k**2 + 0 + 3/2*k**3 - 17*k + 9/40*k**5 + 13/16*k**4. Factor v(a).
3*(a + 1)**2*(a + 2)**2/4
Let h be ((-38)/12)/(14/(-84)). Suppose h*a - 24 = 11*a. Factor -1/5*s**a + s - 3/5 - 1/5*s**2.
-(s - 1)**2*(s + 3)/5
Let p(k) be the first derivative of 3*k**5/5 - 2*k**3 + 3*k - 441. Determine h, given that p(h) = 0.
-1, 1
Let i(o) = o**2 - 3*o. Let m(f) = -4*f**2 + 8*f. Let l(r) = -3*i(r) - m(r). Factor l(q).
q*(q + 1)
Let b(i) be the third derivative of i**8/1512 - i**7/21 + 337*i**6/270 - 37*i**5/3 - 25*i**4/4 + 125*i**3 + 6*i**2 + 10*i. Let b(p) = 0. What is p?
-1, 1, 15
Let s(f) be the first derivative of 27*f**2 + 1/5*f**6 + 132/5*f**3 + 62/25*f**5 + 59/5*f**4 + 54/5*f - 5. Determine t so that s(t) = 0.
-3, -1, -1/3
Let w = -55159/20 - -2758. Let q(b) be the third derivative of 0 + 1/8*b**4 + 0*b + 0*b**3 + w*b**5 - 10*b**2. Factor q(k).
3*k*(k + 1)
Let k(u) = 12*u**2 - 20*u - 112. Let o(x) = -x**2 + 3*x + 4. Let q(r) = 2*k(r) + 20*o(r). What is g in q(g) = 0?
-9, 4
Let d be 6/21 + (256/16 - 16). Find o, given that -4/7*o**2 + 2/7*o**3 + 0 + d*o = 0.
0, 1
Factor -16/7*l**2 - l**3 - 4/7*l + 0.
-l*(l + 2)*(7*l + 2)/7
Let v(s) be the second derivative of 25*s**7/42 - 8*s**6 + 125*s**5/4 + 15*s**4/2 - 640*s**3/3 - 240*s**2 + 397*s. Suppose v(t) = 0. What is t?
-1, -2/5, 3, 4
Let t(f) be the third derivative of -f**6/30 - 7*f**5/15 - 5*f**4/2 - 6*f**3 - 3*f**2 + 6. Find q, given that t(q) = 0.
-3, -1
Suppose 0 = 9*t - 11*t + 4. Suppose 9*g**3 + 0*g**4 + 12*g**t + 10*g**5 - 2*g - 12*g**4 - 17*g**3 = 0. Calculate g.
-1, 0, 1/5, 1
Let s(x) be the third derivative of 5*x**8/1008 + 19*x**7/630 + 13*x**6/180 + 7*x**5/90 + x**4/72 - x**3/18 - 15*x**2 + 4*x. Factor s(q).
(q + 1)**4*(5*q - 1)/3
Let h(b) = 4*b**2 + 19*b - 10. Let m(s) = -s**2 + 2. Let l(c) = -h(c) - 5*m(c). Factor l(p).
p*(p - 19)
Let b(s) = s**3 - 7*s**2 + 8*s - 7. Let f be b(6). Suppose -2*z = 6, z + 24 = f*m - 2*z. Factor -12*i - 9*i**m - 11*i**2 - 19*i**2 + 3 + 4 + 17.
-3*(i + 2)**2*(3*i - 2)
What is a in 75 - 724*a**3 + 20*a + 721*a**3 + 127*a + 69*a**2 = 0?
-1, 25
Let z(n) be the first derivative of -8/5*n**2 + 4/25*n**5 - 4/5*n**4 + 8/5*n**3 + 4/5*n - 7. What is o in z(o) = 0?
1
Let a(q) be the first derivative of -2/5*q**5 + 0*q + 23 - 4/3*q**3 + 0*q**2 - 3/2*q**4. Factor a(t).
-2*t**2*(t + 1)*(t + 2)
Let z be (20 - 1834/91)/(1/(-4)). Determine y, given that -z*y + 6/13 + 2/13*y**2 = 0.
1, 3
Let j(q) be the third derivative of -1/135*q**6 + 0 - 4/27*q**3 + 0*q - 1/9*q**4 + 1/18*q**5 - 2*q**2. Factor j(t).
-2*(t - 2)**2*(4*t + 1)/9
Let h be 2618/(-40) + -5 + (-147)/(-28). Let n = h + 66. Solve -n*b + 0 - 2/5*b**2 = 0 for b.
-2, 0
Let t = 29/533 + 4177/1599. Factor t*v**3 + 0 + 4/3*v + 2/3*v**4 + 10/3*v**2.
2*v*(v + 1)**2*(v + 2)/3
Determine v, given that 6*v**5 + 21*v**5 + 718*v**4 + 382*v**3 + 626*v**4 + 22*v**5 - 1162*v**3 + 112*v**2 = 0.
-28, 0, 2/7
Suppose 8/7*a**2 - 10/7*a**3 + 0 + 2/7*a = 0. Calculate a.
-1/5, 0, 1
Suppose 0 + 10/7*s**3 + 32/7*s**2 + 8/7*s - 2*s**4 = 0. What is s?
-1, -2/7, 0, 2
Let b(r) be the first derivative of -r**6/3 - 2*r**5/5 + 7*r**4/2 + 26*r**3/3 + 6*r**2 - 91. Let b(k) = 0. Calculate k.
-2, -1, 0, 3
Let b = 6751/4 + -1644. Let h = b - 43. Find w, given that 0*w**2 + 3/2*w - 3/2*w**3 + h - 3/4*w**4 = 0.
-1, 1
Let y(p) be the first derivative of p**6/33 - 2*p**5/11 - 7*p**4/22 + 10*p**3/33 + 6*p**2/11 + 168. What is v in y(v) = 0?
-1, 0, 1, 6
Suppose x - 9 = -x - s, 3*s - 3 = 2*x. Suppose -2 + 5 - 3 + 2*w**2 - 2*w**x + 4*w = 0. Calculate w.
-1, 0, 2
Let b(d) be the first derivative of d**5/20 + d**4/16 - d**3 - 7*d**2/2 - 4*d - 157. Factor b(k).
(k - 4)*(k + 1)*(k + 2)**2/4
Let n(k) be the first derivative of 36 - 3/2*k**4 - k**2 + 2/5*k**5 + 0*k + 2*k**3. Factor n(h).
2*h*(h - 1)**3
Let k = 490/51 - 152/17. Find z, given that 4/3*z + k*z**2 + 0 = 0.
-2, 0
Let k(b) be the first derivative of 3*b**5/5 + 6*b**4 + 21*b**3 + 33*b**2 + 24*b + 71. Suppose k(s) = 0. Calculate s.
-4, -2, -1
Let a(i) be the third derivative of 7*i**6/360 + 4*i**5/45 - 13*i**4/18 - 8*i**3/9 + 83*i**2 + 1. Factor a(g).
(g - 2)*(g + 4)*(7*g + 2)/3
Let l = -3 - 0. Let t be (3/117)/(185/60 + l). Find w, given that 0 - 2/13*w**2 + t*w = 0.
0, 2
Suppose 0 = 5*d + 7*h - 35, 0 = -d + 6*h - 4*h - 10. Let m be (4/15)/(1/20). Let d*n**3 + m*n + 2/3*n**4 - 4*n**2 - 2 = 0. What is n?
-3, 1
Suppose 1/3*b**4 - 2/3*b - 1/3*b**2 + 0 - 1/3*b**5 + b**3 = 0. Calculate b.
-1, 0, 1, 2
Determine k so that -17*k - 25*k + 2*k**2 - 30 + 68 + 2*k = 0.
1, 19
Let p(d) = d + 3. Let s be p(3). Let o be ((-1)/(-2))/((3/18)/1). Factor s*w**4 - w**4 - 8*w**o - w**4.
4*w**3*(w - 2)
Let h(s) be the second derivative of -s**6/60 - s**5/40 + s**4/6 + s**3/3 + 44*s - 2. Determine r, given that h(r) = 0.
-2, -1, 0, 2
Determine h, given that -9/5*h**5 - 6/5*h + 27/5*h**2 + 0 - 9*h**3 + 33/5*h**4 = 0.
0, 2/3, 1
Factor -22*a - 68*a**3 + 30*a**3 - 38*a + 35*a**3 - 32*a**2 - 36 + 5*a**2.
-3*(a + 1)*(a + 2)*(a + 6)
Let u(m) be the second derivative of 13*m + 0*m**3 + 1/21*m**4 + 0 - 8/7*m**2. Factor u(c).
4*(c - 2)*(c + 2)/7
Let t be (-76)/38*(-61)/56. Let i = 17/7 - t. Factor 0 - i*s**3 + 0*s**2 + 1/4*s.
-s*(s - 1)*(s + 1)/4
Determine k, given that 0*k - 5/6*k**3 + 5/6*k**4 + 0 - 5/3*k**2 = 0.
-1, 0, 2
Find s, given that 1/3*s**2 + s + 2/3 = 0.
-2, -1
Factor -18/11*g + 28/11 + 2/11*g**2.
2*(g - 7)*(g - 2)/11
Determine i, given that -424*i**3 - 4*i**2 - 2*i**4 - 12*i**5 - 8*i**4 + 450*i**3 = 0.
-2, 0, 1/6, 1
Let p be ((-905)/(-362))/(1/2). Factor 2/9*r**p + 2/9*r**4 + 2/9 - 4/9*r**2 + 2/9*r - 4/9*r**3.
2*(r - 1)**2*(r + 1)**3/9
Suppose -13 = -8*p + 3. Factor 3*o**2 - 2*o**2 - 3*o**2 - 30 - 27*o + 5*o**p.
3*(o - 10)*(o + 1)
Let h(d) = d**5 + 16*d**3 - 4. Let q(m) be the second derivative of -3*m**5/4 + 3*m**2/2 - 13*m. Let s(n) = 3*h(n) + 4*q(n). Determine k so that s(k) = 0.
-2, 0, 2
Let p be (-1)/(-6)*-10*(-1386)/990. Factor p*l**3 - 2/3*l + 5/3*l**2 + 0.
l*(l + 1)*(7*l - 2)/3
Let t(v) = -v**3 - 13*v**2 - v - 15. Let w be t(-13). Let x(r) = r**2 + r - 1. Let a(s) = -3*s**2 - 18*s - 17. Let f(l) = w*x(l) + a(l). Factor f(b).
-5*(b + 1)*(b + 3)
Factor 0 + 0*p - 11/5*p**3 - 1/5*p**4 - 2*p**2.
-p**2*(p + 1)*(p + 10)/5
Let r(m) be the second derivative of 1/15*m**6 - 3/10*m**5 + 7*m + 1/2*m**4 + 0 - 1/3*m**3 + 0*m**2. Solve r(t) = 0 for t.
0, 1
Let 54 + 3*u**2 + 1087*u + 0*u**2 - 243 - 1033*u = 0. Calculate u.
-21, 3
Suppose -2*l + 0*l = -8. Suppose 0 = -3*c + 3 + 9. Find w such that w**4 - 4*w + 6*w**2 - l*w**4 + 3*w**c - 2*w**4 = 0.
-2, 0, 1
Let o(g) be the third derivative of -g**10/37800 + g**9/15120 + g**8/2520 + 11*g**5/60 - 9*g**2. Let l(t) be the third derivative of o(t). Factor l(n).
-4*n**2*(n - 2)*(n + 1)
Determine o so that -18/5*o + 0 - 6/5*o**2 + 4/5*o**3 = 0.
-3/2, 0, 3
Solve 194672/15 + 4232/5*a + 92/5*a**2 + 2/15*a**3 = 0.
-46
Let h(s) = s**3 - 13*s**2 + 11*s + 16. Let p be h(12). Let n(r) = -2*r**2 - 143*r - 1015. Let t be n(-8). Factor -t + p*d**2 + 5/2*d**3 + 1/2*d.
(d + 1)**2*(5*d - 2)/2
Let a = 126/19 + -359/57. Let c(x) be the second derivative of 5/2*x**2 + 1/60*x**4 + x - a*x**3 + 0. Suppose c(n) = 0. What is n?
5
Let r(q) be the first derivative of 4*q**6/3 + 28*q**5/5 + 7*q**4 + 8*q**3/3 - 788. Find z, given that r(z) = 0.
-2, -1, -1/2, 0
Let i(z) be the second derivative of -z**5/25 + z**4/5 + 8*z**3/15 - 24*z**2/5 - 61*z. Suppose i(g) = 0. Calculate g.
-2, 2, 3
Let l = 5927/24 - 739/3. Find z, given that -z - 1/8*z**3 + 1/2 + l*z**2 = 0.
1, 2
Let s be (-848)/184 + -3*(-15)/9. Let i = -53/253 + s. Solve -10/11*a - 10/11*a**5 + i - 4/11*a**2 + 2/11*a**4 + 20/11*a**3 = 0.
-1, 1/5, 1
Determine m so that -3*m**4 - 520*m**5 - 6*m**3 + 4*m - 12*m**2 - 3*m**4 + 521*m**5 + 19*m**3 = 0.
0, 1, 2
Let n(s) = -s + 1. Let a(d) = -36*d**2 + 26*d - 6. Suppose -y + 15 = -5*x, -4*x + 6*y - 23 = 3*y. Let m(z) = x*n(z) - a(z). Determine k so that m(k) = 0.
1/3
Factor q - 6*q**2 + q - 14*q + 4*q**2 + 8*q**3 - 2*q**4.
-2*q*(q - 3)*(q - 2)*(q + 1)
Solve 20/3*y**2 - 12 + 148/3*y**3 - 148/3*y + 16/3*y**4 = 0.
-9, -1, -1/4, 1
Let v = -60 + 64. Let d(k) be the first derivative of -12/5*k**5 - 9/2*k**v - 4*k**3 + 1 - 1/2*k**6 + 0*k - 3/2*k**2. Solve d(o) = 0.
-1, 0
Factor 9/2*g + 1/2*g**3 + 3*g**2 + 2.
(g + 1)**2*(g + 4)/2
Let