the first derivative of -t**5/80 + 3*t**4/32 - 15*t**2 - 53. Let g(v) be the second derivative of i(v). Factor g(w).
-3*w*(w - 3)/4
Let o(m) be the first derivative of -m**5/130 - 2*m**4/39 - m**3/39 + 6*m**2/13 - 72*m - 3. Let i(n) be the first derivative of o(n). Factor i(a).
-2*(a - 1)*(a + 2)*(a + 3)/13
Suppose -4*f - 36*i = -37*i - 201, 5*f = -i + 240. Let d be f/5 - 24/30. What is n in -27/2 - 15*n**2 + 9/2*n**4 - d*n**3 + 63/2*n + 3/2*n**5 = 0?
-3, 1
Let u = -443 + 448. Let 4*z**u - 6*z**4 - 10*z**5 - 9*z**4 + 15*z**2 - 19*z + 25*z = 0. What is z?
-2, -1, -1/2, 0, 1
Let -2491637*p**3 + 3*p**4 + 2491556*p**3 - p + 82*p - 44*p**2 + 84 - 43*p**2 = 0. What is p?
-1, 1, 28
Let j(k) = 7*k**2 - 195*k - 228. Let z be j(29). Let g(v) be the first derivative of 39 + 0*v - 5*v**2 - 5/3*v**3 + 5/4*v**z. Suppose g(x) = 0. Calculate x.
-1, 0, 2
Let p(q) = -4*q**2 - 65*q - 138. Let h(l) = -l**2 + l - 2. Let a(r) = -12*h(r) + 4*p(r). Factor a(o).
-4*(o + 2)*(o + 66)
Let j(b) be the second derivative of 0 - 6*b**2 - 1/6*b**3 - 97*b + 1/12*b**4. Factor j(k).
(k - 4)*(k + 3)
Let -3920*y - 2175*y**3 - 559*y**5 - 1200 - 564*y**5 - 1034*y**2 + 1118*y**5 - 3531*y**2 - 335*y**4 = 0. What is y?
-60, -4, -1
Let d(w) be the first derivative of w**6/150 + 7*w**5/75 + w**4/5 + 11*w**2 - w - 90. Let q(v) be the second derivative of d(v). Let q(g) = 0. What is g?
-6, -1, 0
Let g(b) be the third derivative of 0 + 0*b - 1/8*b**4 - 1/60*b**5 + 3*b**3 - 228*b**2. Determine u so that g(u) = 0.
-6, 3
Let u(l) be the third derivative of -l**8/252 - 2*l**7/35 - l**6/45 + 92*l**5/45 + 4*l**4/3 - 448*l**3/9 - 4*l**2 - 395. Suppose u(k) = 0. What is k?
-7, -4, -2, 2
Let m(k) be the second derivative of k**6/150 + 11*k**5/100 + 9*k**4/20 + 5*k**3/6 + 4*k**2/5 + 4*k + 126. Suppose m(b) = 0. Calculate b.
-8, -1
Let q(u) be the second derivative of -u**4/4 - 6*u**3 + 135*u**2/2 - 1825*u. Factor q(t).
-3*(t - 3)*(t + 15)
Let r be (-17)/((-136)/(-44))*5/(-55)*1. Factor -4*j**3 + 3*j**2 + 20*j + r*j**4 + 25/2.
(j - 5)**2*(j + 1)**2/2
Let u(b) be the second derivative of b**7/168 + b**6/36 - 5*b**5/24 - 5*b**4/4 + 26*b**3/3 - 58*b. Let z(h) be the second derivative of u(h). Factor z(y).
5*(y - 2)*(y + 1)*(y + 3)
Let x(p) be the second derivative of p**6/90 + 73*p**5/60 + 67*p**4/4 + 195*p**3/2 + 288*p**2 + 2117*p. Factor x(o).
(o + 3)**3*(o + 64)/3
Let l(u) be the third derivative of -u**9/2016 - 3*u**8/1120 + u**6/60 - u**3/3 + 41*u**2 + 2. Let s(t) be the first derivative of l(t). Factor s(j).
-3*j**2*(j - 1)*(j + 2)**2/2
Let r(t) = t**2 + 10*t + 25. Let c be r(-8). Let n(f) = -f**2 - 2*f + 102. Let k be n(c). Find b such that 12/5*b**3 + 6/5*b + 3/5*b**4 + 0 + k*b**2 = 0.
-2, -1, 0
Let j be 25/100*5/(5/4). Let m be -19 + 2584/132 - j/(-11). Solve 5/6*b - m - 1/6*b**2 = 0.
1, 4
Let o(k) = -19*k + 437. Let t be o(23). Let m be (t + 6)*7/63. Factor -28/3*r**3 + 4/3 + 4*r**4 - 6*r - m*r**5 + 32/3*r**2.
-2*(r - 2)*(r - 1)**4/3
Let h(q) be the third derivative of q**7/630 - 3*q**6/20 - q**5/180 + 3*q**4/4 + 91*q**2 + q - 16. Find i such that h(i) = 0.
-1, 0, 1, 54
Let d(a) be the second derivative of -5*a**4/3 + 575*a**3/6 - 210*a**2 - 27*a. Factor d(k).
-5*(k - 28)*(4*k - 3)
Let t = -1978 - -267031/135. Let q(a) be the third derivative of 1/135*a**5 - t*a**6 + 1/945*a**7 + 11*a**2 + 1/27*a**4 + 0*a + 0 - 1/9*a**3. Factor q(g).
2*(g - 3)*(g - 1)**2*(g + 1)/9
Suppose 31*t - 7*t = 4*t. Let n(f) be the third derivative of 0 + 0*f + t*f**4 + 1/50*f**6 + 0*f**3 - 3/350*f**7 - 1/100*f**5 + 8*f**2. Factor n(s).
-3*s**2*(s - 1)*(3*s - 1)/5
Let i be ((-96)/(-20))/(396/(-80) - -5). What is v in -14*v - 6 - 18*v**2 + 2 + 20*v**3 - 30*v**3 - i*v**4 + 94*v**4 = 0?
-2, -1
Let v(g) = -g**3 + 23*g**2 - 12*g - 14. Let z be v(23). Let r = 292 + z. Factor -2/5*d**3 + 0*d + 0 + 4/5*d**r.
-2*d**2*(d - 2)/5
Let x(a) = 11*a**3 + 79*a**2 + 565*a + 1085. Let f(m) = 9*m**3 + 78*m**2 + 564*m + 1086. Let n(g) = 4*f(g) - 3*x(g). Factor n(v).
3*(v + 3)*(v + 11)**2
Let p(a) be the third derivative of a**6/15 - a**5/10 - a**4/4 - 38*a**2 - 1. Let q(y) = -7*y**3 + 5*y**2 + 5*y. Let z(r) = 5*p(r) + 6*q(r). Factor z(i).
-2*i**3
Let o(b) = 6*b**3 + 3*b + 1. Let k be o(-2). Let h = k - -65. Suppose -h*m - m**2 - 4 + 4*m**2 + 4*m**2 + 0*m**2 = 0. What is m?
-2/7, 2
Let i be (-1868)/20 - (-3)/(-5). Let q = i + 471/5. Solve -8/5*v**3 + q + 0*v - 3/5*v**4 - 6/5*v**2 = 0.
-1, 1/3
Let u be 1393/21 + 1/(-3) + 1. Factor u*n**3 - 132*n**3 - 3*n**4 + 66*n**3 - n**5 - 4 + 7*n**2.
-(n - 1)**2*(n + 1)*(n + 2)**2
Let t(p) be the first derivative of -p**6/30 + 4*p**5/15 + 29*p**4/6 + 16*p**3 + p**2/2 + 10*p + 88. Let n(f) be the second derivative of t(f). Factor n(s).
-4*(s - 8)*(s + 1)*(s + 3)
Suppose 1047*w + 21158 = 24299. Factor 2*c - 2*c**2 + 0 + 1/2*c**w.
c*(c - 2)**2/2
Let l(b) be the first derivative of b**5/25 + 7*b**4/20 + b**3/5 - 31*b**2/10 + 4*b - 1347. Let l(h) = 0. Calculate h.
-5, -4, 1
Let c(j) be the third derivative of j**5/24 + 105*j**4/2 + 26460*j**3 - j**2 - 393*j + 2. Factor c(a).
5*(a + 252)**2/2
Let r(g) = 5*g - 4. Let d be r(2). Determine s, given that 3*s**4 + 589*s**3 - 589*s**3 - d*s - 9*s**2 = 0.
-1, 0, 2
Let y = 14966 - 14959. Let u(s) be the third derivative of -1/135*s**6 + 0*s**5 + 0*s + 0*s**4 - 4/315*s**y + 1/216*s**8 + 0 + 0*s**3 + 23*s**2. Factor u(g).
2*g**3*(g - 2)*(7*g + 2)/9
Let q = 96388 - 96385. What is l in 0 + 4/15*l**2 - 2/15*l**q + 2/15*l**5 + 0*l - 4/15*l**4 = 0?
-1, 0, 1, 2
Let u = 38/77 + -36/385. Let d(q) = 4*q - 80. Let z be d(20). Suppose 6/5*m**2 + u*m**3 + 4/5*m + z = 0. Calculate m.
-2, -1, 0
Suppose 0*p = -5*p + s + 631, -5*p - 5*s = -625. Let g be -11 + 15 - (p/(-33))/(-1). Factor -8/11*t**4 + 0*t + 6/11*t**5 + 0 + 0*t**2 + g*t**3.
2*t**3*(t - 1)*(3*t - 1)/11
Factor 80/3*s - 200/3 - 2/3*s**3 + 14/3*s**2.
-2*(s - 10)*(s - 2)*(s + 5)/3
Let h = 1479 - 1477. Let k(b) be the first derivative of 0*b - 18 - 2*b**h + 4/5*b**5 - 4/3*b**3 + b**4. Solve k(c) = 0 for c.
-1, 0, 1
Let f(b) be the first derivative of -1/21*b**3 + 2/7*b**2 - 1/42*b**4 + 12 - 11*b. Let c(q) be the first derivative of f(q). Suppose c(u) = 0. Calculate u.
-2, 1
Suppose -5*g + 7 = c, 7 - 42 = -5*c - 5*g. Factor -6*m**2 - 3*m**2 + m + m**3 + c*m**2.
m*(m - 1)**2
Let d(l) = -4*l**3 + 350*l**2 + 175*l + 90. Let y be d(88). Find j such that -20/9*j - 2/9*j**4 - 52/9*j**y + 0 - 25/9*j**3 = 0.
-10, -2, -1/2, 0
Determine z, given that 480*z**2 + 576 + 627*z - 2607*z**4 + 2595*z**4 + 285*z - 3*z**5 + 72*z**3 = 0.
-4, -2, 6
Let j(w) = 8*w**2 + w + 2. Let a(d) = 45*d**2 - 85*d + 235. Let b(r) = a(r) - 5*j(r). Solve b(s) = 0 for s.
3, 15
Suppose -190/9*m**2 + 28/3*m - 14/9*m**3 + 0 = 0. What is m?
-14, 0, 3/7
Let d(c) be the third derivative of c**8/14 - 26*c**7/21 + 139*c**6/30 + 259*c**5/15 - 239*c**4/2 - 84*c**3 + c**2 + 2*c + 3172. Let d(v) = 0. What is v?
-2, -1/6, 3, 7
Let l(o) = -3*o**3 + 6*o**2 + 9*o - 5. Let p(x) be the first derivative of -x**4/4 + x**2/2 - x + 14. Let f(q) = l(q) - 5*p(q). Find h, given that f(h) = 0.
-2, -1, 0
Let l(a) = 2*a**3 + 42*a**2. Let q(w) = 7*w**3 + 30*w**2 + 1989*w + 15606. Let o(k) = 3*l(k) - q(k). Let o(d) = 0. What is d?
-6, 51
Let z = -73 + 5. Let b = z - -70. Factor -6*o**3 - 6*o**b + 4 - 12*o + 41*o**2 + o**4 - 22*o**2.
(o - 2)**2*(o - 1)**2
Let w be (-13)/((-273)/(-42))*(3/3 + -2). Factor -1/5*f**w + 1/5 + 0*f.
-(f - 1)*(f + 1)/5
Factor 228*s - 27015*s**2 - 27017*s**2 - 612 + 54071*s**2.
3*(s - 2)*(13*s + 102)
Let d be (18/(-21))/((-72427)/(-10350) - 7). What is r in d*r**2 + 16/7 + 6750/7*r**3 + 360/7*r = 0?
-2/15
What is k in -74/3*k**4 + 0 - 25*k**3 + 0*k**2 + 0*k + 1/3*k**5 = 0?
-1, 0, 75
What is w in -544/7*w**3 + 16928/7 + 17664/7*w - 11952/7*w**2 - 6/7*w**4 = 0?
-46, -2/3, 2
Let k(f) = -125*f**3 - 125*f**2 + 11105*f - 51395. Let d(t) = 9*t**3 + 9*t**2 - 793*t + 3671. Let g(n) = -55*d(n) - 4*k(n). What is v in g(v) = 0?
-15, 7
Let r(i) = -6*i - 34. Let n be r(-7). Let q(t) = -17*t + 139. Let z be q(n). Factor 4 + 1/2*l**z - l**2 - 2*l.
(l - 2)**2*(l + 2)/2
Let b = -375 - -410. Suppose -5*x - 4*p + 61 - 29 = 0, 5*x + 5*p - b = 0. Factor 9/7*q**3 + 3/7*q + 15/7*q**2 + 0 - 27/7*q**x.
-3*q*(q - 1)*(3*q + 1)**2/7
Let m(k) be the third derivative of -k**6/8 + 13*k**5/5 + 93*k**4