 p(z) be the third derivative of 0*z**4 + 2/135*z**5 + 0*z**3 - 71*z**2 - 4/945*z**7 + 0 + 1/540*z**6 + 0*z - 1/1512*z**8. Suppose p(x) = 0. Calculate x.
-4, -1, 0, 1
Let d(p) be the first derivative of -p**4/26 - 16*p**3/3 - 2365*p**2/13 + 36300*p/13 + 1964. Determine y, given that d(y) = 0.
-55, 6
Determine a so that 4155*a**2 + 957*a + 8*a**4 + 2475*a**3 - 563 + 68*a - 8*a**4 + 35*a**4 - 127 = 0.
-69, -1, 2/7
Let f(h) be the first derivative of -104 + 108/11*h + 2/55*h**5 + 1/2*h**4 + 30/11*h**3 + 81/11*h**2. Let f(y) = 0. What is y?
-3, -2
Let o(z) be the second derivative of 5/72*z**4 - 15*z + 25/6*z**2 + 1 - 35/36*z**3. Factor o(i).
5*(i - 5)*(i - 2)/6
Let q(g) be the third derivative of g**8/112 + 131*g**7/280 - 169*g**6/160 + 17*g**5/40 - 740*g**2. Let q(t) = 0. Calculate t.
-34, 0, 1/4, 1
Let z(m) be the third derivative of m**8/23520 - m**7/8820 - m**4/12 + 9*m**3 + 7*m**2 - 1. Let d(a) be the second derivative of z(a). Solve d(w) = 0.
0, 1
Suppose 562933*k = 562910*k. Find o, given that -o**4 - 3/2*o + k - 1/2*o**5 + o**2 + 2*o**3 = 0.
-3, -1, 0, 1
Let i be 42090/(-1610) - (-81)/3. Find b, given that 0*b**3 + 0 + 3/7*b - i*b**4 + 6/7*b**2 - 3/7*b**5 = 0.
-1, 0, 1
Suppose 14*l + 14 = 4*s + 15*l, -2*s + 16 = -4*l. Determine i, given that -3*i - 2 - 2*i + 4*i**s - 3*i - 8*i**3 - 12*i**2 - 4*i**4 - 2*i**4 = 0.
-1
Let j(t) be the first derivative of 15 + 33*t + 1/9*t**4 + 338/3*t**2 + 52/9*t**3. Let n(q) be the first derivative of j(q). Let n(y) = 0. What is y?
-13
Suppose 0 = -5*z + 2*n, 51*n - 55*n = -2*z - 16. Suppose -t**3 - 6*t**2 + 0*t**2 + 2*t**2 - 11*t**z + t**4 + 19*t - 2*t**3 + 30 = 0. What is t?
-3, -1, 2, 5
Let x(p) be the first derivative of 0*p - 81 + 4/25*p**5 - 4/5*p**4 + 8/5*p**2 - 4/15*p**3. Let x(m) = 0. Calculate m.
-1, 0, 1, 4
Let b(u) be the third derivative of 48*u**2 - 1/90*u**5 + 0*u - 64/9*u**3 + 0 + 4/9*u**4. Factor b(o).
-2*(o - 8)**2/3
Suppose 0 = f - 4*o - 5, 4*f - 5*o = -3*o + 62. Factor -f + 6*q + 17 - 32*q**2 + 26*q**3.
2*q*(q - 1)*(13*q - 3)
Let m be ((-12)/(-78))/(120/65). Let w(a) be the second derivative of 9*a + 0 + m*a**4 - 4/3*a**3 + 8*a**2. Suppose w(o) = 0. What is o?
4
Let b(g) = -g**3 + 4*g**2 - 53*g + 393. Let y be b(6). Determine m, given that 111/2*m**y + 9/2*m**4 + 82*m + 113*m**2 + 20 = 0.
-10, -1, -2/3
Let c(m) = -10*m**2 + 192*m + 922. Let h(x) = -4*x**2 + 63*x + 307. Let k(n) = -3*c(n) + 8*h(n). What is z in k(z) = 0?
-31, -5
Let o(n) be the second derivative of n**8/560 + 2*n**7/175 - 3*n**6/50 + 247*n**2/2 - 21*n - 1. Let f(q) be the first derivative of o(q). Factor f(w).
3*w**3*(w - 2)*(w + 6)/5
Let p(c) be the first derivative of -1/8*c**3 + 2*c - 11/8*c**2 + 72. Factor p(g).
-(g + 8)*(3*g - 2)/8
Let s(v) = 3*v**2 + 2*v + 1. Let d be s(-1). Factor 67*f**d + 8109 + 6471 + 540*f - 62*f**2.
5*(f + 54)**2
Let b(y) be the third derivative of y**5/180 + 13*y**4/72 - 5*y**3 + 6*y**2 - 42*y. Factor b(g).
(g - 5)*(g + 18)/3
Let n(y) be the second derivative of y**4/36 - 265*y**3/9 + 70225*y**2/6 + 412*y. Factor n(h).
(h - 265)**2/3
Let m(a) be the first derivative of 0*a + 8*a**3 + 1/3*a**6 + 7*a**4 + 8/3*a**2 + 38/15*a**5 - 49. Factor m(s).
2*s*(s + 2)**3*(3*s + 1)/3
Let q(u) be the second derivative of -2/5*u**5 - 7*u**3 + 4*u**2 + 7/2*u**4 + 0 + 39*u. Factor q(r).
-2*(r - 4)*(r - 1)*(4*r - 1)
Let h(z) = -4*z**4 - 30*z**3 + 25*z**2 + 17*z - 21. Let j(f) = -f**4 - 7*f**3 + 6*f**2 + 4*f - 5. Let l(x) = 3*h(x) - 13*j(x). Suppose l(r) = 0. What is r?
-2, -1, 1
Let u(h) be the third derivative of h**7/350 + 29*h**6/25 + 461*h**5/100 + 23*h**4/4 - h**2 - 195*h + 2. Factor u(s).
3*s*(s + 1)**2*(s + 230)/5
Let t = 185/5016 - -1/209. Let v(s) be the third derivative of 0*s + 0*s**3 + 12*s**2 + 0*s**4 - 1/12*s**5 - t*s**6 + 0. Factor v(n).
-5*n**2*(n + 1)
Let x = 900112/5 + -180022. What is z in 0*z + 0 + 2*z**3 + 0*z**2 - x*z**4 = 0?
0, 5
Factor 41*h + 100*h - 9*h**2 + 18*h**2 + 375*h - 13*h**2.
-4*h*(h - 129)
Let a(q) = -420*q**3 - 933*q**2 - 426*q - 21. Let k(w) = 60*w**3 + 133*w**2 + 61*w + 3. Let i(r) = 5*a(r) + 36*k(r). Factor i(p).
3*(p + 1)**2*(20*p + 1)
Let d be (-78848)/(-32256)*6/11. Factor 1/3*r**3 + 4/3*r**2 + 0 + d*r.
r*(r + 2)**2/3
Let h(z) be the second derivative of 25/8*z**4 - 81*z - 1/56*z**7 - 2 + 4/15*z**6 - 4*z**2 - 23/16*z**5 - 4/3*z**3. Let h(w) = 0. What is w?
-1/3, 1, 2, 4
Let s(k) = 9*k**2 - 21*k + 17. Let t(c) = -8*c**2 + 20*c - 15. Let f(n) = -5*s(n) - 6*t(n). Let y be f(5). Solve 0*v - 5/4*v**2 + y = 0.
-2, 2
Let r(n) be the second derivative of n**6/15 - 17*n**5/10 - 19*n**4/3 + 121*n - 5. Let r(j) = 0. What is j?
-2, 0, 19
Let u(n) be the first derivative of n**3/3 + 55*n**2 - 111*n + 80. Factor u(d).
(d - 1)*(d + 111)
Let b(i) be the second derivative of -i + 0*i**2 - 193/190*i**5 + 52/19*i**4 - 48/19*i**3 + 0 - 1/399*i**7 + 26/285*i**6. Let b(x) = 0. Calculate x.
0, 1, 12
Factor 0 + 6*b - 2/7*b**2.
-2*b*(b - 21)/7
Suppose -2*x = 4*k + 2*x - 100, 5*k + 2*x - 125 = 0. Factor k*w + 5*w**4 - 130*w**2 + 15*w**3 + 210*w**2 - 125*w**2.
5*w*(w - 1)**2*(w + 5)
Let j(s) be the third derivative of s**5/600 + s**4/20 - 3*s**3/4 + 2*s**2 - 157. Find v, given that j(v) = 0.
-15, 3
Let u(b) be the first derivative of -2*b**5/15 + b**4/2 - 4*b**3/9 + 4083. Factor u(n).
-2*n**2*(n - 2)*(n - 1)/3
Suppose 9 + 6 = 3*x. Suppose 15 = 3*j + v, -x*j = -2*j - 2*v - 6. Factor 7*i + 4*i**3 - i**4 - 3*i**j - 7*i.
-4*i**3*(i - 1)
Let v(n) be the third derivative of n**7/8820 - n**6/2520 - n**5/70 + n**4/12 + 11*n**3/6 + 61*n**2 - 2. Let h(j) be the second derivative of v(j). Factor h(r).
2*(r - 3)*(r + 2)/7
Let b(a) be the third derivative of -a**6/540 + a**5/10 - 47*a**4/108 - 25*a**3/9 + 3061*a**2. Factor b(k).
-2*(k - 25)*(k - 3)*(k + 1)/9
Find u, given that -580/7*u**4 - 12/7*u**5 + 0 + 28*u**2 + 396/7*u**3 + 0*u = 0.
-49, -1/3, 0, 1
Let a(r) = -35*r**3 + 223*r**2 + 1182*r + 1440. Let s(k) = 16*k**3 + k**2. Let m(l) = -a(l) - 2*s(l). Factor m(d).
3*(d - 80)*(d + 2)*(d + 3)
Factor 0 + 2/7*i**5 - 30/7*i**3 + 16/7*i**2 + 0*i + 12/7*i**4.
2*i**2*(i - 1)**2*(i + 8)/7
Let j(a) be the third derivative of -19/22*a**4 + 2*a + 1/110*a**5 + 27*a**2 + 361/11*a**3 + 0. Factor j(b).
6*(b - 19)**2/11
Let k(v) = -3*v**2 - 65*v - 197. Let b be k(-18). Let u be 0/b + (-2)/((-72)/675). Factor -u*q**4 - 33*q**2 + 0 + 6*q + 105/2*q**3.
-3*q*(q - 2)*(5*q - 2)**2/4
Let f be 39/(-6)*2 - 4. Let z = 19 + f. Let 21*d**3 + z*d**3 - 4*d**4 - 3*d**4 + 0*d - 20*d**2 + 4*d = 0. Calculate d.
0, 2/7, 1, 2
Let p(h) be the second derivative of -7*h**7/24 + 63*h**6/40 - 27*h**5/16 + 9*h**4/16 - 483*h - 1. Factor p(y).
-y**2*(y - 3)*(7*y - 3)**2/4
Let t(l) be the third derivative of -l**8/1680 - l**7/90 - l**6/30 - l**4/12 - 26*l**3/3 - 251*l**2. Let k(z) be the second derivative of t(z). Factor k(m).
-4*m*(m + 1)*(m + 6)
Suppose 0 = -3*t + 5*d + 32, -t - 5*d - 16 = -0*t. Suppose 3 + 9 = t*z. Solve 8 + 3*q + 4*q + z*q - 2*q**2 - 4*q = 0 for q.
-1, 4
Factor 0*k + 4*k**2 + 90/7*k**4 + 0 - 118/7*k**3.
2*k**2*(k - 1)*(45*k - 14)/7
Let t(u) = 14*u**4 - 78*u**3 - 332*u**2 - 252*u. Let c(x) = -10*x**4 + 78*x**3 + 334*x**2 + 254*x. Let z(i) = -3*c(i) - 2*t(i). Factor z(g).
2*g*(g - 43)*(g + 1)*(g + 3)
Let u = -3182 + 3184. Let x(p) be the third derivative of 5/24*p**4 - 1/12*p**5 + 3*p**u + 0 - 1/24*p**6 + 0*p + 5/6*p**3. Factor x(v).
-5*(v - 1)*(v + 1)**2
Factor -2/9*z**2 - 88/3 - 74/9*z.
-2*(z + 4)*(z + 33)/9
Let f(a) be the first derivative of 3*a**5/20 + 7*a**4/16 - 3*a**3 + 5*a**2/2 + 5086. Factor f(l).
l*(l - 2)*(l + 5)*(3*l - 2)/4
Let r(f) be the first derivative of -5*f**4/4 + 415*f**3/3 + 425*f**2 + 3038. Factor r(l).
-5*l*(l - 85)*(l + 2)
Let t(n) = -n**3 + 20*n**2 - 36*n + 2. Let w be t(18). Suppose w*c - 2 = c. Factor -3*r**c + r**2 + r**2 - 5*r + r**3 + 6 - r**2.
(r - 3)*(r - 1)*(r + 2)
Let t(h) = 44*h**2 - 22*h + 8. Let x(y) = 29*y**2 - 15*y + 5. Let l(o) = -5*t(o) + 8*x(o). Let s(k) = -13*k**2 + 13*k. Let d(v) = -3*l(v) - 2*s(v). Factor d(z).
-2*z*(5*z - 2)
Let a = 268263/7 - 38317. Let -a*z + 24/7 + 0*z**2 + 4/7*z**5 + 40/7*z**3 - 24/7*z**4 = 0. Calculate z.
-1, 1, 2, 3
What is v in -755/4*v + 0 - 1/4*v**2 = 0?
-755, 0
Suppose 0 = -22*w + 444 + 18. Suppose -w*k = -13*k - 16. Factor 0 + 6/7*q**k - 3/7*q - 3/7*q**3.
