 - 1)*(4*o - 1)**2
Let g(n) = 7*n - 6*n**2 + 4*n - 3*n + n**3 + 110 - 107. Let l be g(7). Find p such that 27*p - 29*p + 3*p**2 - 34*p + l = 0.
6
Factor -62/3*c + 1/3*c**2 + 961/3.
(c - 31)**2/3
Let u(a) be the second derivative of a**5/60 - a**4/18 - 14*a**3/3 + 60*a**2 - 146*a + 7. Solve u(l) = 0 for l.
-10, 6
Let w(u) be the second derivative of 23*u**5/5 - 274*u**4/3 + 458*u**3/3 + 44*u**2 + 3201*u. Let w(s) = 0. Calculate s.
-2/23, 1, 11
Let t be (-30)/80 + 93/120. Let h be (1 - 3 - 4)*5/(-25). Factor h*g - t*g**2 - 4/5.
-2*(g - 2)*(g - 1)/5
Suppose g + 64 = -5*s - 311, 4*g + 3*s = -1483. Let r = 374 + g. Factor 12/5*q - 8/5*q**3 + 4/5 + 3/5*q**r - 3/5*q**2.
(q - 2)**2*(q + 1)*(3*q + 1)/5
Suppose -4*b = 2*h - 26, 2*b = -b - 4*h + 12. Suppose 76 = b*p - 4. What is l in 5*l - 11*l**2 - 6*l - l + p*l**2 = 0?
-2, 0
Let c = -6123 + 6148. Let b(s) be the first derivative of c*s + 13 + 1/3*s**3 + 5*s**2. Factor b(k).
(k + 5)**2
Determine x so that 6/11*x**5 - 842700/11 - 1984332/11*x**2 + 2394010/11*x + 436224/11*x**3 - 3208/11*x**4 = 0.
2/3, 1, 3, 265
Suppose 0 = -4*s - 111 - 9. Let q = s - -34. Factor d + 2*d + d - q*d**3.
-4*d*(d - 1)*(d + 1)
Let g(r) be the first derivative of 2*r**3/3 - 404*r**2 + 1608*r - 2757. Factor g(u).
2*(u - 402)*(u - 2)
Let t be 2*(0 + 1) - (-88172)/(-5358). Let j = -34/19 - t. Factor 50/3*x**3 + 14/3*x - 2/3 + 8/3*x**5 - j*x**2 - 32/3*x**4.
2*(x - 1)**3*(2*x - 1)**2/3
Let j(d) = -5*d**4 - 11*d**3 - 2*d**2 - 5*d. Let q(l) = 4*l**4 + 9*l**3 + 2*l**2 + 6*l. Let w(z) = 6*j(z) + 5*q(z). Find c such that w(c) = 0.
-2, -1/10, 0
Let y(c) be the first derivative of 2*c**3/21 - 198*c**2/7 + 19602*c/7 - 63. Suppose y(h) = 0. Calculate h.
99
Determine p, given that -65/3*p**4 - 179/3*p**2 + 28/3 - 5*p - 67*p**3 = 0.
-7/5, -1, 4/13
Find f such that -9/2*f**3 + 27/4 - 81/4*f + 39/2*f**2 + 3/4*f**5 - 9/4*f**4 = 0.
-3, 1, 3
Let d(a) be the second derivative of 0*a**2 + 2 + 4*a + 31/21*a**3 - 1/42*a**4. Factor d(i).
-2*i*(i - 31)/7
Let u(l) be the third derivative of -l**7/735 - 37*l**6/420 - 6*l**5/35 + 722*l**2. Factor u(h).
-2*h**2*(h + 1)*(h + 36)/7
Let x(r) = -2*r**4 - 2*r**3 + 3*r**2. Let q(c) = -19*c**4 + 196*c**3 - 1719*c**2 - 9890*c - 7935. Let m(a) = -q(a) + 7*x(a). Determine s, given that m(s) = 0.
-3, -1, 23
Let z(i) = 163*i + 15016. Let a be z(-92). Factor a*g + 20/3*g**3 - 55/3*g**2 - 15/2 - 5/6*g**4.
-5*(g - 3)**2*(g - 1)**2/6
Let o be -9 + 18/(16/8) + (-40)/(-32). Find h, given that -1/4*h**2 + o + h = 0.
-1, 5
Let n = -38/137 + 1224/3425. Let u(i) be the first derivative of 0*i + 2*i**3 + 35 + n*i**5 - 9/5*i**2 - 7/10*i**4. Factor u(s).
2*s*(s - 3)**2*(s - 1)/5
Suppose 0 = b - 4*d - 16, 261*b + d = 258*b + 9. Let c(f) be the first derivative of 3/4*f**b + 32 + 0*f - 9/2*f**2 - 2*f**3. Let c(k) = 0. Calculate k.
-1, 0, 3
Let v(w) be the first derivative of -1/18*w**3 - 7/12*w**2 + 4/3*w - 109. Determine h, given that v(h) = 0.
-8, 1
Find c, given that -44*c**2 - 1/3*c**4 - 400/3*c - 19/3*c**3 - 448/3 = 0.
-7, -4
Suppose f - 600 = -596. Let v(b) be the first derivative of 4/7*b**3 - 2/7*b**f - 19 - 4/35*b**5 + 0*b**2 + 0*b. Factor v(r).
-4*r**2*(r - 1)*(r + 3)/7
Let q = 470/107 - -294766/321. Let p = 952 - q. Solve 49/3*n**4 + 16/3 - 56*n**3 + p*n**2 + 32*n = 0 for n.
-2/7, 2
Let c(l) = -l**2 + 10*l + 81. Let n be c(15). Let y(u) be the third derivative of 0*u + 5*u**2 + 0*u**4 + 0 + 1/30*u**5 + 0*u**3 + 1/30*u**n. Factor y(f).
2*f**2*(2*f + 1)
Factor 2608*s - 3790 - 265413*s**2 - 36*s**3 + 462 + 265013*s**2.
-4*(s - 2)*(s + 16)*(9*s - 26)
Let o(c) be the third derivative of 0*c**4 + 0*c**3 - 56 + 1/20*c**5 + 0*c - 2*c**2 - 1/280*c**7 + 3/160*c**6. Suppose o(r) = 0. Calculate r.
-1, 0, 4
Let m(y) = -y**3 + 18*y**2 - 17*y + 3. Let v be m(17). Suppose 0 = g - 7 + v. Factor g*r + 14*r**2 - 10*r**3 - 10*r + 2*r.
-2*r*(r - 1)*(5*r - 2)
Let i(w) be the third derivative of 0*w + 3/560*w**7 - 43/80*w**5 + 1/10*w**6 - 13/16*w**3 - 85*w**2 - 2 + w**4. Suppose i(z) = 0. Calculate z.
-13, 1/3, 1
Let a = -39 - -14. Let q = a + 27. Determine b so that 44*b - 28*b**q - 26 + 44*b**3 - 40*b**3 + 6 = 0.
1, 5
Let w(u) be the third derivative of 1/1064*u**8 + 0*u**4 - 8/1995*u**7 + 0*u - 1/76*u**6 - 2/285*u**5 + 0 - 4*u**2 + 0*u**3. Find f, given that w(f) = 0.
-1, -1/3, 0, 4
Let -56/11*j**4 + 0*j + 200/11*j**3 - 192/11*j**2 + 0 + 2/11*j**5 = 0. What is j?
0, 2, 24
Let o(a) = -64*a**3 - 295*a**2 - 1890*a - 2923. Let y(v) = -18*v**3 - 98*v**2 - 630*v - 974. Let x(f) = 2*o(f) - 7*y(f). What is u in x(u) = 0?
-3, 54
Let d(a) be the third derivative of a**6/540 - 13*a**5/18 + 4225*a**4/36 - 274625*a**3/27 + 3*a**2 - 12*a. Factor d(x).
2*(x - 65)**3/9
Let j(h) be the third derivative of 176/3*h**3 - 2/3*h**4 + 0 + 0*h - 186*h**2 + 1/330*h**5. Factor j(v).
2*(v - 44)**2/11
Let h(d) be the first derivative of -d**3/12 + 963*d**2/4 - 927369*d/4 - 1132. Factor h(k).
-(k - 963)**2/4
Let a(w) be the third derivative of 5/3*w**4 + 13*w + 0 - 2*w**2 - 11/4*w**5 + 0*w**3 + 1/6*w**6. Suppose a(s) = 0. What is s?
0, 1/4, 8
Suppose 5*d = 3*f - 46, 0 = 2*f + 4*d - 805 + 833. Factor -25/3 - 5/2*y + 5/6*y**f.
5*(y - 5)*(y + 2)/6
Let q(w) be the second derivative of w**5/20 - 6073*w**4/12 + 1537228*w**3 - 4608648*w**2 - 7937*w. Factor q(a).
(a - 3036)**2*(a - 1)
Let g = 19214 + -19193. Let h(d) be the third derivative of 0*d + 0 + 0*d**6 - g*d**2 - 1/210*d**7 + 0*d**4 - 1/336*d**8 + 0*d**5 + 0*d**3. Factor h(k).
-k**4*(k + 1)
Factor -24 - 120*t - 9084*t**2 + 37 + t**3 - 285 + 9075*t**2.
(t - 17)*(t + 4)**2
Let f(k) = 3053*k + 48851. Let u be f(-16). Factor -1/4*p**u - 121 - 132*p - 45/4*p**2.
-(p + 1)*(p + 22)**2/4
Let c(m) = 6*m - 86. Let y be c(27). Let -284*k - 76*k**2 + 147*k + y - 4*k**3 + 141*k = 0. Calculate k.
-19, -1, 1
Let r = 343 + -347. Let h be (9/(-60))/(r/32). Factor -3/5*z**2 + 0 - h*z.
-3*z*(z + 2)/5
Let h(n) = -2*n**3 - 1781*n**2 - 154832*n + 480630. Let a(v) = -13*v**3 - 10684*v**2 - 928993*v + 2883775. Let l(y) = -3*a(y) + 17*h(y). Factor l(z).
5*(z - 3)*(z + 179)**2
Let r(g) be the third derivative of 0*g + 0*g**3 + 0 - 30*g**2 - 1/30*g**6 + 1/6*g**4 + 0*g**5. Factor r(a).
-4*a*(a - 1)*(a + 1)
Solve -168/17 - 62/17*a - 2/17*a**2 = 0 for a.
-28, -3
Factor -57/2*o + 3/2*o**2 + 27.
3*(o - 18)*(o - 1)/2
Suppose -15 - 9 = -8*m. Factor 0*g**3 + 12*g + 221 + 5*g**m + 21*g**2 - 229 - 3*g**2.
(g + 2)**2*(5*g - 2)
Suppose -5*k + 6*v = v - 60, 2*v - 21 = -3*k. Let 6*z**3 + k*z**2 - 4*z**3 - 17*z**2 + 6*z = 0. Calculate z.
0, 1, 3
Suppose 5222934/5*v - 1624332474/5 + 2/5*v**3 - 5598/5*v**2 = 0. What is v?
933
Let j(i) be the first derivative of -i**4 + 64*i**3/3 - 126*i**2 - 281. Factor j(k).
-4*k*(k - 9)*(k - 7)
Let w(t) be the second derivative of -3*t**5/20 - 7*t**4 + 62*t**3 - 192*t**2 - 254*t. Factor w(z).
-3*(z - 2)**2*(z + 32)
Let l = 1/291490 - -72872/145745. Factor -l + 1/2*c**2 - 1/2*c + 1/2*c**3.
(c - 1)*(c + 1)**2/2
Let h(o) be the first derivative of 4*o**3/21 - 1360*o**2/7 + 388*o + 558. Factor h(t).
4*(t - 679)*(t - 1)/7
Factor -225/2*r - 5/4*r**3 + 180 + 85/4*r**2.
-5*(r - 8)*(r - 6)*(r - 3)/4
Let q = -203 - -212. Find b, given that -8*b + q - 2*b**2 - 12 - 5 = 0.
-2
Suppose -1451*s**2 - 36*s**4 - 202906*s + 204922*s - 1901*s**2 + 672*s**3 - 324 = 0. Calculate s.
1/3, 9
Let t(n) be the first derivative of 4/3*n + 45 - n**2 + 2/9*n**3. Suppose t(s) = 0. What is s?
1, 2
Suppose 0 = -5*k - 20, x + x + 5*k = -16. Let q be -4 + (-10)/2 - (-1175)/125. Suppose 0 + 0*s + q*s**x = 0. What is s?
0
Suppose -8*k + 25 = -3*k. Let n be 9 + -1 + ((-25)/k - -3). Factor -6*s**3 + 5*s**5 - 10*s**2 - 14*s**3 + 9*s + n*s + 0*s**4 + 10*s**4.
5*s*(s - 1)**2*(s + 1)*(s + 3)
Let p(x) = -4*x**3 - 3695*x**2 - 7353*x - 3707. Let y(z) = -2*z**3 - 1846*z**2 - 3676*z - 1850. Let g(l) = 4*p(l) - 10*y(l). Factor g(s).
4*(s + 1)**2*(s + 918)
Let k = 166 + -176. Let b be (-96)/(-90) - (-1)/k*4. Let 11/2*o**4 - b + 0*o + 31/6*o**2 + 53/6*o**3 + 7/6*o**5 = 0. What is o?
-2, -1, 2/7
Let 10712*y**2 + 1092416/3*y + 311/3*y**3 - 1124864/3 + 1/3*y**4 = 0. Calculate y.
-104, 1
Let q(x) be the second derivative of -x**4/28 - 23*x**3/14 - 135*x**2/7 - 2884*x + 1. Factor q(s).
-3*(s + 5)*(s + 18)/7
Suppose g + g + 12 = 5*g. Let s(b) be the second derivative of 0*b**2 + 0*