - 1/8*j**2 + 0*j + u. Solve q(o) = 0.
0, 1
Let l(h) = -h**3 - h**2 + 2*h - 6. Let s be l(-3). Suppose -6*p + s = -3*p. Factor p*n**2 + 2/3*n**3 + 0 + 4/3*n.
2*n*(n + 1)*(n + 2)/3
Let y(g) = -10*g**3 - 4*g**2 + 8*g - 24. Let w(b) = -b**3 - b**2 - 2. Let j(x) = 12*w(x) - y(x). Let j(k) = 0. What is k?
-2, 0
Let p(u) be the second derivative of 0 + 1/2*u**2 - 4*u + 1/24*u**4 + 1/30*u**5 - 1/3*u**3 - 1/120*u**6. Let k(f) be the first derivative of p(f). Factor k(b).
-(b - 2)*(b - 1)*(b + 1)
Let k(u) be the second derivative of -2/45*u**6 - 42*u + 0*u**2 + 0 + 1/189*u**7 + 1/9*u**3 - 5/27*u**4 + 2/15*u**5. Let k(f) = 0. What is f?
0, 1, 3
Let x(i) be the first derivative of -4*i**3/3 + i**2/2 - 4. Let m(a) = a**3 - 16*a**2 + 4*a. Let u = -77 + 55. Let r(b) = u*x(b) + 6*m(b). Factor r(y).
2*y*(y - 1)*(3*y - 1)
Let t = -22 + 31. Let x(s) = -1 + 5*s + t*s**2 + 1 - 8*s. Let k(m) = -5*m**2 + m. Let c(z) = 5*k(z) + 3*x(z). Let c(v) = 0. Calculate v.
0, 2
Solve -2/13*i**5 + 0 - 8/13*i**2 - 4/13*i**4 + 14/13*i**3 + 0*i = 0.
-4, 0, 1
Let n(t) be the third derivative of t**6/540 - t**5/270 - 5*t**4/54 - 8*t**3/27 - t**2 - 217. Solve n(w) = 0 for w.
-2, -1, 4
Suppose -81/7*d**3 + 3/7*d**4 - 261/7*d**2 - 90/7 - 267/7*d = 0. Calculate d.
-1, 30
Let q(k) = -75*k**4 + 243*k**3 + 547*k**2 + 135*k - 50. Let a(h) = 15*h**4 - 49*h**3 - 109*h**2 - 27*h + 10. Let g(m) = -11*a(m) - 2*q(m). Solve g(c) = 0.
-1, -2/3, 1/5, 5
Let c(h) be the first derivative of h**5/60 + 5*h**4/36 - h**3/18 - 5*h**2/6 + 15*h - 23. Let z(a) be the first derivative of c(a). Factor z(l).
(l - 1)*(l + 1)*(l + 5)/3
Let i(b) be the second derivative of b**6/20 - b**5/20 - 3*b**4/8 + b**2 + 191*b. Factor i(u).
(u - 2)*(u + 1)**2*(3*u - 2)/2
Let w be ((-90)/(-200)*-5)/(3/(-16)). Let f(o) be the third derivative of 1/360*o**6 - 1/180*o**5 + w*o**2 - 1/72*o**4 + 1/18*o**3 + 0*o + 0. Factor f(i).
(i - 1)**2*(i + 1)/3
Let p = -3 + -2. Let b = p - -27. Factor 3*n - 3*n - 4*n**3 - b*n**4.
-2*n**3*(11*n + 2)
Let t(c) be the third derivative of c**7/140 + 19*c**6/60 - 53*c**5/120 - 13*c**4/24 + 133*c**2. Find y such that t(y) = 0.
-26, -1/3, 0, 1
Let i(v) = -5*v - 21. Let d be i(-5). Factor d*g**2 + 5/3*g**3 + 4/3*g + 0.
g*(g + 2)*(5*g + 2)/3
Let m(c) = -11*c**3 + 18*c**2 - 13*c + 11. Let r(i) = -6*i**3 + 9*i**2 - 6*i + 6. Let g(u) = 3*m(u) - 5*r(u). Find f such that g(f) = 0.
1
Let x = -10 - -12. Suppose 2*p = -w + 12 - 0, x*w - 29 = -5*p. Determine z so that -2*z**2 + w*z**3 + z**2 - z**3 = 0.
0, 1
Let d = 101 - 96. Factor 6*t**3 + d - 1 + 3*t**3 - 5*t - 5 - 3*t**2.
(t - 1)*(3*t + 1)**2
Let w(y) be the third derivative of -y**7/1470 + y**6/420 + y**5/35 - 5*y**4/21 + 16*y**3/21 + 85*y**2 - 1. Factor w(v).
-(v - 2)**3*(v + 4)/7
Let m = -5833 - -17501/3. What is v in m*v**2 + 2 - 8/3*v = 0?
1, 3
Suppose 0 = -61*l + 71*l - 12 - 8. Factor -1/2*h + 1/2*h**3 + 2*h**2 - l.
(h - 1)*(h + 1)*(h + 4)/2
Let y = 364 + -360. Let r(p) be the second derivative of 2/9*p**y + 1/12*p**2 + 0 - 2/9*p**3 + 3*p. Factor r(a).
(4*a - 1)**2/6
Suppose -8 = l - 10. Let u = 1 + l. What is t in -18*t**2 - 4*t**3 - t**5 - 2*t**2 - 6*t**3 - 8*t - 7*t**4 - 8*t**u = 0?
-2, -1, 0
Factor -21/5*h + 9/5 - 3/5*h**3 + 3*h**2.
-3*(h - 3)*(h - 1)**2/5
Let z be 0 + -3 - ((-185)/(-60))/(-1). Let p(i) be the first derivative of 0*i + z*i**3 + 1/4*i**4 + 3/20*i**5 + 0*i**2 - 2. Let p(g) = 0. What is g?
-1, -1/3, 0
Let x = -14 + 17. Let g(y) = 16*y + 112. Let u be g(-7). Factor u - h**x - 1/4*h + h**2.
-h*(2*h - 1)**2/4
Find m, given that -2/9*m**3 + 0 + 0*m + 2/9*m**5 + 4/9*m**2 - 4/9*m**4 = 0.
-1, 0, 1, 2
Let t(p) be the first derivative of -p**4/4 + 4*p**3 + p**2/2 - 9*p - 7. Let g be t(12). Factor 3*h**3 + h**3 + 4*h**2 + g*h**3 - 8*h - 3*h**3.
4*h*(h - 1)*(h + 2)
Let t(z) be the second derivative of -z**4/12 - 7*z**3/6 - 3*z**2 + 2*z + 14. Factor t(c).
-(c + 1)*(c + 6)
Let c(d) be the first derivative of d**4/16 - 7*d**3/12 - d**2 + 448. Factor c(k).
k*(k - 8)*(k + 1)/4
Let w be -1*47/7 + 301/(-49 - -92). Factor 6/7*n**2 + 12/7*n**3 + 0 + w*n**4 - 20/7*n.
2*n*(n - 1)*(n + 2)*(n + 5)/7
Let m(o) = 245*o**3 + 47*o**2 - 24*o - 6. Let k(l) = -2*l**2 - l + 1. Let i(c) = -6*k(c) - m(c). Factor i(g).
-5*g*(7*g - 2)*(7*g + 3)
Suppose -4*m - 40 = -356. Let -2*k - 2*k**2 - 47*k**3 + 27*k**4 + 5*k**4 + m*k**3 = 0. Calculate k.
-1, -1/4, 0, 1/4
Suppose 678 = 135*f + 408. Determine k, given that 2/5*k**f - 2/5*k - 4/5 = 0.
-1, 2
What is j in -j**2 + 0*j**3 - 104*j**2 + 15606*j - 48*j**2 - 265302 - 153*j**2 + 2*j**3 = 0?
51
Factor -24 + 3*o**4 + 288*o**2 - 36*o - 616*o**2 + 9*o**3 + 322*o**2.
3*(o - 2)*(o + 1)*(o + 2)**2
Let n be (72/(-10))/(-2)*(-10)/(-66). Suppose 4/11 + 2/11*y**2 - n*y = 0. What is y?
1, 2
Let j(o) be the first derivative of -5/3*o**3 - 8 + 0*o**2 + 5*o. Factor j(f).
-5*(f - 1)*(f + 1)
Let j(s) be the first derivative of -1/6*s**4 - 1/27*s**6 + 0*s**2 + 2/15*s**5 - 7 + 2/27*s**3 + 0*s. Find i, given that j(i) = 0.
0, 1
Let q be 9/(-3)*(-32)/24. Factor q - 3*l + 16*l**3 - 4*l**2 - 2*l - 11*l.
4*(l - 1)*(l + 1)*(4*l - 1)
Let r = -933 - -933. Factor -2/3*x**3 + r + 4/3*x**2 + 2*x.
-2*x*(x - 3)*(x + 1)/3
Determine p so that -1/6*p**2 - 5/3*p - 7/2 = 0.
-7, -3
Factor 1/7*q**5 + 26/7*q**3 + 9/7*q**4 + 3*q + 34/7*q**2 + 5/7.
(q + 1)**4*(q + 5)/7
Suppose 10 = -g - 3*g - 5*i, -5*i = g + 10. Let k = 12091/60380 + -3/12076. Determine a so that g*a + k - 1/5*a**2 = 0.
-1, 1
Let l(w) be the second derivative of 2/3*w**3 + 0*w**2 + 0 + 1/3*w**4 - 4*w. Factor l(m).
4*m*(m + 1)
Let d(x) be the second derivative of 1/40*x**6 + 52*x - 1/56*x**7 + 3/40*x**5 + 0 + 0*x**2 + 0*x**3 + 0*x**4. Factor d(t).
-3*t**3*(t - 2)*(t + 1)/4
Suppose -5*l + 26 = 11. Let c(t) be the second derivative of 0*t**l + 0 - 1/30*t**6 + 0*t**2 + 3*t + 1/10*t**5 + 0*t**4. Factor c(p).
-p**3*(p - 2)
Let l = -151/12 - -63/5. Let y(v) be the third derivative of 0*v - 1/360*v**6 + l*v**5 + 2*v**2 + 0 + 0*v**3 - 1/36*v**4. Let y(q) = 0. What is q?
0, 1, 2
Let i = -194 + 198. Let c(n) be the third derivative of -n**2 + 0 + 0*n**3 - 1/120*n**5 + 0*n - 1/48*n**i. Factor c(p).
-p*(p + 1)/2
Let w(v) be the second derivative of -v**7/105 + v**6/25 + 17*v**5/50 + 3*v**4/10 - 16*v**3/15 - 12*v**2/5 + 261*v. Determine d so that w(d) = 0.
-2, -1, 1, 6
Let p(o) = -o**2 - 3. Let a(s) = -6*s**2 - 21. Let l(m) = 7*m - 3. Let t be l(1). Let v(g) = t*a(g) - 27*p(g). Find x, given that v(x) = 0.
-1, 1
Let f(g) be the first derivative of 2*g**3/27 + 14*g**2/9 - 34*g/3 + 3. Suppose f(c) = 0. What is c?
-17, 3
Factor 1/9*n**2 + 8/9 + 2/3*n.
(n + 2)*(n + 4)/9
Let w(h) be the third derivative of h**7/210 + h**6/45 + h**3/3 + 6*h**2. Let g(c) be the first derivative of w(c). Solve g(m) = 0.
-2, 0
Let l(a) be the second derivative of 1/50*a**5 + 0 - 27*a + 8/15*a**3 + 4/5*a**2 + 1/6*a**4. Find j such that l(j) = 0.
-2, -1
Let g be 4/44*341/62. Suppose -g + 2/3*f - 1/6*f**2 = 0. What is f?
1, 3
Solve -192*m**2 + 2304/5*m + 0 - 92/5*m**3 - 2/5*m**4 = 0.
-24, 0