2580)/(-48160)). Factor s*m**2 + 50/9*m**4 + 0 - 140/9*m**3 - 16/9*m.
2*m*(m - 2)*(5*m - 2)**2/9
Let g(i) be the second derivative of -i**4/24 + 15*i**3/2 - 89*i**2/4 + 16*i - 6. Determine u, given that g(u) = 0.
1, 89
Let x be 19 + (-2)/2 + (-8)/(-4). Factor -x*o - 255*o**4 - 32*o**2 - o**3 + 254*o**4 + 48*o**2.
-o*(o - 2)**2*(o + 5)
Let l = 282 - 151. Let a = l + -111. Factor -f + 10*f**4 - 2*f**2 + a*f**2 + 24*f**3 + 5*f.
2*f*(f + 1)**2*(5*f + 2)
Let y be (-4 + 16)*(-30)/(-64)*90/50. Factor -27/8*u**2 + 81/8*u + 3/8*u**3 - y.
3*(u - 3)**3/8
Let b(q) be the first derivative of -1/24*q**6 + 24*q**2 + 0*q + 0*q**3 + 5/24*q**4 + 0*q**5 + 47. Let l(j) be the second derivative of b(j). Factor l(w).
-5*w*(w - 1)*(w + 1)
Let a be 2167/143 + (-6)/39. Suppose 5*u + a = -5*l, -12 = -4*u + 2*u + 4*l. Factor -2/5*p**2 - 2*p + u.
-2*p*(p + 5)/5
Let y(h) be the second derivative of -2*h**6/15 - 86*h**5/5 - 163*h**4 - 480*h**3 + 4*h - 143. Factor y(s).
-4*s*(s + 3)**2*(s + 80)
Let x(q) = -5*q**2 + 30*q. Let b(i) = 7*i**2 - 45*i - 2. Let p = -205 + 197. Let o(k) = p*x(k) - 5*b(k). Factor o(m).
5*(m - 2)*(m - 1)
Let k = -23603/3 + 118057/15. What is p in 16/5*p + 2/5*p**2 + k = 0?
-7, -1
Let t be 63/6*60/105. Let z be t + 4*3/(-12). Let 16/9*r**2 - 10*r**3 - 98/9*r**z + 0 - 196/9*r**4 + 8/9*r = 0. What is r?
-1, -2/7, 0, 2/7
Let m(y) = -2*y**2 + 675*y + 716. Let a(n) = n**2 - 225*n - 238. Let o(h) = -13*a(h) - 4*m(h). Factor o(i).
-5*(i - 46)*(i + 1)
Let o(k) = -21 + 37 + 5 - 22. Let p = -15 + 11. Let h(m) = m**3 - 3*m - 2. Let l(v) = p*o(v) + h(v). Solve l(x) = 0 for x.
-2, 1
Let p be (3 - 6) + 3 + 2. Suppose -26 = -3*b + 4*c, -c - 4 + 3 = p*b. Find j such that 372*j**3 + 3*j - 9*j - 9*j**b - 375*j**3 = 0.
-2, -1, 0
Factor 1/4*r**2 + 85/4 + 43/2*r.
(r + 1)*(r + 85)/4
Suppose 12*u = 15*u. Let f(d) = d**3 - d**2 - 40*d + 14. Let i be f(-6). Factor -1/3*o**3 + 0 + u*o + 1/3*o**i.
-o**2*(o - 1)/3
Let k(h) be the third derivative of h**6/280 - 19*h**5/12 - 297*h**4/56 - 223*h**3/42 + 82*h**2 + 7*h. Solve k(v) = 0 for v.
-1, -1/3, 223
Let s be ((-10)/4 - -1)/((-129)/430). Suppose 0 = -s*v - 9*v + 2*v. Determine c, given that 10/7*c**2 + v - 2/7*c**3 - 8/7*c = 0.
0, 1, 4
Let p = 140 - 129. Suppose 5*m = 2*n + 17, -4*m - p + 27 = -n. Factor -2/5*j**5 - 2*j**3 + 0 + 4/5*j**2 + 8/5*j**n + 0*j.
-2*j**2*(j - 2)*(j - 1)**2/5
Let n(t) be the third derivative of 1/3*t**6 - 63*t**2 - 5*t**3 + 0*t**7 + 1/2*t**5 - 35/24*t**4 + 0*t - 5/336*t**8 + 0. Determine b so that n(b) = 0.
-2, -1, 1, 3
Let x(b) be the first derivative of b**5 + 25*b**4/4 - 215*b**3/3 - 1225*b**2/2 - 1470*b - 8867. Suppose x(n) = 0. Calculate n.
-7, -3, -2, 7
Suppose -3*z = -5*d + 3353 - 3430, 4*z - 76 = 4*d. Factor 39/7*s + z*s**2 + 6/7.
3*(3*s + 1)*(7*s + 2)/7
Let a = 151 + -131. Let h = 22 - a. Factor 6*w**2 + 21*w**h + w**4 + 28*w - 9*w**3 - 55*w.
w*(w - 3)**3
Suppose 0*s + 21/2*s**3 - 3/4*s**5 + 0*s**2 - 39/4*s**4 + 0 = 0. Calculate s.
-14, 0, 1
Suppose 13*q**2 - 1/4*q**5 + 3/4*q**4 - 16 - 6*q + 17/2*q**3 = 0. Calculate q.
-2, 1, 8
Let h(w) be the third derivative of 1/15*w**3 + 1/300*w**5 + 0*w - 1/40*w**4 - 4*w**2 + 4. Factor h(i).
(i - 2)*(i - 1)/5
Suppose 7 - 1 = 2*i, 2*v = -i + 39. Let b be (-146)/(-30) - (v/(-135))/1. Determine r so that 0*r + 1/6*r**b + 1/6*r**4 - 1/6*r**3 + 0 - 1/6*r**2 = 0.
-1, 0, 1
Let c(k) be the second derivative of -k**7/42 - 2*k**6/5 - 23*k**5/20 + 3*k**4 - 1121*k. Determine v so that c(v) = 0.
-9, -4, 0, 1
Let d(p) be the second derivative of -7*p**6/120 - p**5/5 + 15*p**4/16 - 7*p**3/12 - p**2 + 35*p - 3. Suppose d(u) = 0. What is u?
-4, -2/7, 1
Let s be ((-10)/(-165))/(1*(-44)/(-363)). Let a = 1/85 + 247/680. Suppose a + s*k + 1/8*k**2 = 0. Calculate k.
-3, -1
Let d(a) be the third derivative of 1/24*a**5 + 1/24*a**6 - 1/1344*a**8 + 1/210*a**7 + 24*a**2 + 0*a + 2 - 7/12*a**3 - 19/96*a**4. Solve d(z) = 0 for z.
-2, -1, 1, 7
Let i = 785901 + -2357701/3. Find m such that -i*m**2 + 84*m - 2646 = 0.
63
Let h(y) be the first derivative of -y**4/18 + 224*y**3/27 - 221*y**2/9 + 220*y/9 - 2955. Determine f, given that h(f) = 0.
1, 110
Solve -60 + 15*x**5 - 20*x**4 - 796*x - 84*x**3 + 80*x**2 - 106*x**3 + 971*x = 0.
-3, -1, 1/3, 1, 4
Let p(y) be the third derivative of y**2 - 5 + 13/90*y**5 + 0*y + 1/60*y**6 - 7/9*y**4 + 4/3*y**3. Suppose p(i) = 0. Calculate i.
-6, 2/3, 1
Let c be (-126336)/(-1792) - (-244)/(-4). Factor 0 - c*a**2 - 1/2*a**3 + 10*a.
-a*(a - 1)*(a + 20)/2
Suppose 5*i + 5*r - 385 = 0, -3*i + 3*r = -0*r - 261. Let c be 4*(-4)/8 - -81. Factor i*a**4 - c*a**4 + 0*a**3 - 12*a**3.
3*a**3*(a - 4)
Let r = -230160 - -230162. Factor 12/19*g**4 + 32/19*g**r + 2/19*g**5 + 18/19*g + 4/19 + 28/19*g**3.
2*(g + 1)**4*(g + 2)/19
Let 0 + 13/2*f**2 + 0*f + 233/2*f**3 - 35/8*f**5 + 383/8*f**4 = 0. What is f?
-2, -2/35, 0, 13
Let 0 + 3/4*c**5 + 225/2*c**2 - 3*c**4 - 105/4*c**3 + 0*c = 0. Calculate c.
-6, 0, 5
Factor 80 - 14*m - 7*m**2 + 287 + 10*m**2 + 128 - 100*m.
3*(m - 33)*(m - 5)
Let f be ((-3)/4)/((-28)/224). Let x be f/(1 + 2 + -1). Find r, given that -5*r - 22*r**3 + 50*r**4 - 23*r**5 - 40*r**2 - 17*r**5 - 160*r**4 - 83*r**x = 0.
-1, -1/2, -1/4, 0
Let k(f) be the third derivative of 0*f**4 + 0*f + 0*f**3 - 1/15*f**5 + 9*f**2 + 1/60*f**6 + 1/105*f**7 + 0. Factor k(h).
2*h**2*(h - 1)*(h + 2)
Factor -20/9*c**2 - 268*c + 3416/9.
-4*(c + 122)*(5*c - 7)/9
Let b = -6066 - -6071. Suppose 4/13*i**4 + 28/13*i**2 + 0 + 2/13*i**b - 24/13*i**3 - 10/13*i = 0. Calculate i.
-5, 0, 1
Let d(l) be the third derivative of 1/3*l**4 - 1/15*l**6 + 1/15*l**5 + 0 + 0*l + 39*l**2 + 1/105*l**7 - l**3. Let d(h) = 0. What is h?
-1, 1, 3
Let x be (6/(-21))/(4 - 29/7). Suppose 2*f = 3*k - 2 - 2, -x*k = -2*f. Determine n, given that 4*n**4 + 8*n**3 - f*n**3 - 2*n**2 - 4*n**5 + n**2 - 3*n**2 = 0.
-1, 0, 1
Let q be (148/(-32) - -5) + 364/(-32). Let h(d) = 6*d + 66. Let a be h(q). Suppose -2/5*c**2 + 0 + a*c = 0. Calculate c.
0
Let p(j) be the first derivative of -2*j**3/27 - j**2 + 572*j/9 - 1781. Let p(l) = 0. What is l?
-22, 13
Let z = 15513/27148 - -1/190036. Factor z*f**3 + 32*f - 58/7*f**2 - 14.
2*(f - 7)**2*(2*f - 1)/7
Let c = -15639329/123306 - -3/20551. Let g = c + 127. Factor 0 + 1/6*r + 0*r**2 - g*r**3.
-r*(r - 1)*(r + 1)/6
Suppose 4*x - 8 = -y, 5*x - 10 = -0*x - 4*y. Determine k, given that 22*k - 3*k**x - 79*k - 26*k**2 + 26*k**2 = 0.
-19, 0
Let x(s) be the second derivative of s**4/42 - 8*s**3/21 + 16*s**2/7 - 223*s + 7. Solve x(j) = 0.
4
Let v(w) be the first derivative of -2*w**3/21 - 26*w**2/7 - 50*w/7 - 11468. What is c in v(c) = 0?
-25, -1
Let a(g) be the second derivative of g**4/42 + 62*g**3/21 - 80*g**2 + 2194*g. Solve a(o) = 0.
-70, 8
Let n(m) = -8*m**2 - 2*m - 1. Suppose 41*d - 44 = 120. Let p(a) = 3*a - 2*a + 4*a**2 - a**2. Let x(w) = d*n(w) + 11*p(w). Find g, given that x(g) = 0.
-4, 1
Let z be 8 - (19 - 12) - 4*-1. Let i be 10/4*-2*(-3)/z. Find l, given that -1/4*l**4 + 5/4*l**i - 9/4*l**2 - 1/2 + 7/4*l = 0.
1, 2
Let r be (-545)/(-10) + -53 + 11. Factor r + 7/4*q**2 - 177/4*q.
(q - 25)*(7*q - 2)/4
Let q(r) = -5*r**2 - 43*r + 82. Let z(k) = 210*k**2 + 1810*k - 3440. Let t(p) = -85*q(p) - 2*z(p). Factor t(j).
5*(j - 2)*(j + 9)
Let d = 4729 - 4729. Let g(f) be the second derivative of -10*f + f**3 + 0*f**2 + d + 1/4*f**4. Factor g(j).
3*j*(j + 2)
Let 50/11*s - 48/11*s**3 - 2/11*s**5 + 0 + 20/11*s**2 - 20/11*s**4 = 0. Calculate s.
-5, -1, 0, 1
Let m(b) be the second derivative of b**6/120 - b**5/80 - 23*b**4/48 - 13*b**3/8 - 9*b**2/4 - 260*b + 3. Suppose m(n) = 0. What is n?
-3, -1, 6
Let u(j) be the first derivative of j**4/4 + j**3/3 - 8*j**2 - 16*j + 7123. Suppose u(d) = 0. Calculate d.
-4, -1, 4
Let g(r) be the first derivative of -r**7/1120 + 13*r**6/160 - 9*r**5/4 - 25*r**4/2 + 23*r**3 - r - 117. Let s(q) be the third derivative of g(q). Factor s(x).
-3*(x - 20)**2*(x + 1)/4
Let g = -5033514/19 - -264922. Suppose -4/19*v**2 - 2/19*v**5 + 0*v + 0 + 2/19*v**3 + g*v**4 = 0. What is v?
-1, 0, 1, 2
Let g(k) be the first derivative of -85*k**5/2 + 105*k**4 - 135*k**3/2 - 5*k**2/2 - 1289. Factor g(l).
-5*l*(l - 1)**2*(85*l + 2)/2
Let u(a) be the first derivative of 1/6*a**4 + 0*a**3 + 0*a + 0*a**2 + 318 + 4/15*a**5 + 1/9*a**6. Factor u(t).
2*t**3*(t + 1)**2/3
Let k = 116678/126105 