*a**5 - 4*a**2 - 2/5*a**3. Let d(u) = 0. What is u?
-4, -3
Let r = 591/11 + -161/3. Let u(j) be the second derivative of r*j**3 + 0 + 15*j - 1/66*j**4 + 3/11*j**2. Find b such that u(b) = 0.
-1, 3
Suppose 18172 = 15*v - 43*v. Let y = -647 - v. Suppose 2/3*k**y + 2/3 + 4/3*k = 0. Calculate k.
-1
Let i(l) = -40*l**2 - 5460*l - 5370. Let d(f) = 5*f**2 + 682*f + 671. Let o(c) = -25*d(c) - 3*i(c). Factor o(v).
-5*(v + 1)*(v + 133)
Let p(z) be the first derivative of -3*z**5/5 - 501*z**4 + 2023. Determine w so that p(w) = 0.
-668, 0
Let s be 0 - (-2 + -1 + 1). Factor 14 - 13*a + 23 - 7 + 3*a**s + 46*a.
3*(a + 1)*(a + 10)
Let h(i) be the first derivative of -i**8/4032 + i**7/2520 + i**6/720 - 3*i**2/2 + 10*i - 4. Let o(v) be the second derivative of h(v). Factor o(p).
-p**3*(p - 2)*(p + 1)/12
Let z = 1975289 + -1104185673/559. Let y = z - 8/43. Factor 12/13*d**2 + 8/13 - 2/13*d**3 - y*d.
-2*(d - 4)*(d - 1)**2/13
Let q(y) be the third derivative of -2*y**7/105 + 11*y**6/15 - 97*y**5/15 - 44*y**4 - 96*y**3 - 1148*y**2. Factor q(u).
-4*(u - 12)**2*(u + 1)**2
Let z(v) = 202*v**2 + 68*v + 253. Let o(a) = -55*a**2 - 17*a - 63. Let i(f) = -22*o(f) - 6*z(f). Let i(w) = 0. What is w?
-11, -6
Suppose -90 = 40*m - 43*m. Suppose 3*l - 13*l + m = 0. Factor 2*p**4 - 166*p**3 + l*p**4 + 151*p**3 - 20*p**2.
5*p**2*(p - 4)*(p + 1)
Let h be -25 + 39 - (-48 - -59). Let i be (-1)/(-4) + (-3)/12. Factor 0*f - 2/9*f**2 - 1/9*f**h + i.
-f**2*(f + 2)/9
Let g(t) be the first derivative of 4*t**5/35 - 185*t**4/7 - 1772*t**3/7 - 5742*t**2/7 - 6912*t/7 + 7752. Find q such that g(q) = 0.
-3, -1, 192
Let b be (-4)/15*(-1587)/4232. Factor 1 + b*s**2 + 11/10*s.
(s + 1)*(s + 10)/10
Let b(t) be the first derivative of -t**4 - 108*t**3 - 3198*t**2 + 6724*t + 972. Factor b(q).
-4*(q - 1)*(q + 41)**2
Determine o, given that 26877*o**2 - 42*o - o**3 + 26887*o**2 - 53721*o**2 = 0.
0, 1, 42
Let m(k) be the second derivative of k**7/27 - 131*k**6/135 + 361*k**5/90 + 1339*k**4/54 + 1036*k**3/27 + 196*k**2/9 - 1797*k + 4. Let m(i) = 0. What is i?
-1, -2/7, 7, 14
Let f(r) be the first derivative of -r**6/6 - 3*r**5/5 + 22*r**4 + 1770. Factor f(h).
-h**3*(h - 8)*(h + 11)
Let o be (-67 + (-1541)/(-23))/(-1 + 3). Let -i**4 - 1/3*i**5 + 0 + 0*i + o*i**2 + 4/3*i**3 = 0. Calculate i.
-4, 0, 1
Let g = -52 + 149. Factor -g*m**5 - 440*m**2 + 242*m - 92*m**3 + 248*m**3 + 40*m**4 + 99*m**5.
2*m*(m - 1)**2*(m + 11)**2
Let j(y) be the first derivative of -4*y**3/3 + 221*y**2/2 - 55*y - 3415. Factor j(s).
-(s - 55)*(4*s - 1)
Let a = 430 - 294. Let -j**3 - a - 76*j + 18*j**2 + 3*j**3 + 182*j**2 + 10*j**3 = 0. What is j?
-17, -2/3, 1
Let u = -22 - -34. Let h(c) = 8*c**2 + u*c + 1 - 1 - 14*c**2. Let t(g) = 6*g**2 - 13*g - 1. Let l(y) = 4*h(y) + 3*t(y). Factor l(b).
-3*(b - 1)*(2*b - 1)
Solve -y**3 - 1/3*y**4 + 22 + 25*y**2 - 137/3*y = 0.
-11, 1, 6
Suppose 42 = 5*i - 6*b + 14*b - 6*b, 0 = 5*b - 80. Solve 0*y + 1/5*y**3 - i*y**2 + 0 = 0 for y.
0, 10
Let o be -47 + 14 - (-11 - 24). Factor 15/2 + 1/2*a**3 - 7/2*a**o + 7/2*a.
(a - 5)*(a - 3)*(a + 1)/2
Let i be -1*(-6)/(5 - 3). Let c = -50628/5 - -10126. Factor -2/5*v - 2/5 + 2/5*v**2 + c*v**i.
2*(v - 1)*(v + 1)**2/5
Let c(z) be the second derivative of 1/4*z**4 + 65*z + 1/4*z**5 + 1/30*z**6 + 0 - 3/2*z**3 + 0*z**2. Factor c(l).
l*(l - 1)*(l + 3)**2
Let b(k) be the third derivative of -1/180*k**5 - 7/9*k**4 + 0*k - 55/18*k**3 + 2*k**2 + 71. Factor b(x).
-(x + 1)*(x + 55)/3
Let f be 272/78 - 282/1833. Let d(p) be the second derivative of -f*p**3 - 14*p - 31/12*p**4 - 2*p**2 - 3/4*p**5 + 0. Factor d(q).
-(q + 1)*(3*q + 2)*(5*q + 2)
Suppose -21/4*p + 21/4*p**3 - 1/4*p**4 + 1/4*p**2 + 0 = 0. Calculate p.
-1, 0, 1, 21
Let j(w) be the second derivative of 297/20*w**5 + 0*w**2 - 121/4*w**4 + 0*w**3 + 21/10*w**6 + 0 + 32*w + 1/14*w**7. Solve j(z) = 0.
-11, 0, 1
Factor 0 + 162/7*j + 60/7*j**2 + 2/7*j**3.
2*j*(j + 3)*(j + 27)/7
Suppose -463 - 489 = 4899*g - 5375*g. Determine n, given that 4/17*n**4 + 0 + 2/17*n**5 - 40/17*n**g - 38/17*n**3 + 0*n = 0.
-5, -1, 0, 4
Let c(a) = -52*a**2 + 4260*a + 4408. Let s(g) = 8*g**2 - 655*g - 678. Let p(i) = -5*c(i) - 32*s(i). Solve p(y) = 0 for y.
-1, 86
Let b(g) be the third derivative of g**8/560 + 3*g**7/350 - g**5/25 - 6243*g**2. Let b(a) = 0. What is a?
-2, 0, 1
Let h(l) be the third derivative of l**8/1176 - 4*l**7/735 - 8*l**6/35 + 6*l**2 + 30*l - 1. Find b such that h(b) = 0.
-8, 0, 12
Let h(w) be the first derivative of -2*w**3/27 + 4*w**2/9 + 280*w/9 - 408. Determine a, given that h(a) = 0.
-10, 14
Find g such that g + 1/2*g**5 + 0 + 5/2*g**4 + 9/2*g**3 + 7/2*g**2 = 0.
-2, -1, 0
Let a(x) be the first derivative of 10*x - 15/2*x**2 + 149 - 5/16*x**4 + 5/2*x**3. Factor a(k).
-5*(k - 2)**3/4
Let z(t) = 665*t - 3982. Let o be z(6). Let w(y) be the first derivative of o*y + 7 + 2/3*y**3 + 5*y**2. Let w(u) = 0. Calculate u.
-4, -1
Let y(x) = 6*x**4 + 13*x**3 - 153*x**2 + 238*x - 129. Let i(q) = 7*q**4 + 14*q**3 - 156*q**2 + 236*q - 131. Let j(t) = -5*i(t) + 6*y(t). Factor j(s).
(s - 7)*(s - 1)**2*(s + 17)
Let j(a) be the first derivative of -13/10*a**4 + 0*a - 2/25*a**5 - 34 + 2/15*a**3 + 13/5*a**2. Determine s so that j(s) = 0.
-13, -1, 0, 1
Let v = -701 - -704. Let a(j) be the first derivative of -5 + v*j**2 + 2/3*j**3 + 4*j. Suppose a(q) = 0. What is q?
-2, -1
Let p(b) = b**5 - 7*b**4 - 3*b**3 + 9*b**2 - b. Let o(z) = z**4 - z**2 + z. Suppose 4*n + 2 = 6, -3 = -2*t - n. Let d(r) = t*p(r) + 5*o(r). Factor d(x).
x*(x - 2)**2*(x + 1)**2
Determine z, given that 2/13*z**2 - 1166/13*z - 1168/13 = 0.
-1, 584
Let b(a) be the second derivative of a**4/12 + a**3/3 + 17*a. Let w(h) = 2*h**3 + h**2 - 12*h - 12. Let i(p) = 2*b(p) + w(p). Find l, given that i(l) = 0.
-2, -3/2, 2
Factor 151023*n**3 - 4039*n + 36608 + 6672*n**2 - 4*n**4 - 151547*n**3 + 2796*n - 25957*n.
-4*(n - 4)**3*(n + 143)
Let f(n) be the third derivative of -n**6/240 - 83*n**5/120 + 872*n**2. What is g in f(g) = 0?
-83, 0
Let b(x) be the second derivative of -x**5/80 - 7*x**4/4 - 27*x**3/2 - 40*x**2 + 692*x. Suppose b(s) = 0. What is s?
-80, -2
Factor 85849/4 + 1/4*j**2 + 293/2*j.
(j + 293)**2/4
Factor 1611 - 1065/2*l - 3/2*l**2.
-3*(l - 3)*(l + 358)/2
Let m = 1898057/6 + -316340. Find c such that 21/2*c**2 + 0 - 27/2*c + m*c**3 + 1/6*c**4 = 0.
-9, 0, 1
Let p be 39/11 + 96/(-176). Let k be (p - 2)/((-143)/(-26)). Factor -k*l - 2/11*l**4 - 2/11*l**5 + 4/11*l**3 + 4/11*l**2 - 2/11.
-2*(l - 1)**2*(l + 1)**3/11
Let f = -3662 + 3662. Let c(o) be the second derivative of 0*o**2 - 1/30*o**6 + f + 6*o - 1/4*o**4 + 1/6*o**3 + 3/20*o**5. Factor c(w).
-w*(w - 1)**3
Let u(a) be the first derivative of -5*a**4 - 215*a**3/3 - 305*a**2/2 + 90*a + 790. Solve u(o) = 0.
-9, -2, 1/4
Let c(b) = -11*b**3 - 106*b**2 + 208*b + 4. Let y(x) = 42*x**3 + 423*x**2 - 834*x - 15. Let r(j) = 15*c(j) + 4*y(j). Factor r(v).
3*v*(v - 2)*(v + 36)
Let t be (-3 - (-124)/40)/((-836)/(-1045)). Determine j so that 5/4 + t*j**3 - 7/8*j - 1/2*j**2 = 0.
-2, 1, 5
Solve -36/5*n**2 - 122/5*n + 2/5*n**3 - 84/5 = 0 for n.
-2, -1, 21
Solve 1/4*l**3 + 9/2*l**2 - 21 + 65/4*l = 0 for l.
-12, -7, 1
Let y(z) be the first derivative of -64*z + 4*z**4 - 8/3*z**6 - 132/5*z**5 + 364/3*z**3 - 84*z**2 - 61. Suppose y(v) = 0. Calculate v.
-8, -2, -1/4, 1
Factor 3*h**2 + 180 - 90*h + 110*h + 37*h.
3*(h + 4)*(h + 15)
Let q(o) = -3*o**2 + 0*o**2 + 1486*o - 1465*o + 21*o**2 + 12*o**3 + 5. Let z(u) = 38*u**3 + 54*u**2 + 64*u + 16. Let v(h) = -16*q(h) + 5*z(h). Factor v(p).
-2*p*(p + 1)*(p + 8)
Let o(m) be the second derivative of m**6/90 + m**5/4 + 3*m**4/2 + 20*m**3/9 + 424*m. Factor o(p).
p*(p + 1)*(p + 4)*(p + 10)/3
Let k(i) be the third derivative of i**6/300 + 397*i**5/150 - 3429*i**2 - i. Factor k(a).
2*a**2*(a + 397)/5
Factor -68*o**2 + 141*o - 57*o**2 - o**3 + 50*o**2 - 237 + 172*o + 0.
-(o - 3)*(o - 1)*(o + 79)
Let g = -219468/17 + 12910. Let r(w) be the first derivative of 1/34*w**4 - g*w - 1/17*w**2 + 2/51*w**3 - 13. Suppose r(j) = 0. What is j?
-1, 1
Determine x, given that -526/9*x - 32/9 + 11/3*x**2 = 0.
-2/33, 16
Suppose 0 = -8*a + 12*a - 4*i, 4*a + i = 15. Let d(q) be the first derivative of -4/3*q + 1/3*q**4 + 20 + 2/3*q**a - q**2. Let d(o) = 0. What is o?
-2, -1/2, 1
Suppose 0 = -4*v - 4*r - 288, 2*v + 2*v = 2*r - 258. 