Let u(w) be the first derivative of -w**4/4 - 8*w**3/3 - 4*w**2 - 7*w - 20. Let m be u(-7). Let 102*c + m*c**2 - 103*c + c**2 = 0. Calculate c.
0, 1
Let y(q) be the second derivative of -5*q**4/12 - 3215*q**3/3 - 2067245*q**2/2 - 49*q - 30. Solve y(x) = 0 for x.
-643
Let b be (28/(-6) + 4)/((-5)/15). Determine l so that 16*l**4 - 4*l**5 - 8 - 68*l**2 - 16*l**3 + 60*l**b + 24*l - 4*l = 0.
-1, 1, 2
Let s(c) = 1296*c + 9074. Let y be s(-7). Factor y*v + 2/13*v**4 + 30/13*v**2 + 14/13*v**3 + 8/13.
2*(v + 1)**3*(v + 4)/13
Let b(a) = -a**3 - 26*a**2 - 49*a - 21. Let s be b(-24). Determine v so that 10 + 13*v + 16*v**3 + 0*v**4 + 24*v**2 + 4*v**4 + s*v - 6 = 0.
-1
Let c(v) = 2*v**2 + 12*v - 11. Let t be c(-7). Factor -6*a + 4*a**3 + 10*a**2 + t*a**3 - 69*a - 2*a**3.
5*a*(a - 3)*(a + 5)
Determine o so that -1148296 + 1148746 + 7343*o**3 - 2498*o**3 + 5835*o + 5938*o**2 - 1805*o**4 + 13777*o**2 = 0.
-2, -3/19, 5
Factor -1/5*j**3 - 556/5 + 4/5*j + 139/5*j**2.
-(j - 139)*(j - 2)*(j + 2)/5
Let z(c) be the first derivative of -47*c**4/4 - 49*c**3/2 - 3*c**2 - 221*c - 77. Let v(a) be the first derivative of z(a). Determine p, given that v(p) = 0.
-1, -2/47
Determine b so that 59/8*b**2 + 33/2 + 227/8*b + 1/8*b**4 - 35/8*b**3 = 0.
-1, 4, 33
Suppose 5*w = 0, 78 = v - 4*w - w. Let k = -54 + v. Factor -3*p**3 - 54 - 25*p - 14*p - k*p**2 - 24*p.
-3*(p + 2)*(p + 3)**2
Factor -2166 + 73/2*h**2 - 608*h - 1/2*h**3.
-(h - 38)**2*(h + 3)/2
Let s be 3 + -3*(-12)/(-9) - (48 - (17 + 35)). Solve -152/3*n**2 - 44*n**s - 4/3*n**4 + 4 + 22/3*n**5 - 34/3*n = 0 for n.
-1, 2/11, 3
Let p be -11*(-12)/(-132)*-24. Determine h so that p + 903*h**3 - 147*h**4 + 846*h**2 + 1740/7*h = 0.
-2/7, 7
Let t be 4/(-10)*(-615)/82 - -17. Suppose 0 = -746*j + 756*j - t. Determine o so that -1/6*o**j - 1 + 5/6*o = 0.
2, 3
Suppose -3/2 + f**4 + 5*f**3 - 23/2*f**2 + 31/4*f - 3/4*f**5 = 0. What is f?
-3, 1/3, 1, 2
Let g be 2 - (-5 - (-901)/187 - (30/(-55))/3). Factor 0*k**3 + 2/13*k**4 - 4/13*k**g + 2/13 + 0*k.
2*(k - 1)**2*(k + 1)**2/13
Let g(l) be the first derivative of 5/48*l**4 + 0*l**2 - 28 + 20*l - 1/24*l**3. Let s(x) be the first derivative of g(x). Find y such that s(y) = 0.
0, 1/5
Suppose -l - 4*y + 17 = 0, 0 = l + 2*y - 5 - 6. Let r be (2 + l*-2)*-1. Factor -b**5 - r*b**2 + 7*b**3 + 3 + 4*b**2 + 2*b**2 - 12*b + 5.
-(b - 2)*(b - 1)**2*(b + 2)**2
Find r such that 30*r**5 - 15*r**5 + 144 - 7*r**2 + 35*r + 207*r**2 - 11*r**5 - 359*r - 24*r**4 = 0.
-3, 1, 3, 4
Let u(h) be the third derivative of -1/80*h**6 + 34*h**2 + 1/45*h**5 + 0 + 0*h + 1/1260*h**7 + 0*h**3 + 0*h**4. Determine c, given that u(c) = 0.
0, 1, 8
Let h(z) = -2*z**2 + 5. Let y(l) = 43*l**2 - 101*l + 18. Let x(c) = -4*h(c) + y(c). Factor x(w).
(w - 2)*(51*w + 1)
Let o(g) = -3 - 3*g + 4*g**2 - 3*g - 3 - 10*g**3. Let b(w) = 11*w**3 + 3*w - 8625 + 8632 - 4*w**2 + 4*w + 0*w. Let c(x) = -6*b(x) - 7*o(x). Factor c(n).
4*n**2*(n - 1)
Let g(s) = 223*s**2 + 135*s - 486. Let h(b) = 84*b**2 + 45*b - 162. Let r(o) = -3*g(o) + 8*h(o). Factor r(p).
3*(p - 9)*(p - 6)
Let s be 4*7/(-196) - 57/(-7). Let z be ((-290)/36 + s)*-2. Factor -2/9*q - 1/9*q**4 + z + 2/9*q**3 + 0*q**2.
-(q - 1)**3*(q + 1)/9
Suppose 9*o - 5*o - 5*x + 55 = 0, 0 = 2*o - 4*x + 26. Let y(w) = -5*w**2 - 30*w + 75. Let c(n) = -5. Let l(k) = o*c(k) - y(k). Solve l(u) = 0 for u.
-6, 0
Let u(y) be the third derivative of 14/3*y**3 + 0 - 83*y - 1/120*y**5 + 13/24*y**4 + 2*y**2. Determine v so that u(v) = 0.
-2, 28
Let m be -13 + 14 - 3/(-33). Let n = m - 86/99. Factor 1/9*j + 0 + 1/9*j**3 + n*j**2.
j*(j + 1)**2/9
Let n = -363 + 365. Factor 28*o - 21*o + 21 + 11*o**2 - 4*o**n + 3*o**3 + 38*o + 20*o**2.
3*(o + 1)**2*(o + 7)
Let g(v) be the third derivative of 49*v**2 + 1/30*v**5 + 0 + 0*v + 7/6*v**4 + 49/3*v**3. Find h, given that g(h) = 0.
-7
Let v(o) be the first derivative of -2*o**5/75 - o**4/3 + 2*o**3/45 + 2*o**2/3 + 4257. Solve v(i) = 0.
-10, -1, 0, 1
Let l(d) be the first derivative of -4/5*d - 7/10*d**3 + 1/50*d**5 + 1/8*d**4 + 23/20*d**2 - 37. Factor l(f).
(f - 1)**3*(f + 8)/10
Let y(o) be the first derivative of 1/30*o**5 + o**3 + 1/3*o**4 - 14 + 0*o**2 + 7*o. Let h(u) be the first derivative of y(u). Determine t so that h(t) = 0.
-3, 0
Let h = 720 - -21. Let y = h + -1479/2. Factor -1/2 - y*u**2 - 2*u.
-(u + 1)*(3*u + 1)/2
Suppose -o + 5*y - y = 13, -y = 0. Let u(g) = -g**3 - 13*g**2 + 2. Let p be u(o). Suppose 8 - 20*x + 2*x**p + 7*x + 5*x = 0. Calculate x.
2
Suppose -1/7*b**2 + 0 - 216/7*b = 0. What is b?
-216, 0
Let x(b) be the third derivative of -38*b**2 + 0 - 1/420*b**6 + 8/21*b**3 + 1/30*b**5 + 0*b - 1/6*b**4. Factor x(v).
-2*(v - 4)*(v - 2)*(v - 1)/7
Suppose -579 = -23*s - 579. Suppose 0 = 4*w + 3*v - 223, -81 = -2*w + 2*v + 13. What is h in -29 - 20*h**2 - 2*h**3 + 17 - w + s*h**2 - 64*h = 0?
-4, -2
Let r = -4315401/2 - -2174874. Solve 3/2*k**2 - 321*k + r = 0.
107
Let u(g) = -4*g**3 + g**2 - g + 1. Let s(r) = -2*r**4 + 106*r**3 + 128*r**2 + 80*r - 10. Let b(f) = -2*s(f) - 20*u(f). Factor b(l).
4*l*(l - 35)*(l + 1)**2
Let g be (25/(-55))/((-16490)/4268). Factor 22/17*r - 8/17 + 2/17*r**3 - 18/17*r**2 + g*r**4.
2*(r - 1)**3*(r + 4)/17
Let x(f) be the third derivative of -f**5/110 - 5*f**4/66 + 13*f**3/33 + 1293*f**2 + 1. Factor x(r).
-2*(r - 1)*(3*r + 13)/11
Let 90*v + 0 + 3/8*v**4 - 39*v**2 + 21/8*v**3 = 0. What is v?
-15, 0, 4
Suppose -37 = -3*c + 2. Let b be 5 + 6 + -5 + -4. Factor -4*k - 6*k - k**b + c*k - 9*k - 5.
-(k + 1)*(k + 5)
Let y = 833 + -823. Let u(t) be the second derivative of -40/3*t**3 + 0 - 15/4*t**4 + 6*t + y*t**2. Factor u(h).
-5*(h + 2)*(9*h - 2)
Suppose -d = 2*j - 4*j - 10, -4*d - 3*j = -7. Let o be (2 + -3)/(-10 - 225/(-24)). Factor 0*c + 0 - o*c**3 + 4/5*c**2 + 3/5*c**d.
c**2*(c - 2)*(3*c - 2)/5
Let t(n) = n. Suppose 4*m = 6*m - 2, -3*z + 17 = -4*m. Let g = z - 3. Let i(p) = p**2 - 3*p - 9. Let h(f) = g*i(f) - 20*t(f). Factor h(q).
4*(q - 9)*(q + 1)
Let u(f) be the third derivative of -f**6/160 + 7*f**5/60 - 17*f**4/32 + 7*f**3/12 + 24*f**2 + 64*f. Factor u(v).
-(v - 7)*(v - 2)*(3*v - 1)/4
Let k be ((-32)/(-12))/((-18)/(-27)). Let c(n) = n**3 + 4. Let i be c(0). Suppose -55*g**3 + 4*g**k - i*g**2 + 55*g**3 = 0. What is g?
-1, 0, 1
Suppose -3*s + 2*p - 18 = 0, -4*s - 13 = 5*p - 4*p. Let m = s - -13. Factor 39*l**4 - m*l + 5*l**5 + 116*l**2 + 31*l**3 - 2 - 117*l**2 + 9*l**5.
(l + 1)**3*(2*l - 1)*(7*l + 2)
Let k(s) be the third derivative of 0*s + 1/3*s**5 - 13/96*s**6 - 2/21*s**7 + 0*s**3 + s**2 + 15/448*s**8 - 1 + 5/24*s**4. Solve k(r) = 0.
-1, -2/9, 0, 1, 2
Let p = -126 + 129. Factor -217*m - 413 - p*m**2 + 31*m - 2470.
-3*(m + 31)**2
Let b = -1346147/2 - -673075. Let v = 12 - 21/2. Suppose -3/2*z**2 + v*z + b - 3/2*z**3 = 0. Calculate z.
-1, 1
Factor -1/2*o**4 - 33/4*o**2 - 23/4*o**3 + 0 + 27*o.
-o*(o + 4)*(o + 9)*(2*o - 3)/4
Suppose -7*g - 10 = -12*g. Suppose 4*n + 6 = 7*n. Suppose -30*w**2 + 12*w**g + 19*w**n + w + 7*w = 0. Calculate w.
-8, 0
Let f(u) be the third derivative of u**6/60 + 9*u**5/20 + u**4/3 - 16*u**3/3 - 103*u**2. Let l(a) = -a**2 - 2*a + 2. Let z(i) = -f(i) - 5*l(i). Factor z(n).
-2*(n - 1)*(n + 1)*(n + 11)
Let m = -2279 - -2283. Suppose -5*l - 25 = -0*l, -3*l = -3*u + 21. Factor -96/5*w**3 - 13824/5*w + 1728/5*w**u + 41472/5 + 2/5*w**m.
2*(w - 12)**4/5
Let l(j) = 40*j - 222. Let a be l(6). Suppose -2*b = -3*t - 9, 17*t - 3 = 5*b + a*t. Find s, given that 0 + 3/7*s**4 + b*s**2 - 6/7*s**3 + 0*s = 0.
0, 2
Let v be 1/(-3) - (-14)/6. Let f = -176513/5 - -35303. Factor -1/5*l**v + f*l - 1/5.
-(l - 1)**2/5
Suppose -21/5*d**2 - 36/5*d - 3/5*d**3 + 0 = 0. Calculate d.
-4, -3, 0
Let s(h) be the third derivative of -h**7/2940 + h**6/140 - 2*h**5/105 - 11*h**3/2 - 19*h**2. Let x(r) be the first derivative of s(r). Factor x(c).
-2*c*(c - 8)*(c - 1)/7
Factor -2/7*b**2 + 120 - 32/7*b.
-2*(b - 14)*(b + 30)/7
Let q(t) be the second derivative of -5*t**4/12 + 645*t**3/2 + 1945*t**2 + 9095*t. Suppose q(m) = 0. Calculate m.
-2, 389
Suppose -15 = 3*c - 5*x, -7*x = -2*c - 10*x - 10. Let l be (24/21)/(c/7 + 1). Factor 89*p**3 - 40*p**2 - 15*p**l - 9*p**4 + 28*p**3 - 4*p**5 - 165*p**3 - 12*p.
-4*p*(p + 1)**3*(p + 3)
Factor 13/4 + 1/4*u**3 - 1/4*u - 13/4*u**2.
(u - 13)*(u - 1)*(u + 1)/4
Let x be 8 - 26 - -23 - 8/(24/15). Find a, given that 