105*p**6 + 1/21*p**3. Find k, given that h(k) = 0.
-2, -1, 1, 3
Suppose -172*d + 42 + 97 + 205 = 0. Let h(s) be the first derivative of -5/24*s**4 - 1/36*s**6 - 2/15*s**5 + 0*s**d + 4 - 1/9*s**3 + 0*s. What is t in h(t) = 0?
-2, -1, 0
Let t(m) be the first derivative of -m**4/36 - m**3/6 - m**2/3 + 45*m + 57. Let b(o) be the first derivative of t(o). Determine z, given that b(z) = 0.
-2, -1
Let j(u) be the second derivative of -137*u**4/8 - u**3/6 + 511*u - 1. Let j(z) = 0. Calculate z.
-2/411, 0
Let s be (42/(-35))/(57/(-190))*(-3 - (-60)/16). Suppose 10*a + 25/2*a**s + 0 + 30*a**2 = 0. Calculate a.
-2, -2/5, 0
Let o(z) = -4*z - 37. Let y be o(-11). Suppose 5*c = 5, 2*c = 4*k - y*k + 47. Solve 7*r**2 + k*r**3 + 2*r**2 + 5*r**2 - 4 + 5*r**2 = 0.
-1, -2/3, 2/5
Let i(l) be the second derivative of -2 + 4/7*l**3 + 21*l + 1/42*l**4 + 20/7*l**2. Factor i(t).
2*(t + 2)*(t + 10)/7
Suppose 0 = -41*u + 30*u + 132. Suppose 3 + 0 = j. Let -15*n**3 - 16*n**j + 22*n + 33*n**3 - 12*n**2 - u = 0. What is n?
1, 2, 3
Let i(n) be the second derivative of 1/80*n**5 - 1/12*n**4 - 2 + 30*n - 1/6*n**3 + 2*n**2. Determine w so that i(w) = 0.
-2, 2, 4
Let z(x) be the third derivative of -x**5/240 - 119*x**4/48 + 239*x**3/24 - 744*x**2 - 2. Let z(k) = 0. Calculate k.
-239, 1
Factor -9*b**2 - 3*b + 12 + 3/4*b**4 - 3/4*b**3.
3*(b - 4)*(b - 1)*(b + 2)**2/4
Factor -4/3*y**4 - 3*y + 4*y**2 + 2/3*y**3 - 1/3*y**5 + 0.
-y*(y - 1)**2*(y + 3)**2/3
Let y(g) be the first derivative of g**4/8 - 49*g**3/6 + 12*g**2 + 1363. Factor y(f).
f*(f - 48)*(f - 1)/2
Let z(d) = 0*d + d**3 - 16*d + 9*d + 20 + 8*d**2. Let s be z(-9). Determine t so that 3*t**2 + 50*t + 125 + 6*t**s + 3*t**2 - 7*t**2 = 0.
-5
Let h = -213/37 - -2806/481. Let g(r) be the first derivative of -6/13*r**4 - 1/13*r**6 + 7 - 4/13*r**3 + 0*r - h*r**2 - 4/13*r**5. Suppose g(v) = 0. What is v?
-1, -1/3, 0
Let n = -402 - -406. Suppose -3*b + 4*b - 3 = 0. Factor 4*x**2 - x**3 + 3*x**b - 2*x**5 + 4*x**n - 6*x**2 - 2*x**4.
-2*x**2*(x - 1)**2*(x + 1)
Let f(c) = 4*c**3 + 664*c**2 - 1316*c - 4. Let a(h) = -10*h**3 - 1993*h**2 + 3949*h + 11. Let p(x) = 4*a(x) + 11*f(x). Factor p(g).
4*g*(g - 165)*(g - 2)
Let a be 177/5 - (-1417 - -1452). Solve -8/5*v**3 + 3/5*v**4 + 0*v + a*v**5 + 3/5*v**2 + 0 = 0 for v.
-3, 0, 1/2, 1
Let l be 6*(-1 - ((-21)/9 + 0)). Suppose -v - 1 = -2*q, l + 0 = q + 2*v. Suppose -24*w**2 - 11*w + 10 + 15*w**q - 10*w + 21*w**3 - 1 = 0. Calculate w.
-1, 3/7, 1
Factor -52*r**4 + 0 + 372/7*r**3 + 120/7*r**5 + 4/7*r - 132/7*r**2.
4*r*(r - 1)**3*(30*r - 1)/7
Factor -5694*f - 8099716 + 986*f**2 - 495*f**2 - 5690*f - 495*f**2.
-4*(f + 1423)**2
Factor 75*a**2 + a**3 - a**4 + 88*a**2 + a**3 - 2*a + 1 - 163*a**2.
-(a - 1)**3*(a + 1)
Let d be 148/36 - ((-872)/(-72) - 12). Let i(o) = o**3 + 6*o**2 - 3*o - 8. Let t be i(-6). Find b, given that 2/5*b**2 + d*b + t = 0.
-5
Factor 12/7*j**3 + 15 - 198/7*j + 81/7*j**2.
3*(j - 1)**2*(4*j + 35)/7
Let v(y) be the third derivative of y**8/161280 + y**7/8064 + y**6/1440 + 133*y**5/60 - 42*y**2 - 1. Let u(b) be the third derivative of v(b). Factor u(s).
(s + 1)*(s + 4)/8
Let l(s) be the first derivative of 17*s**5/5 + s**4/3 - 172*s - 13. Let p(w) be the first derivative of l(w). Suppose p(c) = 0. Calculate c.
-1/17, 0
Let j(o) be the third derivative of -11*o**2 - 7/240*o**4 - 1/600*o**5 + 3*o - 1/5*o**3 + 0. Factor j(t).
-(t + 3)*(t + 4)/10
Let y(d) = 14*d**2 - 38*d + 6. Let c(t) be the first derivative of -t**3/3 - t**2/2 - t - 3. Let q(s) = 2*c(s) - y(s). Solve q(j) = 0 for j.
1/4, 2
Let a(v) be the third derivative of -v**9/25200 + v**7/600 + v**6/200 + 23*v**4/8 - 97*v**2. Let k(o) be the second derivative of a(o). Factor k(n).
-3*n*(n - 3)*(n + 1)*(n + 2)/5
Let n(l) be the third derivative of -1/60*l**6 + 13/12*l**4 - 2/5*l**5 - l**2 + 0*l - 4 + 0*l**3. Factor n(q).
-2*q*(q - 1)*(q + 13)
Let k(t) = 7068*t - 325128. Let b be k(46). What is d in 0 - 52/7*d**2 - 8*d**3 - 4/7*d**4 + b*d = 0?
-13, -1, 0
Let s(f) be the first derivative of 2*f**5/15 - 8*f**4/3 + 18*f**3 - 42*f**2 - 6413. Factor s(k).
2*k*(k - 7)*(k - 6)*(k - 3)/3
Let r(u) = u**2 + u + 8. Let y(v) = 2*v**2 + 7*v + 28. Let m(x) = -x**2 - 7*x - 23. Let o(a) = 3*m(a) + 4*y(a). Let n(w) = -4*o(w) + 22*r(w). Factor n(l).
2*(l - 2)*(l - 1)
Let a(p) be the third derivative of p**5/80 - 255*p**4/16 - 511*p**3/8 - 64*p**2. Factor a(m).
3*(m - 511)*(m + 1)/4
Let m(b) be the third derivative of b**6/200 - 2*b**5/25 + b**4/8 - 35*b**3/3 + 73*b**2. Let z(g) be the first derivative of m(g). What is r in z(r) = 0?
1/3, 5
Let p(g) = -4 - 22*g - g**2 - 4 - 95 - 18. Let j(m) = -22*m + m**2 + m**2 - 121 - 3*m**2. Let t(x) = -5*j(x) + 4*p(x). Factor t(z).
(z + 11)**2
Let h be (-15)/2*(-79)/395*2. Let n = -198 + 599/3. Factor -n*w**h - 25/3*w**2 - 35/3*w - 5.
-5*(w + 1)**2*(w + 3)/3
Suppose -2/7*p**5 - 20/7*p**4 - 274/7*p + 36 - 232/7*p**2 + 276/7*p**3 = 0. Calculate p.
-18, -1, 1, 7
Suppose 0 = -16*z - 2*z + 19*z - 22*z. Let c(y) be the third derivative of 0*y**3 + 0 + 1/840*y**6 - 1/105*y**5 - 23*y**2 + z*y - 5/168*y**4. Factor c(i).
i*(i - 5)*(i + 1)/7
Factor 6*n**2 + 1456 + 3*n**2 - 4*n**2 - 14*n**2 - 4*n + 7*n**2.
-2*(n - 26)*(n + 28)
Suppose 1867*x = -96*x + 11778. Factor -x*f**2 - 36*f - 1/3*f**3 - 72.
-(f + 6)**3/3
Let x(i) be the first derivative of 9*i**5/5 + 219*i**4/8 + 93*i**3 - 669*i**2/4 - 63*i - 2043. Solve x(l) = 0.
-7, -6, -1/6, 1
Let x(v) be the first derivative of v**3/6 + 41*v**2 + 3362*v + 1273. Factor x(r).
(r + 82)**2/2
Determine p, given that -2*p**2 - 62/13*p - 36/13 = 0.
-18/13, -1
Let y(f) be the second derivative of -5*f**4/12 + 1120*f**3 - 1128960*f**2 + 391*f - 1. Factor y(u).
-5*(u - 672)**2
Let c = 50337/2 - 25167. What is n in -3/2*n**5 - c*n**4 + 6*n**3 + 0 + 6*n**2 + 0*n = 0?
-2, -1, 0, 2
Let h(c) be the third derivative of -c**8/448 + 3*c**7/70 + 13*c**6/160 - 2*c**2 + 10*c - 70. Factor h(y).
-3*y**3*(y - 13)*(y + 1)/4
Let k(y) = -y**3 + 854*y**2 - 180593*y - 364658. Let p(t) = 3*t**3 - 2563*t**2 + 541765*t + 1093974. Let n(g) = -21*k(g) - 6*p(g). Factor n(w).
3*(w - 427)**2*(w + 2)
Factor 5*n**2 + 479 + 281 + 1080*n + 315.
5*(n + 1)*(n + 215)
Let w(k) be the first derivative of -5/12*k**4 + 15*k**2 - 8*k - 13 - 5/6*k**3. Let l(c) be the first derivative of w(c). Solve l(u) = 0.
-3, 2
Determine g, given that 73528*g + 5*g**3 + 38 - 73511*g - 26*g**2 + 6 - 6*g**2 + 10 = 0.
-1, 2, 27/5
Let q = -34 - -51. What is n in 80*n**2 - 83*n**2 + q*n + 4*n = 0?
0, 7
Let x(t) be the first derivative of t**5/20 - 3*t**4/4 - 8*t**3 - t**2 - 26*t - 24. Let q(b) be the second derivative of x(b). Factor q(k).
3*(k - 8)*(k + 2)
Let c = 1509 - 1507. Let x(j) be the third derivative of 0 - 4/45*j**5 + 0*j + 4/9*j**3 + 6*j**c - 1/30*j**6 + 5/18*j**4. Factor x(m).
-4*(m - 1)*(m + 2)*(3*m + 1)/3
Let a(t) = t**2 - 12*t - 589. Let g be a(31). Let d(b) be the third derivative of 17*b**2 + 0*b**3 + g*b + 1/12*b**6 - 1/48*b**5 + 0*b**4 + 0. Factor d(s).
5*s**2*(8*s - 1)/4
Let n(a) be the second derivative of 1/3*a**4 + 10/3*a**3 - 2*a + 0*a**2 + 2. Factor n(q).
4*q*(q + 5)
Let o(p) = -6*p**2 - 1200*p - 2121. Let a(y) = 3*y**2 + 604*y + 1060. Let f(w) = 15*a(w) + 8*o(w). Factor f(r).
-3*(r + 2)*(r + 178)
Factor -2/5*b**2 - 1212 - 6062/5*b.
-2*(b + 1)*(b + 3030)/5
Suppose -100*p + 812 = 512. Find k, given that -1/2*k**5 + 1/2*k**2 - 1/2*k**4 + 0*k + 1/2*k**p + 0 = 0.
-1, 0, 1
Let s(g) = 5*g**3 - g**2 - g + 3. Let a(q) = -5*q**4 + 70*q**3 + 325*q**2 + 225*q - 15. Let p(f) = -a(f) - 5*s(f). Factor p(k).
5*k*(k - 22)*(k + 1)*(k + 2)
Let l(d) = 27*d**3 + 36*d**2 - 45*d + 15. Suppose -22*n + 4 = -26*n. Let w(i) = i**3 - i**2 - i - 1. Let y(a) = n*l(a) - 3*w(a). Let y(b) = 0. What is b?
-2, 2/5, 1/2
Factor -1992/7 + 2004/7*y - 510/7*y**2 + 3/7*y**3.
3*(y - 166)*(y - 2)**2/7
Let z(b) be the first derivative of b**6/4 - 7*b**5/2 + 97*b**4/8 + 67*b**3/6 - 114*b**2 + 126*b - 658. Solve z(i) = 0 for i.
-2, 2/3, 3, 7
Let l(o) be the third derivative of 50*o**2 - 1/14*o**7 - 5/84*o**8 + 0*o**3 + 0*o + 0 - 5/6*o**4 + 17/24*o**6 + o**5. Solve l(s) = 0.
-2, -1, 0, 1/4, 2
Let x = 93346/5 + -373349/20. Determine c so that x*c**2 - 3/4 - c = 0.
-3/7, 1
Let -130/3*r**3 - 18*r + 4/3 + 46*r**2 + 14*r**4 = 0. Calculate r.
2/21, 1
Let v = 1275 + -1272. 