
Suppose 16 = 3*r + r. Let y(w) be the first derivative of 0*w**3 - 3 + 0*w**2 + 1/4*w**6 + 0*w + 3/2*w**r + 6/5*w**5. Solve y(a) = 0 for a.
-2, 0
Let t be (-2)/(-5) + 24/15. Solve -11*a**t - 4*a - 6*a**2 - 9*a**2 = 0 for a.
-2/13, 0
Let r(a) be the first derivative of -a**2/2 + 11*a + 55. Let i be r(9). What is l in -6 + i*l + 10/3*l**2 + 2/3*l**3 = 0?
-3, 1
Factor -3/4*u**2 - 1/4*u**3 + 2 + 3/2*u.
-(u - 2)*(u + 1)*(u + 4)/4
Let a(h) = h**2 - 2*h + 4. Let x be a(2). Find g such that 8*g - x*g**2 - 5 + 3 + 2 - 4 = 0.
1
Let f(t) be the second derivative of 2*t**7/21 + 8*t**6/5 + 7*t**5 - 4*t**4 - 24*t**3 - 106*t. Factor f(x).
4*x*(x - 1)*(x + 1)*(x + 6)**2
Let b(z) = -4*z**2 - 20*z + 2. Let c(j) = -j**2 + 2*j + 1. Let i(q) = b(q) - 2*c(q). Suppose i(u) = 0. What is u?
-12, 0
Let q(j) be the third derivative of j**5/12 - 5*j**4/8 - 58*j**2. Find s, given that q(s) = 0.
0, 3
Let y = 8 + 92. Suppose 64 + 100*o**2 + 384*o**2 - 435*o**3 + y*o**4 + 75*o**3 - 288*o = 0. What is o?
4/5, 1
Let i be (-4)/(-6)*(198/(-10))/(-11). Let 18/5*b**3 + i*b**5 + 0 - 4*b**4 - 4/5*b**2 + 0*b = 0. Calculate b.
0, 1/3, 1, 2
Let j(n) be the first derivative of -7*n**4/120 + 23*n**3/60 - 3*n**2/10 - 8*n + 14. Let d(r) be the first derivative of j(r). What is c in d(c) = 0?
2/7, 3
Let f(d) = 2*d + 24. Let p be f(-15). Let n be 4/(-6)*3/p + 4. Factor n*m + 38/3*m**3 + 32/3*m**2 + 2/3 + 5/3*m**5 + 22/3*m**4.
(m + 1)**4*(5*m + 2)/3
Suppose -5*v = -0*v - 4*z - 4, 5 = -5*z. Let c(j) be the second derivative of 0 - j + 1/6*j**4 + 1/15*j**6 - 1/5*j**5 + 0*j**3 + v*j**2. Factor c(q).
2*q**2*(q - 1)**2
Let n be (0 - -2)/((-2)/(-10)). Let c(b) = n*b**2 + 60*b + 2*b**2 + 192 + 27*b + 0*b**2. Let f(u) = 3*u**2 + 22*u + 48. Let t(m) = 2*c(m) - 9*f(m). Factor t(v).
-3*(v + 4)**2
Let n(t) be the first derivative of -t**8/1680 + t**7/840 - 14*t**3/3 + 8. Let j(o) be the third derivative of n(o). Factor j(a).
-a**3*(a - 1)
Let 15*y**3 - 10*y**3 + 4*y**2 + y**4 - 8*y - 2*y**2 + 0*y**2 = 0. What is y?
-4, -2, 0, 1
Suppose -10*n + 4*n = -18. Let -5*p**5 + 10*p**4 - 10*p**2 + 2*p + n*p + 9*p**2 - 9*p**2 = 0. What is p?
-1, 0, 1
Let y(f) be the first derivative of f**7/98 + f**6/70 - 12*f - 10. Let z(g) be the first derivative of y(g). Determine q so that z(q) = 0.
-1, 0
Let g be ((-26)/6)/((-8)/(-12) - 1). Factor -14*z - 2*z**3 - z + g*z - 4*z**2.
-2*z*(z + 1)**2
Let x(w) be the second derivative of 2*w**7/77 - 19*w**6/55 + 21*w**5/22 + 7*w**4/2 - 145*w**3/11 + 150*w**2/11 - 2*w - 243. Solve x(u) = 0 for u.
-2, 1/2, 1, 5
Let n = -65 - -67. Let q be (n/2)/(0 + (-6)/(-12)). Factor 0 - 1/4*z**3 - 1/4*z**4 + 0*z + 0*z**q.
-z**3*(z + 1)/4
Factor 0*r**2 + 4/5*r**3 + 2/5 - 2/5*r**4 - 4/5*r.
-2*(r - 1)**3*(r + 1)/5
Let b be 33/(-110) - (-30)/100. Suppose b*c**2 - 4/17*c**3 + 0 + 2/17*c**5 + 0*c - 2/17*c**4 = 0. What is c?
-1, 0, 2
Suppose 92*t = 63*t + 116. Determine f, given that -9/2*f + 39/2*f**2 + 3/2*f**t - 27 + 21/2*f**3 = 0.
-3, -2, 1
Let x(b) = -b**3 + 10*b**2 - 8*b - 9. Let p = 27 + -18. Let m be x(p). Factor 2/5*q - 2/5*q**2 + m.
-2*q*(q - 1)/5
Suppose 4*h + 20 = -2*q, 0 = -0*h + h - q - 1. Let o be h*(-1 - (-1)/(-3)). Suppose 3 - 6 - o - 8*z - 2*z**2 - 1 = 0. What is z?
-2
Let q be (-1 - (-3)/(-4))*(-304)/171. Factor 2/9*k**2 + 98/9 - q*k.
2*(k - 7)**2/9
Factor -11104/3*h**3 - 2066/3*h - 2760*h**2 - 172/3 - 128/3*h**4.
-2*(h + 86)*(4*h + 1)**3/3
Let m(y) be the first derivative of -16/25*y**5 + 2/5*y**4 + 8 - 1/3*y**6 + 1/5*y**2 + 4/3*y**3 - 4/5*y. Let m(u) = 0. What is u?
-1, 2/5, 1
Let i(z) be the third derivative of z**6/24 - 7*z**5/6 + 95*z**4/8 - 60*z**3 + 2*z**2 + 61*z. Factor i(f).
5*(f - 8)*(f - 3)**2
Factor 24*c**3 + 564*c**2 - 1197*c**2 + 48 - 4*c**4 - 16*c + 597*c**2.
-4*(c - 3)*(c - 2)**2*(c + 1)
Let g(p) be the second derivative of p**4/78 + 2*p**3/39 + 13*p. Solve g(b) = 0 for b.
-2, 0
Let q(y) be the third derivative of y**8/112 - 2*y**6/5 + 19*y**5/10 - 33*y**4/8 + 5*y**3 - 50*y**2. Factor q(m).
3*(m - 2)*(m - 1)**3*(m + 5)
Let x(d) = -5*d**2 - d. Let n(y) = 4*y**2 + 2*y. Let b(p) = -2*n(p) - 3*x(p). Let w be b(1). Solve 9 - 49*f**2 - 7 - 28*f - w = 0.
-2/7
Let t(p) be the first derivative of -5/4*p**4 + p**3 + 1/5*p**5 + 1/6*p**6 + 0*p - 38 + 0*p**2. Determine w so that t(w) = 0.
-3, 0, 1
Let v(u) = 15*u**2 - 5*u + 10. Let n(d) = -d + 1. Let k = 47 - 62. Let c(w) = k*n(w) + v(w). Determine b so that c(b) = 0.
-1, 1/3
Let l(p) be the second derivative of 1/18*p**4 - 6*p + 0 - 1/18*p**3 + 1/60*p**5 - 1/3*p**2. Factor l(c).
(c - 1)*(c + 1)*(c + 2)/3
Let a(b) = -6*b**2 - 4*b + 6. Let x(i) = 1 + 0*i**2 - i**2 + i + 3*i - 5*i. Let v be -2 - (2 - (-6)/(-2)). Let d(y) = v*a(y) + 4*x(y). Factor d(p).
2*(p - 1)*(p + 1)
Let b(d) be the second derivative of 23*d**4/2 - 49*d**3/2 + 9*d**2/2 - 2*d - 56. Factor b(o).
3*(o - 1)*(46*o - 3)
Suppose 5*v + 0*u + 15 = 3*u, 0 = -3*u + 15. Let n = -30843 + 30847. Suppose v*w + 0 - 5*w**3 + 5/2*w**n + 5/2*w**2 = 0. What is w?
0, 1
Let f(w) = -8*w**5 + 20*w**4 - 40*w**3 + 20*w**2. Let k(m) = 7*m**5 - 21*m**4 + 41*m**3 - 21*m**2. Let i(z) = 3*f(z) + 4*k(z). Let i(g) = 0. Calculate g.
0, 1, 2, 3
Let f be 375/45 + 80/(-15). Suppose -2/5*d**f - 24/5*d + 144/5 - 4*d**2 = 0. Calculate d.
-6, 2
Let l be (-58)/5*(-7)/14*-7. Let s = -40 - l. Determine b so that -3*b + 6/5 + s*b**5 - 12/5*b**4 + 6/5*b**2 + 12/5*b**3 = 0.
-1, 1, 2
Suppose 37 = 5*l - 43. Suppose 26 - 9 - 7 + 12*i**2 + 15*i - 9*i**3 - l = 0. Calculate i.
-1, 1/3, 2
Determine l, given that 7 - 17 + 74 - 256*l - 28*l**4 + 103*l**2 - 7*l**2 + 64*l**3 = 0.
-2, 2/7, 2
Let i(r) = -r**3 - 6*r**2 - 4*r - 8. Let o be i(-6). Let j = 16 - o. Factor j + 2/5*x**2 + 4/5*x.
2*x*(x + 2)/5
Let g(p) be the first derivative of -p**4/4 + 3*p**3 - 6*p**2 - 5*p - 9. Let v be g(7). Factor v*d**3 + 3*d - 15*d**2 + 3*d - 3*d**5 + 7*d**4 - 2*d**4 - 2*d**4.
-3*d*(d - 1)**3*(d + 2)
Let z(x) be the third derivative of 0*x**3 + 0*x**4 - 1/75*x**5 + 0*x + 0 - 7*x**2. Factor z(g).
-4*g**2/5
What is w in 13/4 - 7/2*w + 1/4*w**2 = 0?
1, 13
Let r = -3 - -6. Suppose 2*v = z + 54, v + 58 = r*v + z. Factor 5*h**3 + 30*h**2 - 2*h**2 - 8*h + 3*h**3 - v*h**4.
-4*h*(h - 1)*(h + 1)*(7*h - 2)
Let w(n) = -n**3 - n**2 + 1. Let l(p) = 3*p**5 + 162*p**4 + 2922*p**3 + 17502*p**2 - 6. Let d(j) = l(j) + 6*w(j). Factor d(b).
3*b**2*(b + 18)**3
Let f(j) be the first derivative of -j**5/25 + j**4/10 + 4*j**3/5 - 9*j**2/5 - 27*j/5 + 333. Factor f(q).
-(q - 3)**2*(q + 1)*(q + 3)/5
Let u be (4/34)/((-12)/(-96)). Let a be (13 - 10) + 19/(-17). Determine w, given that a - u*w + 2/17*w**2 = 0.
4
Let j(r) = -7*r**4 + 67*r**3 + 68*r**2 + 3*r + 3. Let g(q) = -15*q**4 + 135*q**3 + 136*q**2 + 7*q + 7. Let m(c) = -3*g(c) + 7*j(c). Factor m(b).
-4*b**2*(b - 17)*(b + 1)
Let i = -13073 - -13075. Factor -2/13*b**3 - 10/13 - 22/13*b - 14/13*b**i.
-2*(b + 1)**2*(b + 5)/13
Let d = -221/4 + 56. Let m(y) be the first derivative of 10 + 1/6*y**3 - d*y**2 + y. Find t, given that m(t) = 0.
1, 2
Let m(k) be the second derivative of -32*k**7/273 + 64*k**6/195 + 19*k**5/65 - 79*k**4/78 - k**3/13 + 18*k**2/13 + 378*k. Find o such that m(o) = 0.
-1, -1/2, 3/4, 2
Suppose 2*q**4 - 4*q**4 - 2*q**2 - 35*q**3 + 4 + 15*q**3 + 14*q**3 + 0*q**4 + 6*q = 0. Calculate q.
-2, -1, 1
Let m be (-2 - 14/(-6)) + 380/(-15). Let p be (-5)/m*25/2. Factor p*c + 1 + 1/2*c**3 + 2*c**2.
(c + 1)**2*(c + 2)/2
Solve 22*c**5 + 25 - 306*c**4 + 82*c**4 + 128 + 72*c**2 + 52*c**2 - 590*c - 53 + 568*c**3 = 0.
-1, 2/11, 1, 5
Let x be ((-20)/(-6))/5 + 84/9. Suppose -t + 25 = 5*m, -5*t - 3*m - x = -5*m. Find b, given that 3/2*b**3 - 3/2*b**5 + b**4 + 0*b + t - b**2 = 0.
-1, 0, 2/3, 1
Let a(y) be the third derivative of -y**6/480 - 9*y**5/80 + 6*y**2 + 4. Determine z, given that a(z) = 0.
-27, 0
Let h(z) = -z + 50. Let j be h(0). Let v(q) = -q**2 - 4*q + 7. Let l be v(-5). Find k, given that -2*k**3 - j - k**3 + 44 + 6*k**l + 3*k = 0.
-1, 1, 2
Let h be 8/28*(-1 + 55). Let s be ((-1872)/65)/(-16)*(-3 + 42/9). Determine n, given that 108/7 + 36/7*n**2 + h*n + 4/7*n**s = 0.
-3
Let u(d) be the third derivative of 0*d**4 + 1/2016*d**8 + 0 + 1/210*d**7 + 0*d**5 + 0*d**3 - 37*d**2 + 1/144*d**6 + 0*d. Factor u(n).
n**3*(n + 1)*(n + 5)/6
Factor 5*m**4 + 65*m**2 - 44 - 8*m - 46 + 35*m**3 + 0*m**4 - 7*m.
5*(m - 1)*(