 i(x) be the second derivative of x**4/48 - 27*x**3/8 + 81*x**2 - 49*x + 2. Find u such that i(u) = 0.
9, 72
Let i(v) be the second derivative of -v**4/24 + 89*v**3/6 - 1197*v**2/4 - 2*v - 3966. Factor i(b).
-(b - 171)*(b - 7)/2
Let j(r) = -r**2 + 1. Let p(s) be the second derivative of s**4/3 - s**3 + s**2 + 4*s. Let g be 9/30*45/54*4. Let k(h) = g*p(h) + 3*j(h). Factor k(c).
(c - 5)*(c - 1)
Let n be (-312)/(-20) + -19 + 1472/80. Factor 0 + 145/2*x**3 + 45/2*x**4 + n*x**2 + 0*x.
5*x**2*(x + 3)*(9*x + 2)/2
Let v(q) be the first derivative of -4*q**3/9 - 152*q**2/3 - 804*q - 308. Suppose v(k) = 0. What is k?
-67, -9
Let p = 4 + -2. Let r(s) = 85*s + 2. Let c be r(0). Factor -p*v**4 - 78*v**2 + v**4 + 79*v**c + v**3 - v + 0*v**3.
-v*(v - 1)**2*(v + 1)
Let g(w) be the first derivative of 2*w**3/3 - 34*w**2 - 70*w + 2530. Factor g(u).
2*(u - 35)*(u + 1)
Suppose 273*v - 272*v + 5*p = 17, 0 = -4*p + 12. Determine w, given that -2/7*w + 0 - 2/7*w**v = 0.
-1, 0
Let t(k) be the first derivative of 2/21*k**3 - 27/7*k**2 + 0*k - 12. Factor t(m).
2*m*(m - 27)/7
Let h be 4/3*(225/18 + -10 - -2). Let a(g) be the first derivative of 0*g + 2/5*g**2 - h - 14/15*g**3. Factor a(i).
-2*i*(7*i - 2)/5
Factor -3968 - 8385*o**4 - 10616*o**2 + 2*o**5 - 9*o**5 + 8254*o**4 + 2306*o**3 + 16736*o.
-(o - 4)**3*(o + 31)*(7*o - 2)
Let t(r) = -785*r**2 - 475*r + 2065. Let n(l) = -1106*l**2 - 713*l + 3098. Let d(s) = 5*n(s) - 7*t(s). Factor d(g).
-5*(g - 3)*(7*g + 69)
Let d(g) = 3*g**2 - 31*g + 8. Let x be d(9). Let m be (-12)/x*56/(-16)*-1. Factor -3 + m*u**2 + 3/2*u.
3*(u - 1)*(u + 2)/2
Let k(y) = 4*y**2 - 12*y + 20. Let d(c) = -13*c**2 + 35*c - 60. Suppose 0 = 14*a + 186 - 214. Let r(b) = a*d(b) + 7*k(b). Factor r(x).
2*(x - 5)*(x - 2)
Let r(q) = -243*q**3 + 3320*q**2 + 3343*q + 5. Let h(z) = -98*z**3 + 1660*z**2 + 1670*z + 2. Let p(i) = 5*h(i) - 2*r(i). Solve p(v) = 0.
-1, 0, 416
Let q be (1 - (-20)/(-12))*(-30)/4. Suppose q + 4 = 3*y. Factor -26*z**2 + 7*z**4 - 2*z**4 - 10*z**y + 0*z**2 + 11*z**2.
5*z**2*(z - 3)*(z + 1)
Let g(l) be the first derivative of -l**4/8 + 779*l**3/6 + 2209. Factor g(w).
-w**2*(w - 779)/2
Let w = -43/323 - -409/646. Factor 0 - w*j**3 - 1/2*j**4 + 1/2*j**2 + 1/2*j.
-j*(j - 1)*(j + 1)**2/2
Suppose 0 = -2*w - 6104 + 6108. What is l in -1/5*l**4 - 1/5*l + 3*l**w + 19/5*l**3 - 6/5*l**5 - 2/5 = 0?
-1, -1/2, 1/3, 2
Find m, given that 0 - 6*m - 28/17*m**2 + 2/17*m**3 = 0.
-3, 0, 17
Suppose 5*q - 25 = 5*d, -18 = -3*q + 7*d - 3*d. Suppose -2*p + 8 + q = 0. Factor -9*k**4 - 26*k - 4*k**3 + 16 + 4*k**p - 3*k**4 + 44*k**2 + 0*k**5 - 22*k.
4*(k - 2)*(k - 1)**3*(k + 2)
Let f(z) be the third derivative of z**6/40 - 3*z**5/5 - 27*z**4/8 - 7*z**3 + 298*z**2 - 1. Find h, given that f(h) = 0.
-1, 14
Let u(a) = 7*a**2 - 704*a + 652. Let p(r) = 3*r**2 - 351*r + 330. Let n(c) = 5*p(c) - 2*u(c). Factor n(g).
(g - 346)*(g - 1)
Suppose 2*r + 5*u - 234 = 0, 4*r + 2*u - 486 = u. Factor -2*y**2 + 16*y + 77 - r*y - 1419 - 1467 + y**2.
-(y + 53)**2
Let r be (10 - -2) + -4 - (2 - (-116)/20). Factor 0 + r*o**4 + 0*o + 4/5*o**3 + 4/5*o**2.
o**2*(o + 2)**2/5
Let a be -15*(-1)/(-2)*16/(-20). Let d be (-1)/((-27)/180) - a. Factor 8/3 + d*b**3 - 2*b**2 + 0*b.
2*(b - 2)**2*(b + 1)/3
Suppose 3*m - g = 91 + 17, 5*m + 4*g = 180. Factor -66*h**2 + 32*h**2 + 8 + 8*h + m*h**2.
2*(h + 2)**2
Let v = 4656 - 4652. Suppose -4/3*n**2 - 2/3*n - 8/3*n**v + 14/3*n**3 + 0 = 0. What is n?
-1/4, 0, 1
Suppose 42*r - 37*r + 1126 = 4*z, -2*z + 558 = -5*r. Let p be (-20)/16 + z/112. Factor 3/7*s**5 - 6/7*s**2 - p*s - 3/7 + 9/7*s**4 + 6/7*s**3.
3*(s - 1)*(s + 1)**4/7
Let -11*q**3 + 44*q - 117/2*q**2 + 242 - 1/2*q**4 = 0. Calculate q.
-11, -2, 2
Let p(w) be the second derivative of -79/18*w**3 + 0 + 38/9*w**4 - 64*w + 5/3*w**2 + 4/15*w**5. Suppose p(t) = 0. Calculate t.
-10, 1/4
Let m be ((-3 - (-4 - -1))/(23 + -28))/(-3 + 4). Suppose -3/2*u**2 - 48*u + m = 0. Calculate u.
-32, 0
Factor 40*o**3 - 296*o - 694*o + 40*o**2 + 46*o**2 + 4*o**4 + 206*o - 114*o**2.
4*o*(o - 4)*(o + 7)**2
Let p(k) = 2*k - 16. Let y be p(9). Suppose 52 + 12*w**y - 18 - 6*w**4 + 3*w - 6*w**3 - 22 - 18 + 3*w**5 = 0. Calculate w.
-1, 1, 2
Let u(n) = 4*n**4 - 19*n**3 - 8*n**2 - 6*n - 3. Let m(c) = -25*c**4 + 130*c**3 + 55*c**2 + 40*c + 20. Let g(s) = 3*m(s) + 20*u(s). Let g(p) = 0. What is p?
-1, 0
Suppose -5*x = -7*k + 4*k - 13, x + 2*k = 0. Suppose 4*l**2 - 19*l**x - 5*l**3 - 84*l - 5 + 69*l = 0. What is l?
-1
Let q(j) = j**3 + 5*j - 4. Let b be q(3). Let a = b + -35. Factor 0*f**a - 2*f**3 + 2*f**2 + 2*f + 0*f**3 + 2 - 4*f**2.
-2*(f - 1)*(f + 1)**2
Let h(r) be the first derivative of r**4/4 + 4*r**3/3 - 8*r**2 + 2*r + 208. Let g(l) = l**3 - 2*l**2 + 1. Let u(m) = 4*g(m) - 2*h(m). Factor u(b).
2*b*(b - 4)**2
Let j(n) be the first derivative of n**4/4 - 92*n**3/3 + 960*n**2 + 9216*n - 104. Suppose j(o) = 0. What is o?
-4, 48
Solve 0*a - 20*a**4 + 32/5*a**3 + 0 - 84/5*a**5 + 48/5*a**2 = 0 for a.
-1, -6/7, 0, 2/3
Let y = -189 - -194. Let 54*x**2 - 6*x + 44*x - y*x + 7*x**3 - 14 = 0. Calculate x.
-7, -1, 2/7
Let q(z) be the second derivative of 1/42*z**7 - z - 3/20*z**5 + 0*z**3 + 0*z**4 - 24 + 1/15*z**6 + 0*z**2. Factor q(n).
n**3*(n - 1)*(n + 3)
Let d(t) be the third derivative of 0*t**5 + 1/50*t**6 - 1/840*t**8 + 116*t**2 + 0*t**4 + 1/105*t**7 + 2*t + 0 + 0*t**3. Factor d(l).
-2*l**3*(l - 6)*(l + 1)/5
Let s be -3*(-60)/18 - 2. Suppose 0 = 5*v - s*v + 27. Let -3*p**4 + 0*p**4 - 1983*p + 1989*p + v*p**2 = 0. What is p?
-1, 0, 2
Let q(c) = -43*c**2 - 135*c - 11. Let v(w) = -4*w**2 + 2*w - 1. Let k(r) = 5*q(r) - 55*v(r). Find i such that k(i) = 0.
0, 157
Let y be (-2556)/(-17040)*(26 - 1). Determine z, given that -y*z**2 - 15/4*z**4 + 5/2 + 35/4*z**3 - 15/4*z = 0.
-2/3, 1
Let u(m) be the first derivative of m**5/80 + 3*m**4/16 - m**3/24 - 9*m**2/8 + 185*m + 27. Let j(h) be the first derivative of u(h). Factor j(v).
(v - 1)*(v + 1)*(v + 9)/4
Let z(a) be the third derivative of 293*a**6/40 - a**5/10 + 4395*a**2. Let z(j) = 0. What is j?
0, 2/293
Factor -1694259004/3 + 4502/3*k**3 + 2/3*k**4 + 1124998*k**2 + 840361490/3*k.
2*(k - 2)*(k + 751)**3/3
Find d such that -89/2*d**4 - 421/4*d**3 + 89/2*d**2 + 102*d + 0 + 13/4*d**5 = 0.
-2, -1, 0, 1, 204/13
Let d(o) be the third derivative of 33*o**2 - 7/6*o**3 - 1/210*o**7 + 0 + 0*o - 1/4*o**4 + 1/20*o**6 + 2/15*o**5. Suppose d(h) = 0. What is h?
-1, 1, 7
Let 696/7*v**3 - 56*v + 18/7*v**4 - 78/7 - 244/7*v**2 = 0. What is v?
-39, -1/3, 1
Let t(x) be the second derivative of -x**7/7560 + x**6/432 - x**5/90 - 77*x**4/12 + 2*x - 9. Let v(n) be the third derivative of t(n). What is z in v(z) = 0?
1, 4
Let x(s) be the third derivative of 2*s**7/105 + 29*s**6/60 + 13*s**5/30 - 7*s**4/6 + 3*s**2 + 4*s + 1. What is i in x(i) = 0?
-14, -1, 0, 1/2
Solve 145 - 1039/4*x + 119/4*x**3 + 1/4*x**4 + 339/4*x**2 = 0 for x.
-116, -5, 1
Let f = -3039 + 3041. Let h = -7055/9 + 784. Factor 10/9*q - 11/9 + h*q**f.
(q - 1)*(q + 11)/9
Let l be (81/(-6))/(-9)*214. Factor 22*f**2 + 13*f**2 + l - 5*f**3 - 55*f - 296.
-5*(f - 5)*(f - 1)**2
Let g(v) be the first derivative of v**6/57 - 256*v**5/95 - 195*v**4/19 - 784*v**3/57 - 131*v**2/19 + 4303. Factor g(f).
2*f*(f - 131)*(f + 1)**3/19
Let y(o) be the second derivative of 2 - 19*o + 6/5*o**3 + 1/20*o**4 + 0*o**2. Factor y(r).
3*r*(r + 12)/5
Let g(w) = -w**2 + w. Let o(a) = -a**3 + 9*a**2 - 9*a. Let t = 10 + -6. Suppose -5*d - t = 1. Let u(q) = d*o(q) - 5*g(q). Factor u(p).
p*(p - 2)**2
Let y(q) be the third derivative of -q**7/840 + q**6/60 + 7*q**4/6 + 21*q**2. Let t(i) be the second derivative of y(i). Factor t(s).
-3*s*(s - 4)
Let z(r) be the second derivative of 0 + 0*r**5 + 0*r**2 - 18*r - 1/80*r**6 + 3/32*r**4 - 1/8*r**3. Factor z(a).
-3*a*(a - 1)**2*(a + 2)/8
Let c(t) be the first derivative of 2*t**7/21 + 2*t**6/5 + t**5/5 - t**4 - 4*t**3/3 + 67*t + 87. Let i(g) be the first derivative of c(g). Factor i(a).
4*a*(a - 1)*(a + 1)**2*(a + 2)
Let s(g) = 38*g**2 + 486*g - 235. Let p(n) = -22*n**2 - 243*n + 117. Let q(i) = 7*p(i) + 4*s(i). Factor q(d).
-(d - 121)*(2*d - 1)
Solve -4*v**4 + 0*v**4 - 52*v**3 - 1510*v**2 + 31*v + 4*v**5 + 17*v + 1514*v**2 = 0.
-3, -1, 0, 1, 4
Let y be (-2 + -1)*1720/(-30). Factor -17*x + 42*x + 167*x**2 - y*x**2.
-5*x*(x - 5)
Suppose 21*u - 34*u