**2 - 8/5 - 8/5*k**3.
2*(k - 2)**2*(k - 1)*(k + 1)/5
Suppose 3*y = -173*u + 172*u - 4, -5*u + 12 = -y. What is s in 39/4*s + 3/4*s**3 + 9/2 + 6*s**u = 0?
-6, -1
Find x such that -6/7*x**5 - 15/7*x**2 + 15/7*x**4 + 15/7*x**3 + 0 - 9/7*x = 0.
-1, -1/2, 0, 1, 3
Let 2809/6*g**2 + 2/3 + 106/3*g = 0. What is g?
-2/53
Let u(y) = -11*y**2 - 66*y + 3. Let w be u(-6). What is n in 49/5*n**5 - 53/5*n**w + 8/5 + 98/5*n**4 - 106/5*n**2 + 4/5*n = 0?
-2, -1, -2/7, 2/7, 1
Solve 81/5*b**4 + 684/5*b**3 + 292/5*b**2 + 0 + 32/5*b = 0.
-8, -2/9, 0
Determine l, given that 12 + 16*l**3 + l**2 - 9*l**2 - 2*l**5 - 4*l**4 - 4 + 4*l**2 - 14*l = 0.
-4, -1, 1
Factor -15/2*p - 36 + 3/2*p**2.
3*(p - 8)*(p + 3)/2
Suppose j + 30 = 7*j. Suppose 1 = j*m - 9. Determine v, given that -2/3 - 1/3*v**m - v = 0.
-2, -1
Let r(d) be the third derivative of -d**5/20 - 2*d**4 + 18*d**3 - 3*d**2 + 144*d. Let r(h) = 0. Calculate h.
-18, 2
Let v(l) = -2*l**2 - 2*l + 1. Let w(m) = -9*m**2 + 360*m - 360. Let p(f) = -3*v(f) + w(f). Suppose p(b) = 0. What is b?
1, 121
Let v be (2/(-8))/(-5 + 3158/632). Let o = v - 76. Determine a, given that 3/2*a**5 - 9/2*a**2 - 3*a + 9/2*a**4 + 3/2*a**o + 0 = 0.
-2, -1, 0, 1
Let i(u) be the third derivative of 0*u**3 - 7/30*u**5 + 0 - 2/105*u**7 - 3*u**2 + 1/6*u**4 + 7/60*u**6 + 0*u. Let i(j) = 0. What is j?
0, 1/2, 1, 2
Suppose -l - 3*j + 17 = 0, 0 = 7*l - 12*l + 4*j + 28. Factor 13*n**2 - 26*n**2 - 5*n + l*n**2.
-5*n*(n + 1)
Let q(g) be the first derivative of -g**3/3 + 3*g**2 - 5*g - 2. Factor q(i).
-(i - 5)*(i - 1)
Let s(w) = -285*w + 569*w - 3*w**2 - 2 - 289*w. Let f(v) = v**2 + v + 1. Let r(k) = k - 4. Let m be r(6). Let c(l) = m*f(l) + s(l). Factor c(n).
-n*(n + 3)
Suppose -4*k + 3 = 2*s - 3*s, -8 = -4*k. Suppose 2*d = 5*r, -3*d - s*r = -0*d. Solve -47 - 4*x**2 + d*x**2 + 47 = 0.
0
Let r(k) = -k**3 + 52*k**2 - 3*k + 159. Let m be r(52). Factor 16/9*g**2 - 8/9*g - 10/9*g**m + 0 + 2/9*g**4.
2*g*(g - 2)**2*(g - 1)/9
Let a(p) be the third derivative of -p**8/168 + 29*p**7/105 - 149*p**6/30 + 207*p**5/5 - 567*p**4/4 + 243*p**3 + 2*p**2 + 8*p. Factor a(w).
-2*(w - 9)**3*(w - 1)**2
Factor 8 + 5*a**2 - 4*a**2 + 8*a + 11 - 4.
(a + 3)*(a + 5)
Let k be -1 + -4 - (-472)/120. Let l = 19/15 + k. Solve 1/5*f - l*f**3 + 0 + 0*f**2 = 0.
-1, 0, 1
Let c(f) be the second derivative of 3*f**4/4 - 8*f**3 - 18*f**2 + 30*f. Solve c(y) = 0 for y.
-2/3, 6
Let c(p) be the second derivative of -p**6/135 - p**5/30 + p**4/54 + p**3/9 - 3*p + 12. Factor c(u).
-2*u*(u - 1)*(u + 1)*(u + 3)/9
Let q(y) = -4*y**2 - y. Let n be q(1). Let t be (-2)/(-6) - n/3. What is c in -3 - 21*c**t - 29*c**2 + 30*c + 108*c**3 - 49*c**2 = 0?
1/4, 1/3
Suppose -11*x + 371 = -245. Determine t, given that -2*t**2 - 3*t**2 - x*t + 3*t**2 + 0*t**2 - 392 = 0.
-14
Let w(d) be the first derivative of d**5/70 + d**4/14 + 2*d**3/21 + 19*d + 2. Let y(z) be the first derivative of w(z). Let y(q) = 0. What is q?
-2, -1, 0
Let z(o) = -4*o - 6. Let q be z(-9). Solve 6*a - 9*a**2 + 26*a**4 + q*a**4 - 9*a**3 - 50*a**4 = 0 for a.
-1, 0, 1/2, 2
Suppose 18 = 15*u - 12. Suppose 5*p + u*p + 14*p = 0. Factor -1/6*b + p - 1/6*b**3 + 1/3*b**2.
-b*(b - 1)**2/6
Let s(l) be the first derivative of 2*l**3 + 13*l**2/5 + 4*l/5 - 39. Factor s(w).
2*(3*w + 2)*(5*w + 1)/5
Let h be 60/(-110) - 140/(-55). Determine o so that h + 1/2*o**2 + 3/4*o**3 - 1/4*o**4 - 3*o = 0.
-2, 1, 2
Let h(c) be the first derivative of c**5/20 - c**3/12 - 25. Let h(o) = 0. Calculate o.
-1, 0, 1
Let f = -8628 + 8630. What is p in 3/5 + 9/5*p**f + 3/5*p**3 + 9/5*p = 0?
-1
Let i be (2/27)/(2020/909). Let a(q) be the third derivative of 3/28*q**4 + 0*q + 0 - i*q**5 - 2/21*q**3 + q**2. What is r in a(r) = 0?
2/7, 1
Let f(y) = 2*y**2 - 275*y - 274. Let c be f(-1). Factor -116/5*q**c - 2/5*q**5 - 34*q - 10 - 212/5*q**2 - 26/5*q**4.
-2*(q + 1)**3*(q + 5)**2/5
Let p be 2*(-3 - -2) + 3. Let a be p + 2 + (-19)/57. Factor 25/3*n**3 + 44/3*n + a + 70/3*n**2.
(n + 2)*(5*n + 2)**2/3
Let g(u) = -4*u**2 - 2*u - 1. Let h be g(-1). Let i be (-2)/h + 120/9. Factor 12*c - 36*c - 75*c**3 + 55*c**2 + i*c.
-5*c*(3*c - 1)*(5*c - 2)
Suppose 3*p + 8*g - 7*g - 38 = 0, -4*p + 5*g = -38. Let x be p/(-21) + (-78)/(-63). Let 0 - x*r**2 - 4/3*r = 0. Calculate r.
-2, 0
Suppose 7*a + 1326 - 1340 = 0. Factor 22/5*i**3 + 0 + 8/5*i - 48/5*i**a.
2*i*(i - 2)*(11*i - 2)/5
Suppose -2*h - 15 = -5*l, -4*l + 12 = -0*h - h. Let p(o) be the second derivative of -4*o + h*o**2 + 0*o**4 + 0 + 3/20*o**5 - 1/2*o**3. Let p(y) = 0. What is y?
-1, 0, 1
Suppose -8*g + g = -7. Suppose -3*p + g = -5. Factor t**p + 0*t - t - 7 + 7 - 2.
(t - 2)*(t + 1)
Let a(b) be the first derivative of -5 - 35/4*b**4 - b**5 - 30*b**3 - 40*b - 50*b**2. Factor a(w).
-5*(w + 1)*(w + 2)**3
Let p be ((-12)/10)/((-176)/20). Let f(h) be the second derivative of 0 + 10*h - 1/33*h**3 + p*h**2 - 1/132*h**4. Find r, given that f(r) = 0.
-3, 1
Let i(m) be the first derivative of -5*m**6/6 + 5*m**5 - 10*m**4 + 20*m**3/3 + 100. Find a such that i(a) = 0.
0, 1, 2
Let o be (-8)/12 + (80/(-3))/(-1). Suppose -2*y = o - 32. Factor -2/3*z**2 + 2/3*z - 2/3*z**y + 2/3.
-2*(z - 1)*(z + 1)**2/3
Suppose p = -2*m - m + 14, -16 = -2*m - 2*p. Let k(d) be the second derivative of 3/70*d**5 + 0*d**4 + 0*d**2 - 4/21*d**m + 1/105*d**6 + 0 - 4*d. Factor k(u).
2*u*(u - 1)*(u + 2)**2/7
Suppose 0 = -4*m + 20 - 0. Let i(c) = c**3 - 5*c**2 + c - 2. Let j be i(m). Factor 2*h**2 + h**j - 4*h**3 + h**2 - h + h**4.
h*(h - 1)**3
Let v(q) be the third derivative of -q**7/140 - q**6/80 + 7*q**5/40 + q**4/16 - 3*q**3/2 - 42*q**2 - 2*q. Solve v(u) = 0.
-3, -1, 1, 2
Let n = -88/5 + 1399/15. Let q = n + -75. Factor -2/3*g + q*g**2 + 0.
2*g*(g - 1)/3
Let t(q) be the second derivative of -5*q**4/12 + 10*q**2 + 79*q. Factor t(v).
-5*(v - 2)*(v + 2)
Let s(d) be the third derivative of -d**5/20 + 45*d**4/4 + 91*d**3/2 - 3*d**2 + 5*d. Factor s(o).
-3*(o - 91)*(o + 1)
Let t be (20/8 + -4)*-2. Determine l so that 2*l**3 - 23*l - 3*l**t - 18*l**2 - 58*l = 0.
-9, 0
Let b(f) be the third derivative of f**6/180 + 11*f**5/270 - 19*f**4/108 + 5*f**3/27 + 4*f**2 - 5. Suppose b(d) = 0. What is d?
-5, 1/3, 1
Let q(z) = -31*z**2 - 5*z + 4. Let r(v) = 30*v**2 + 5*v - 5. Let w = 73 - 68. Let b(m) = w*q(m) + 4*r(m). Factor b(y).
-5*y*(7*y + 1)
Suppose 0 = -4*g, w + 2*g = -0*w - 5. Let a be ((-8)/10)/(2/w). Solve p**2 + 3 - 5*p**2 - 1 + 2*p**a = 0 for p.
-1, 1
Determine o, given that 0 - 80/3*o**2 + 10*o**4 + 5*o**3 - 5/3*o**5 - 20*o = 0.
-1, 0, 2, 6
Suppose -3/5*t**2 + 0*t + 27/5 = 0. What is t?
-3, 3
Let r = -9608/3 + 3204. Suppose 0*v + r*v**4 + 0 + 2/3*v**5 + 0*v**2 + 2/3*v**3 = 0. Calculate v.
-1, 0
Factor 141/7*j**2 + 1587/7 + 1725/7*j + 3/7*j**3.
3*(j + 1)*(j + 23)**2/7
Factor -52*z + 23*z**2 - 407*z**2 + 146*z + 8*z + 108*z**3 - 4*z**4 + 266*z.
-4*z*(z - 23)*(z - 2)**2
Let i be -3 - (144/6)/(-4). Let x(d) be the first derivative of -2 + 4/15*d**i + 0*d + 8/25*d**5 - 7/10*d**4 + 1/5*d**2. Suppose x(p) = 0. Calculate p.
-1/4, 0, 1
Suppose -6 = 4*h - 18. Suppose -2*i - h = -3*i. Determine a, given that 4*a**2 - 2*a**2 + 20*a**3 - i*a**2 - 3*a**2 - 16*a**4 = 0.
0, 1/4, 1
Factor 130/21 - 16/21*h - 2/21*h**2.
-2*(h - 5)*(h + 13)/21
Let v(k) be the first derivative of 0*k**4 + 1/15*k**5 - 1/60*k**6 + 6 + 0*k + 0*k**3 - 3*k**2. Let m(z) be the second derivative of v(z). Factor m(j).
-2*j**2*(j - 2)
Suppose 2/5 - 102/5*l + 2601/10*l**2 = 0. Calculate l.
2/51
Let f(w) be the second derivative of w**9/720 - 33*w**8/2240 + 3*w**7/140 + w**6/30 + w**4/2 - 28*w. Let t(o) be the third derivative of f(o). Factor t(l).
3*l*(l - 4)*(l - 1)*(7*l + 2)
Suppose -20*j - 10*j - 14*j = 0. Find b, given that j - 4/3*b + 1/3*b**2 = 0.
0, 4
Suppose g - 6 = -3*g + 3*q, 2*q - 13 = -3*g. Determine b so that -191*b**2 - 3*b**4 - 3 - g*b**5 + 3*b**3 + 194*b**2 + 3 = 0.
-1, 0, 1
Let y(t) be the first derivative of 8*t + 1 - 2*t**3 + t**4 - 1/5*t**5 + 2*t**2. Let q(b) be the first derivative of y(b). Factor q(j).
-4*(j - 1)**3
Let l = 55 + -49. Factor -12*b - l*b - 21*b**2 + 33*b - 9*b.
-3*b*(7*b - 2)
Let a be 6/(-1 + -1) + 95. Let j be (-18)/99 - (1 + a/(-22)). Let 0 - 1/6*d**4 - 1/3*d + 1/3*d**j + 1/6*d**2 = 0. What is d?
-1, 0, 1, 2
Let o be 69/(-138)*(-4)/5. Let g be 1 + 26*(-2)/60. Let -g*u**2 - o*u - 4/15 = 0. Calculate