
Let w(d) be the first derivative of 23/2*d**2 - 1/4*d**4 + 1/80*d**5 + 2*d**3 - 26 + 0*d. Let q(x) be the second derivative of w(x). Factor q(k).
3*(k - 4)**2/4
Suppose 23*c - 6 = 20*c. Determine i, given that -20*i**2 - 28*i + 10*i**c - 66*i - 36 = 0.
-9, -2/5
Let g(j) be the second derivative of j**7/21 - 13*j**6/5 + 51*j**5/2 - 217*j**4/6 - 1154*j. Determine k, given that g(k) = 0.
0, 1, 7, 31
Let s be (-34)/6 + 31959/5427. Determine b so that -4/3*b**2 + 4/3 - 2/9*b**3 + s*b = 0.
-6, -1, 1
Let b(n) = -3*n + 2*n + n**3 - 2*n**2 + 6*n**2 - 7*n**2 - 3. Let l be b(4). Determine w so that -2 + 14*w**2 + 8 - l*w**2 - 17*w = 0.
2/5, 3
Let y(f) be the first derivative of f**6/20 - 6*f**5/5 + 21*f**4/2 - 36*f**3 + 78*f - 52. Let r(l) be the first derivative of y(l). Factor r(o).
3*o*(o - 6)**2*(o - 4)/2
Let l(h) be the third derivative of -h**8/5040 + h**7/840 + h**6/1080 - h**5/120 - 5*h**3 - h**2. Let o(u) be the first derivative of l(u). Factor o(g).
-g*(g - 3)*(g - 1)*(g + 1)/3
Let i be 240/18*(-204)/(-170). Let u(c) be the second derivative of -1/70*c**5 + 0*c**2 - 2/21*c**3 + i*c - 1/14*c**4 + 0. Solve u(p) = 0 for p.
-2, -1, 0
Let j(i) be the second derivative of i**7/42 - 23*i**6/30 - 27*i**5/20 + 67*i**4/12 + 59*i**3/3 + 24*i**2 - 2805*i. Solve j(u) = 0.
-1, 2, 24
Let -64*a**2 - 99*a**2 - 84 + 488*a + 93*a**3 - 149*a**3 + a**4 + 94*a**3 - 280*a = 0. Calculate a.
-42, 1, 2
Suppose -3781*t - 4*t**2 - 910189 - 842787 - 1515*t = 0. Calculate t.
-662
Solve -17*u**2 - 1/2*u**5 + 7/2*u**3 + 2*u**4 + 0 + 12*u = 0.
-3, 0, 1, 2, 4
Factor 21*k**3 + 128*k + 6*k**3 - 48*k**2 + 45*k**3 + 276*k**2 - 91 + 111.
4*(2*k + 5)*(3*k + 1)**2
Let g be 10/14*21/6 - 49/98. Suppose -1/7*l**3 - 20/7 + 9/7*l**g + 12/7*l = 0. Calculate l.
-2, 1, 10
Let m = -489 + 645. Let s be (25/(-20))/((-65)/m). Factor 0*y + 3*y**2 + 0 - 3/2*y**4 + 3/2*y**s.
-3*y**2*(y - 2)*(y + 1)/2
Let l(c) be the third derivative of 0*c - 2/3*c**3 - 78*c**2 + 1/12*c**4 + 1/30*c**5 + 0. Let l(o) = 0. Calculate o.
-2, 1
Let g(x) = 4*x - 3. Let l be g(2). Factor 22*a - 6 - l*a + 4*a**2 - 12*a - 5*a**2.
-(a - 3)*(a - 2)
Let d(h) be the third derivative of -1/18*h**4 + 0*h + 106*h**2 + 1/90*h**6 - 4/27*h**3 + 0 + 1/135*h**5 + 2/945*h**7. Factor d(q).
4*(q - 1)*(q + 1)**2*(q + 2)/9
Let p(d) = 21*d**2 - 1108*d - 1121. Let j(m) = -80*m**2 + 4430*m + 4480. Let y(n) = -4*j(n) - 15*p(n). Find r, given that y(r) = 0.
-1, 221
Let k(l) be the third derivative of l**6/420 + l**5/14 - 11*l**4/28 + 17*l**3/21 - 566*l**2. Factor k(v).
2*(v - 1)**2*(v + 17)/7
Suppose -5*q + d + 38 = 3*d, -5 = -q - 3*d. Factor g**3 + 10 + 18 - q*g + 20 - 5*g**2.
(g - 4)**2*(g + 3)
Let a = -3074 + 3074. Let o(h) be the first derivative of 0*h + a*h**4 + 0*h**3 + 0*h**2 - 1/25*h**5 - 1/15*h**6 - 7. Determine l, given that o(l) = 0.
-1/2, 0
Let o(q) be the first derivative of q**3/12 - 4*q**2 + 255*q/4 + 1409. Factor o(x).
(x - 17)*(x - 15)/4
Let i(p) be the second derivative of p**5/4 + 75*p**4/4 + 320*p**3/3 + 210*p**2 - 5548*p. Let i(v) = 0. What is v?
-42, -2, -1
Let x(c) = c**2 - 9*c - 49. Let q be x(13). Suppose -21 = -3*y + q*d, 4*y - 3*d + 12 = -7*d. What is j in 13/4*j**3 + 3/2*j**4 + 3*j**y + j + 1/4*j**5 + 0 = 0?
-2, -1, 0
Let q(t) be the first derivative of t**4/12 - 11*t**3 + 833*t**2/2 - 2401*t/3 - 2593. Factor q(r).
(r - 49)**2*(r - 1)/3
Let l(t) be the second derivative of t**4/66 + 119*t**3/33 - 130*t**2 + 4*t - 81. Let l(b) = 0. What is b?
-130, 11
Let c(t) be the second derivative of 8/3*t**3 + 2*t - 1/3*t**4 - 6*t**2 + 18. Factor c(w).
-4*(w - 3)*(w - 1)
Let c be 24/660*11 - (-2 + (-12)/(-5)). Let i(z) be the second derivative of 2/15*z**6 + 0*z**2 - 4*z + c*z**3 + 2/5*z**5 + 1/3*z**4 + 0. Factor i(b).
4*b**2*(b + 1)**2
Let f(p) be the second derivative of p**6/15 + p**5/10 - 5*p**4/3 - 4*p**3/3 + 24*p**2 - 9*p - 48. Factor f(o).
2*(o - 2)**2*(o + 2)*(o + 3)
Let d(o) be the first derivative of -2*o**3/27 - 385*o**2/9 - 256*o/3 + 12313. Determine s, given that d(s) = 0.
-384, -1
Let h = -1283 - -52619/41. Let l = h - -34/123. Let -22/9*g + l*g**3 + 4/3 + 2/3*g**2 - 2/9*g**4 = 0. Calculate g.
-2, 1, 3
Let h(w) be the third derivative of -3*w**6/100 + 26*w**5/75 - w**4 - 16*w**3/15 - 1372*w**2. Determine t, given that h(t) = 0.
-2/9, 2, 4
Let j be (-20)/(-6) + (-4)/(-6) - (-52 - -56). Let y(l) be the second derivative of -1/17*l**3 + j + 20*l + 2/17*l**2 + 1/102*l**4. Factor y(b).
2*(b - 2)*(b - 1)/17
Let l be 0/(16 - (-7 + 21 + 4)). Factor -8/3*y**2 - 1/6*y**4 + 0 + l*y - 4/3*y**3.
-y**2*(y + 4)**2/6
Find b, given that -1701/2*b - 3/4*b**2 - 1698 = 0.
-1132, -2
Let a be (-15)/(-147)*7 + (-111)/(-21). Find x such that -a*x - 1/3*x**2 + 0 = 0.
-18, 0
Suppose -210 = -152*k + 145*k. Suppose -33*q = -k*q - 12. Factor -i**2 + 0 + 11/2*i**3 - 9/2*i**q + 0*i.
-i**2*(i - 1)*(9*i - 2)/2
Let t(o) be the third derivative of -12 + 0*o + 55/24*o**4 - 1/24*o**6 + 4*o**2 - 1/3*o**5 - 5*o**3. Factor t(j).
-5*(j - 1)**2*(j + 6)
Let t(s) be the second derivative of 129*s + 7/3*s**4 + 0*s**2 - 2*s**3 - 19/20*s**5 - 1 + 2/15*s**6. Factor t(h).
h*(h - 2)**2*(4*h - 3)
Let y(a) = 2*a**2. Let f(l) = -20*l**2 - 20*l - 12. Let h(d) = -41*d**2 - 40*d - 23. Let p(r) = -7*f(r) + 3*h(r). Let q(w) = p(w) - 6*y(w). Factor q(i).
5*(i + 1)*(i + 3)
Let j be (2/4 + -3)*(-2)/1. Factor -3*u**j + 75*u - 36*u**2 + 416 - 2*u**5 - 64*u**2 - 436 + 50*u**3.
-5*(u - 1)**4*(u + 4)
Let r be (-4)/(-10) - 9082/21280. Let a = r - -59/112. Factor 0*u + u**2 + 0 + a*u**3.
u**2*(u + 2)/2
Let g(m) = -15*m - 330. Let w be g(-23). What is s in 735*s - 55*s**3 + 7*s**2 - 2*s**4 - 22*s**2 - w*s**2 - 5*s**2 - 3*s**4 = 0?
-7, 0, 3
Suppose -56*i + 1761 - 1481 = 0. Let q(b) be the second derivative of -3/5*b**i + 8*b**2 + 2/15*b**6 + 3*b + 0 - 5/3*b**4 + 2*b**3. Factor q(v).
4*(v - 4)*(v - 1)*(v + 1)**2
Let y = 1 - -1. Suppose 2*z - 5*z = y*v - 36, 4*v = 2*z - 24. Factor -z*d**3 + 3*d**3 + 7*d - 4*d + 6*d**2.
-3*d*(d - 1)*(3*d + 1)
Let q(a) = -17*a**3 + 6121*a**2 - 1878836*a + 1872732. Let u(i) = 65*i**3 - 24485*i**2 + 7515345*i - 7490925. Let w(d) = 15*q(d) + 4*u(d). Solve w(j) = 0.
1, 612
Let m(u) = -2*u + 4. Let f(v) = v**2 - 279*v - 16. Let a(j) = -f(j) - 4*m(j). Factor a(s).
-s*(s - 287)
Suppose 0 = 95*h + 104*h - 255*h. Determine r, given that h - 2*r**4 - 14/3*r**2 + 16/3*r**3 + 4/3*r = 0.
0, 2/3, 1
Let q(s) = -77*s - 96. Let m be q(-3). Let l be (130/m)/13*3. What is c in -2/9*c**4 - l*c**5 + 0*c + 0*c**2 + 0*c**3 + 0 = 0?
-1, 0
Suppose -65*z = -10*z - 1485. Find f, given that -19*f**2 + 12*f**2 + 16 + 10*f**2 + 8 + z*f = 0.
-8, -1
Let l(w) be the third derivative of w**4/24 + w**2. Let g be l(4). Factor 4*u**g + 2*u - 2*u**2 - 2*u**5 - 2*u**2 + 0*u.
-2*u*(u - 1)**3*(u + 1)
Determine u so that 7/4*u**3 + 13/4*u - 15/4*u**2 - 1 - 1/4*u**4 = 0.
1, 4
Let v = -705 + 1006. Factor 91*u - v + 3*u**3 + 33*u**2 + 376 - 69*u + 83*u.
3*(u + 1)*(u + 5)**2
Determine b, given that 40/7*b**3 - 128/7*b**2 + 0 - 1536/7*b + 4/7*b**4 = 0.
-8, 0, 6
Let h(a) be the first derivative of -a**4/24 - 50*a**3/9 + a**2/12 + 50*a/3 + 2477. Factor h(n).
-(n - 1)*(n + 1)*(n + 100)/6
Let k(d) be the first derivative of -d**3 - 72*d**2 - 141*d - 162. Determine t, given that k(t) = 0.
-47, -1
Suppose 81 = 4*g - 3*i, 10*g - 9*g + 2*i = 12. Let h = g - 16. Factor -1 - 4*s**h + 3 - 4*s**3 + 31*s - 27*s + 2.
-4*(s - 1)*(s + 1)**2
Let o be -6 + (-1 - (-11 + -8)). Factor o*r**2 + 20062*r**3 + 6 - 20064*r**3 - 18*r + 2.
-2*(r - 4)*(r - 1)**2
Let f(x) be the third derivative of -x**8/140 + 3*x**7/50 + 43*x**6/200 - 79*x**5/25 + 99*x**4/10 - 8*x**3 - 755*x**2. Find u, given that f(u) = 0.
-4, 1/4, 2, 5
Suppose -41*m = -55*m + 896. Let p be (-80)/(-182) - m/416. Let 0 + p*w**4 + 24/7*w**2 + 16/7*w + 12/7*w**3 = 0. Calculate w.
-2, 0
Let c(u) be the third derivative of -u**6/12 - 2*u**5/15 + 5*u**4/12 + 4*u**3/3 - 4133*u**2. Factor c(f).
-2*(f - 1)*(f + 1)*(5*f + 4)
Suppose 5*j = h - 4, j + 18 = 3*h + 6. Let k(l) be the third derivative of 0*l - 1/240*l**6 + j*l**5 + 0 - 15*l**2 + 1/420*l**7 + 0*l**3 + 0*l**4. Factor k(p).
p**3*(p - 1)/2
Factor -100*l**3 + 159*l + 95*l + 32*l**3 - 126*l**2 + 4*l + 66*l**3 - 130.
-2*(l - 1)**2*(l + 65)
Let s(c) be the first derivative of -c**5/10 - 75*c**4/8 - 73*c**3/6 + 75*c*