et w be ((-4)/(-7))/(c - (-51)/21). Let -4/3*a**2 + 0*a - 1/3*a**4 + 0 + w*a**3 = 0. What is a?
0, 2
Let z(s) be the second derivative of 9*s + 0 + 2/21*s**3 - 1/35*s**5 + 4/7*s**2 - 2/21*s**4. Factor z(y).
-4*(y - 1)*(y + 1)*(y + 2)/7
Let s = 52226 + -52222. Factor 8/5*v**s + 4/5*v**2 + 0*v + 0 - 2*v**3 - 2/5*v**5.
-2*v**2*(v - 2)*(v - 1)**2/5
Suppose -47 = -3*t + 2*t - n, 3*n + 223 = 4*t. Let s be 6/39 + 148/t. Factor 2/9*g + 0 - 2/9*g**2 + 2/9*g**4 - 2/9*g**s.
2*g*(g - 1)**2*(g + 1)/9
Solve 2/3*n**3 + 10 - 58/3*n + 26/3*n**2 = 0 for n.
-15, 1
Let v(l) be the first derivative of -3*l**5/5 - 39*l**4/4 - 22*l**3 - 95. Find d, given that v(d) = 0.
-11, -2, 0
Let k(m) = -66*m**2 + 117*m - 51. Let o(v) be the first derivative of -5*v**3/3 + 9*v**2/2 - 4*v + 4. Let z(h) = 2*k(h) - 27*o(h). Factor z(w).
3*(w - 2)*(w - 1)
Let g(s) = -5*s**2 - 212*s - 76. Let u be g(-42). Let b(p) be the first derivative of -p + p**2 + u - 1/3*p**3. Factor b(y).
-(y - 1)**2
Let k(d) be the second derivative of 0*d**2 - 3*d - 2/21*d**3 + 1/70*d**5 + 0 + 1/42*d**4. Factor k(p).
2*p*(p - 1)*(p + 2)/7
Let t(u) be the first derivative of 1/16*u**4 + 1/4*u + 28 - 1/12*u**3 - 1/8*u**2. Factor t(l).
(l - 1)**2*(l + 1)/4
Let t(v) be the second derivative of -v**4/4 + 9*v**3/7 - 12*v**2/7 + 103*v. Factor t(u).
-3*(u - 2)*(7*u - 4)/7
Let r(t) = -t**4 - t**3 + t**2 + t + 1. Let n(o) = -7*o**5 + 13*o**4 + 2*o**3 - 4*o**2 - 4*o - 4. Let p(z) = n(z) + 4*r(z). Determine l, given that p(l) = 0.
0, 2/7, 1
Let l(t) = -6*t**4 + 6*t**3 - 15*t + 3. Let o be (-2)/14 - 1/(21/(-24)). Let p(s) = s**4 + s**3 + s - 1. Let b(n) = o*l(n) + 3*p(n). Factor b(z).
-3*z*(z - 2)**2*(z + 1)
Let q = 5122 + -10217/2. Factor q*t**5 + 8 + 225/2*t**3 - 189/2*t**4 + 68*t + 361/2*t**2.
(t - 4)**2*(3*t + 1)**3/2
Let r(o) be the second derivative of 25*o**7/42 - 13*o**6/6 + 3*o**5/2 + o - 7. Factor r(k).
5*k**3*(k - 2)*(5*k - 3)
Let m be (-1 - 0)/(1883/(-2646) - (-10)/(-135)). What is b in -24/11 - 32/11*b - m*b**2 - 2/11*b**3 = 0?
-3, -2
Determine o, given that 4*o**4 + 17*o**3 + 23*o**3 + 122*o - 2639 - 124*o**2 + 2599 - 2*o**5 = 0.
-5, 1, 4
Let a(u) be the first derivative of -u**6/4 - 39*u**5/10 - 15*u**4 - 18*u**3 + 96. What is w in a(w) = 0?
-9, -2, 0
Let k(l) be the third derivative of l**8/168 - l**7/210 - l**6/20 + 7*l**5/60 - l**4/12 - 61*l**2. Factor k(m).
m*(m - 1)**2*(m + 2)*(2*m - 1)
Let f(r) be the second derivative of r**6/15 + r**5/5 - r**4/6 - 2*r**3/3 + 3*r - 11. Factor f(y).
2*y*(y - 1)*(y + 1)*(y + 2)
Let w = -791 - -110741/140. Let k(z) be the third derivative of 0*z**3 + 1/120*z**5 - 1/80*z**6 - 2*z**2 + w*z**7 + 0*z**4 + 0 - 1/672*z**8 + 0*z. Factor k(t).
-t**2*(t - 1)**3/2
Let h be 1*(6 + (-1)/1). Find f, given that -11 - f**3 + 5*f**3 - 16*f + 4*f**2 - h = 0.
-2, -1, 2
Let a(f) be the third derivative of 2*f**7/735 + 17*f**6/210 + 31*f**5/105 + 5*f**4/14 + 32*f**2 - 3. Solve a(u) = 0.
-15, -1, 0
Factor -211*l**2 + 227*l + 172 + 160*l**3 - 7*l**4 + 354*l**2 + 3*l**4 + 285*l + 361*l**2.
-4*(l - 43)*(l + 1)**3
Factor 3/2*h**2 + 27/2*h + 27.
3*(h + 3)*(h + 6)/2
Let d(u) = 4*u**2 + 132*u + 1804. Let g(c) = 21*c**2 + 666*c + 9022. Let b(s) = 11*d(s) - 2*g(s). Determine q, given that b(q) = 0.
-30
Let c(x) be the first derivative of 7*x**3 - 7 + 9*x**2 + 3*x**4 + 27/40*x**5 + 1/16*x**6 + 6*x. Factor c(h).
3*(h + 1)*(h + 2)**4/8
Let p(w) = -9*w + 82. Let d(a) = 3*a - 27. Let f(n) = -8*d(n) - 3*p(n). Let i be f(11). Let 12/5*u - 4*u**i - 26/5*u**2 + 5*u**4 + 9/5 = 0. What is u?
-3/5, 1
Let s(q) be the second derivative of -q**5/20 - q**4/6 + q**3/6 + q**2/2 - 7*q. Let w be s(-3). Factor 4*x**4 - 6*x**2 + 12*x**3 + 7*x**2 + w*x**2.
4*x**2*(x + 1)*(x + 2)
Suppose -2*u - 3*u - 40 = 0. Let r be ((-15)/(-20))/((-2)/u). Factor 3*q**2 - 7*q - 2*q + 6*q**2 - 3*q**3 + r.
-3*(q - 1)**3
Let s(k) be the third derivative of k**7/1365 + k**6/390 + k**5/390 + 16*k**2 - 16. Factor s(c).
2*c**2*(c + 1)**2/13
Let r be 5/(-15) - 22/(-3). What is k in 17*k**2 + 55*k**5 - 3 - 6*k**5 - 21*k**4 + 24*k + 0 - 73*k**3 + r = 0?
-1, -2/7, 1
Let t(n) = -n + 13. Let q be t(9). Suppose 0*a**4 + a**q + 2*a**2 + 2*a - 5*a**2 - 4*a = 0. What is a?
-1, 0, 2
Let x be 4/(-84)*35 - (-62)/21. Determine s so that -3/7*s**4 + 3/7*s - 9/7*s**2 + 0 + x*s**3 = 0.
0, 1
Let j be ((0 - -7) + -7)/(-4). Let q(r) = 11*r + 2. Let v be q(j). Factor 0 + 1/2*s**3 - 1/2*s + 1/4*s**4 - 1/4*s**v.
s*(s - 1)*(s + 1)*(s + 2)/4
Let b(f) = -5*f**2 - 120*f + 3719. Let q(u) = 18*u**2 + 359*u - 11156. Let j(v) = 7*b(v) + 2*q(v). Factor j(y).
(y - 61)**2
Suppose 10*o = 8*o + 40. Suppose 2*m - o = -2*m. Let -16/7*l**4 - 76/7*l**2 + 2/7*l**m - 16/7 + 8*l + 50/7*l**3 = 0. Calculate l.
1, 2
Let a(f) be the first derivative of -4*f**5/5 - 14*f**4 + 4*f**3 + 80*f**2 - 112*f - 120. Factor a(h).
-4*(h - 1)**2*(h + 2)*(h + 14)
Let n(v) be the first derivative of v**8/1680 + 2*v**7/525 + v**6/200 + 11*v**2/2 + 11. Let u(l) be the second derivative of n(l). What is p in u(p) = 0?
-3, -1, 0
Let z(x) be the first derivative of -4*x**3/21 + 568*x**2/7 - 80656*x/7 + 51. Find a such that z(a) = 0.
142
Let s(r) be the third derivative of 3*r**8/112 + 11*r**7/35 + 47*r**6/40 + 3*r**5/5 - 9*r**4/2 - 286*r**2. Suppose s(d) = 0. Calculate d.
-3, -2, 0, 2/3
Let u = 3357/2 + -1678. Solve 1/3*p + u*p**2 - 3/2*p**3 + 1/2*p**5 + 1/6*p**4 + 0 = 0 for p.
-2, -1/3, 0, 1
Let p(z) be the third derivative of -z**8/1848 - 19*z**7/1155 - 12*z**6/55 - 272*z**5/165 - 256*z**4/33 - 256*z**3/11 + 82*z**2. Factor p(w).
-2*(w + 3)*(w + 4)**4/11
Let d(j) be the first derivative of -j**5/5 - 157*j**4/4 + 347. Find x, given that d(x) = 0.
-157, 0
Let t(b) be the first derivative of b**6/2 - 3*b**4/2 + 3*b**2/2 + 63. Factor t(h).
3*h*(h - 1)**2*(h + 1)**2
Suppose -7*b = -3*b + z - 11, -2*z + 14 = 4*b. Let u = 257/6 - 127/3. What is w in 0 + 5/6*w**b + u*w**3 - 1/3*w = 0?
-2, 0, 1/3
Let h(b) be the third derivative of -b**7/273 + b**6/390 + 2*b**5/13 + 14*b**4/39 - 32*b**3/39 + 16*b**2. What is a in h(a) = 0?
-2, 2/5, 4
Suppose 25*t**3 - 39*t**2 - 3*t**4 + 129150*t - 129132*t - t**3 = 0. What is t?
0, 1, 6
Let u be -4*(21/(-4))/(6/(-4)). Let x be u/70 + 7/10. What is j in x*j**2 + 0*j + 0 = 0?
0
Let n(x) = -2*x + 5. Let w(c) = 3*c - 7. Let g(k) = 7*n(k) + 5*w(k). Suppose 9*z - 12*z = 3. Let p(u) = u**2 - u + 1. Let d(l) = z*p(l) + g(l). Factor d(r).
-(r - 1)**2
Factor 34/9*i + 10/9*i**2 + 4/3.
2*(i + 3)*(5*i + 2)/9
Let n(v) be the third derivative of 1/5*v**5 + 2/15*v**6 - 5*v**2 + 0*v + 0 - 8/3*v**3 - 2/3*v**4 + 2/105*v**7. Determine w so that n(w) = 0.
-2, -1, 1
Let k be (10/3)/(2/3). Suppose -9*f + 8 = -k*f. Suppose 0*v**2 - 3*v**2 + 0 + 4*v - 3 + 2*v**f = 0. Calculate v.
1, 3
Let r(j) = -j**2 - 35*j + 38. Let s be r(-36). Let 2/13*k**5 + 0 - 4/13*k - 2/13*k**4 + 10/13*k**s - 6/13*k**3 = 0. What is k?
-2, 0, 1
Factor 69*s - 49*s + 25*s**4 + 72*s**3 + 2*s**4 + 5*s**4 + 0*s**4 + 4*s**5 + 64*s**2.
4*s*(s + 1)**3*(s + 5)
Let n(t) = 5*t**4 - 80*t**3 + 135*t**2 - 60*t. Let q(r) = 2*r**4 - 27*r**3 + 45*r**2 - 20*r. Let s(o) = 3*n(o) - 10*q(o). Let s(k) = 0. What is k?
0, 1, 4
Suppose 3*n = 6 + 21. Let a(r) = 3 - n*r + r**2 - r**3 - 2 + 9*r. Let q(g) = 10*g**3 - 3*g**2 - 5*g - 7. Let v(l) = 5*a(l) + q(l). Determine z so that v(z) = 0.
-1, -2/5, 1
Let p(z) be the second derivative of -z**6/15 - z**5/5 + 2*z**4 + 8*z**3/3 - 32*z**2 + 801*z. Factor p(l).
-2*(l - 2)**2*(l + 2)*(l + 4)
Let b be 2/18*(-270)/(-60). Let s(o) be the first derivative of -4 - b*o**3 - 9/2*o + 3*o**2. Factor s(r).
-3*(r - 3)*(r - 1)/2
Let b(w) = -22*w + 66. Let f be b(3). Let t(k) be the first derivative of 2 + f*k**3 + 0*k**2 + 0*k**5 + 0*k - 1/10*k**6 + 0*k**4. Factor t(g).
-3*g**5/5
Let p(f) = 6*f**2 - 3*f - 15. Let q(a) = -11*a**2 + 6*a + 31. Let o(y) = 5*p(y) + 3*q(y). Factor o(n).
-3*(n - 3)*(n + 2)
Suppose 2*n - 2 = 6. Suppose -3*z - y - 4 = -6, 4*z = -n*y - 8. Factor h + z*h + h**2 - h - h.
h*(h + 1)
Let g(t) = -13*t**2 + 428*t + 33. Let m be g(33). Find s, given that -1/2*s**2 + m*s + 0 - 3/2*s**3 = 0.
-1/3, 0
Let t = 82 - 84. Let i be -3 - (14/(t - 0) + 2). Factor 0 - v**4 + v**i + 2/3*v**3 - 2/3*v.
-v*(v - 1)*(v + 1)*(3*v - 2)/3
Let c(a) be the second derivative of a**7/168 - 7*a**6/144 + a**5/12 + a**4/6 - 11*a. Let m(i)