5/12 + 2755*p**4/3 - 25230*p**3 - 30*p**2 + 2. Find n such that j(n) = 0.
9, 58
Find f, given that 12*f + 15*f + 29*f + 270*f**3 + 10*f**5 + 232*f**2 - 4 + 104*f**4 + 4 = 0.
-7, -2, -1, -2/5, 0
Suppose x - 12 = -2*z, -2*z - 4 + 22 = 2*x. Determine y, given that 7*y**3 - 5*y**3 + 0*y**5 + 2*y**5 - x*y**3 + 2*y**4 = 0.
-2, 0, 1
Let k = -149 + 145. Let c(t) = -8*t**3 - 4*t**2. Let b(o) = -o**5 + 8*o**3 + 3*o**2 - o. Let f(w) = k*b(w) - 3*c(w). Find h, given that f(h) = 0.
-1, 0, 1
Let a = 197023 - 197013. Suppose -175 - a*z - 1/7*z**2 = 0. What is z?
-35
Let q(x) = 21*x**2 - 680*x - 71. Let p(a) = -59*a**2 + 2044*a + 215. Let j(i) = -3*p(i) - 8*q(i). Let j(n) = 0. Calculate n.
-1/9, 77
Let q = 220 - 209. Let x be 1/4 + 22/8. Determine j, given that -23*j**2 + 12*j**5 + 20*j**4 + 10*j**3 + 3*j**2 - 3*j**x - q*j**3 - 8*j = 0.
-1, -2/3, 0, 1
Let w(c) be the second derivative of -1/168*c**7 - 1/4*c**2 + 0 - 1/6*c**4 + 1/60*c**6 + 1/40*c**5 - 84*c + 7/24*c**3. Find v such that w(v) = 0.
-2, 1
Let t(w) be the first derivative of -9*w**3 + 3/8*w**4 - 254 - 294*w + 315/4*w**2. Factor t(a).
3*(a - 7)**2*(a - 4)/2
Let w(p) = -2*p**5 - 8*p**4 + 4*p**3 - 2*p**2 - 32*p - 5. Let z(x) = x**5 + 3*x**4 - 4*x**3 + 16*x + 2. Let g(u) = 2*w(u) + 5*z(u). Factor g(s).
s*(s - 4)*(s - 1)*(s + 2)**2
Let l = 430 - 429. Let b(u) = u - 2. Let z(g) = -5*g**3 - 115*g**2 - 210*g - 115. Let x(o) = l*z(o) - 5*b(o). Solve x(c) = 0 for c.
-21, -1
Let f(r) be the first derivative of -29/4*r**4 - 43/9*r**3 - 29/15*r**5 + 0*r + 7/6*r**6 - r**2 - 20. Solve f(x) = 0 for x.
-1, -1/3, -2/7, 0, 3
Let k(l) be the first derivative of -l**5/4 + 5*l**4/4 - 5*l**3/3 + 129*l - 152. Let c(j) be the first derivative of k(j). Determine a, given that c(a) = 0.
0, 1, 2
Let a(c) be the third derivative of 0*c**4 - 8/15*c**6 + 3/5*c**7 + 0 + 9*c + 2/15*c**5 + 0*c**3 + c**2. Factor a(x).
2*x**2*(7*x - 2)*(9*x - 2)
Let p(a) be the third derivative of -a**6/120 - 41*a**5/60 + a**4/24 + 41*a**3/6 - 75*a**2 + 3. Solve p(y) = 0.
-41, -1, 1
Factor -1478 + 292 + 684*s**2 + 4*s**3 + 1340*s + 247 - 1089.
4*(s - 1)*(s + 3)*(s + 169)
Factor 3/7*m**4 + 108/7 + 30/7*m**3 + 39/7*m**2 - 180/7*m.
3*(m - 1)**2*(m + 6)**2/7
Factor -825*y - 386*y - y**2 - 749956 - 441*y - 80*y.
-(y + 866)**2
Let v(y) be the second derivative of y**5/60 - y**4/6 - 31*y**3/18 + 6*y**2 - 8199*y. Factor v(z).
(z - 9)*(z - 1)*(z + 4)/3
Suppose -20164/5 + 4473/5*d + 138/5*d**2 + 1/5*d**3 = 0. What is d?
-71, 4
Let n be 0/(4*((-32)/16)/1). Find y, given that 0 + 1/7*y**2 + n*y = 0.
0
Let i be (9/9*1)/((-1)/(-2)). Factor 5*x**2 + 5*x**5 - 5*x**3 - 3*x**4 + x - x - i*x**4.
5*x**2*(x - 1)**2*(x + 1)
Let h = 220394 - 220394. Factor 0 + h*a**2 + 2/15*a**3 - 2/15*a.
2*a*(a - 1)*(a + 1)/15
Let w(y) be the second derivative of -7*y**4/6 + 19*y**3/3 + 6*y**2 - 4*y + 77. Solve w(s) = 0 for s.
-2/7, 3
Let y = -12060 + 12083. Let a(d) be the third derivative of -20/3*d**3 - 1/12*d**5 - 5/4*d**4 + 0*d + 0 + y*d**2. Find g such that a(g) = 0.
-4, -2
Let c(z) = -z**4 - z**3 + 2*z**2 - z + 1. Let g(o) = -o**4 - 13*o**3 + 14*o**2 - 4*o + 4. Let q(p) = 4*c(p) - g(p). Factor q(u).
-3*u**2*(u - 2)*(u - 1)
Suppose -22/7*a**2 - 26/7 + 288/7*a = 0. What is a?
1/11, 13
Let p(j) = j**5 - j**4 - j**3 - 2*j**2 - j. Let l(n) = 0*n**3 + 3*n - 40*n**2 + 2*n**5 - 2*n**4 + 6*n**3 - n + 8*n**2. Let z(a) = -l(a) + 6*p(a). Factor z(d).
4*d*(d - 1)**3*(d + 2)
Let s(h) be the first derivative of -1/5*h**2 - 9/10*h**4 + 1/25*h**5 + 131 - h**3 + 1/5*h**6 + 0*h. Find j such that s(j) = 0.
-1, -1/6, 0, 2
Let c = 41134 - 41130. Factor 1/3*w**c + 160/3*w + 128/3 + 14/3*w**3 + 24*w**2.
(w + 2)*(w + 4)**3/3
Let w be 6/7 + 2309/(-7). Let g = w - -332. Suppose 32/3*q**2 - 4/3 + 10/3*q + 6*q**g = 0. What is q?
-1, 2/9
Factor -35*y**2 + 118*y**4 - 30*y - 75*y**4 - 38*y**4.
5*y*(y - 3)*(y + 1)*(y + 2)
Let w = -4/5097 - -183512/25485. Let n(y) be the first derivative of 1/10*y**4 + 21/5*y**2 - w*y - 16/15*y**3 + 1. Let n(z) = 0. What is z?
2, 3
Let p(m) be the second derivative of m**6/540 + m**5/90 - 4*m**3/27 + 5*m**2 + 46*m. Let s(z) be the first derivative of p(z). Factor s(k).
2*(k - 1)*(k + 2)**2/9
Let s be 1/6 - 340/(-120). Let c be 8 + -6*(4 - s). Find k, given that 0 + 440/3*k**4 - 32/3*k**c + 16/3*k - 175/3*k**5 - 56*k**3 = 0.
-2/7, 0, 2/5, 2
Let k(s) be the first derivative of s**4/18 - 10*s**3/27 + 4*s**2/9 + 1937. Solve k(l) = 0.
0, 1, 4
Let j(c) = -11*c**2 + 56. Let r be j(-7). Let k = -2413/5 - r. Determine u so that 2/5*u**2 - 2/5*u**4 + 0 - 2/5*u**3 + k*u = 0.
-1, 0, 1
Let r(c) be the first derivative of c**6/30 - 23*c**5/15 + 7*c**4 + 4*c**2 - c + 143. Let i(l) be the second derivative of r(l). Factor i(s).
4*s*(s - 21)*(s - 2)
Find a, given that -19605*a**4 + 4*a**2 - 24*a**2 + 5*a**3 - 5*a**5 + 19625*a**4 = 0.
-1, 0, 1, 4
Determine f so that -34445 - 114*f + 33975 - 100*f - 31*f - 5*f**2 = 0.
-47, -2
Let a(k) be the third derivative of k**7/525 - 3*k**6/100 + k**5/75 + 4*k**4/5 - 4113*k**2. Factor a(u).
2*u*(u - 8)*(u - 3)*(u + 2)/5
Suppose 0 = 80*l - 287 - 273. Let p(b) be the third derivative of 1/4*b**4 + 0*b + 0 - 1/2*b**3 - 1/20*b**5 + l*b**2. Let p(o) = 0. What is o?
1
Let w(i) be the second derivative of -i**6/60 - 2*i**5/5 - 7*i**4/12 + 4*i**3/3 + 15*i**2/4 + 1620*i. Factor w(k).
-(k - 1)*(k + 1)**2*(k + 15)/2
Let z(x) be the first derivative of x**4/12 + 7*x**3/9 + 2*x**2 + 576. What is p in z(p) = 0?
-4, -3, 0
Let y(h) = -h**2 + 19*h. Let q(g) = 6*g**2 - 268*g. Let v(i) = q(i) + 4*y(i). Factor v(o).
2*o*(o - 96)
Let a(j) be the third derivative of j**5/45 - 805*j**4/36 - 269*j**3/3 + 9*j**2 - 45*j + 4. What is u in a(u) = 0?
-1, 807/2
Let z = 1257877/4 + -316394. Let g = 1925 + z. Solve 0 + 0*y - 1/4*y**2 + 1/4*y**4 - g*y**3 + 1/4*y**5 = 0 for y.
-1, 0, 1
Let y = 221515 + -221512. Let -1/7*d**y + 1/7*d**2 - 1/7*d**4 + 1/7*d**5 + 0*d + 0 = 0. Calculate d.
-1, 0, 1
Suppose 83*c = 82*c - 5. Let z(m) = -33*m**3 + 33*m**2 + 93*m. Let p(h) = -8*h**3 + 8*h**2 + 23*h. Let d(l) = c*z(l) + 21*p(l). Factor d(u).
-3*u*(u - 3)*(u + 2)
Let l(u) be the second derivative of u**4/18 - 22*u**3/9 + 40*u**2 - 1030*u. Suppose l(y) = 0. Calculate y.
10, 12
Let a(f) be the first derivative of 125000*f**2 - 1562500*f - 4/5*f**5 - 129 - 5000*f**3 + 100*f**4. Factor a(n).
-4*(n - 25)**4
Let y(l) be the second derivative of 0*l**2 + 0*l**4 + 0*l**5 + 0*l**3 + l - 62 + 2/21*l**7 + 22/15*l**6. Factor y(a).
4*a**4*(a + 11)
Suppose 7*c + 12 = -8*k + 3*c, 0 = -k - 5*c - 33. Let m(p) be the second derivative of 12*p - 1/6*p**4 - 4*p**k + 0 - 4/3*p**3. Determine l so that m(l) = 0.
-2
Let r(y) be the first derivative of y**4 - 4*y**3/3 - 2*y**2 + 4*y - 120. Let t(x) = 5*x**3 - 3*x**2 - 5*x + 3. Let a(c) = -3*r(c) + 2*t(c). Factor a(z).
-2*(z - 3)*(z - 1)*(z + 1)
Factor -208*x**4 + 2810*x**2 + 1415*x**3 - 202*x**4 - 188*x**4 + 603*x**4.
5*x**2*(x + 2)*(x + 281)
Suppose 0 = 5*h + s - 4399, -1759 = -7*h + 5*h - s. Factor -86*l**3 + 0*l**4 - h*l**2 - 227*l - 2*l**4 + 1195*l.
-2*l*(l - 1)*(l + 22)**2
Let s(u) = -408*u + 16731. Let y be s(41). Suppose -1/6*c**2 - 1/3*c**y - 2 + 25/6*c = 0. Calculate c.
-4, 1/2, 3
Solve 259337 + 17*p**2 - 14*p**2 + 40231 + 1896*p = 0 for p.
-316
Let p(a) be the third derivative of -1/45*a**7 - 4/45*a**5 + 0*a**3 - 1/126*a**8 + 0*a + 2*a**2 + 0*a**4 + 17/90*a**6 - 28. Let p(s) = 0. What is s?
-4, 0, 1/4, 2
Let o(y) be the third derivative of -y**6/1080 - 11*y**5/180 - 4*y**4/3 - 14*y**3 + 883*y**2. Factor o(r).
-(r + 6)**2*(r + 21)/9
Suppose 2 = -k - 2*j + 11, 4*k + 4*j = 52. Suppose -14 = -k*q + 10*q. Find r, given that -6*r**2 + 7*r**3 + 2*r**4 + 5*r**2 + 8*r**2 - 3*r**q - r**5 = 0.
-1, 0, 4
Let t(u) = u**3 + 21*u**2 - 7*u + 6. Let s be t(-20). Let k = s - 111. What is g in -158*g - 382*g + 90*g**2 - 5*g**3 + 1032 + 483 - k = 0?
6
Let r be (-5)/(-10) - ((-11)/2 - -3). Factor -4*g**r + 236*g + 112*g**2 - 186 + 121 + 185.
-4*(g - 30)*(g + 1)**2
Let c(o) be the third derivative of -135*o**8/28 - 195*o**7/14 + 559*o**6/12 - 51*o**5/4 - 85*o**4/6 + 10*o**3 + 1690*o**2 - 1. Find z, given that c(z) = 0.
-3, -1/4, 2/9, 1
Let t = -96662 - -289988/3. What is q in -10*q + 16/3 + 4*q**2 + t*q**3 = 0?
-8, 1
Let h = 28943 - 868289/30. Let d(k) be the third derivative of 0 + 32*k*