/2)/(-5). Let r = m + -53/5. Determine q so that -27/5*q - 21/5*q**2 - r = 0.
-1, -2/7
Suppose 739*d = 737*d + 3 + 3. Let c(s) be the first derivative of 7/2*s**2 + 1/3*s**d - 8*s - 47. Suppose c(x) = 0. What is x?
-8, 1
Let r = -987282 - -987285. Let -3/2*k**r + 0 + 15*k + 9/2*k**2 = 0. What is k?
-2, 0, 5
Let p(t) be the third derivative of -t**8/2688 - t**7/168 + 7*t**6/96 - t**5/6 - 23*t**4/64 + 15*t**3/8 - 7091*t**2. Let p(y) = 0. What is y?
-15, -1, 1, 2, 3
Determine w so that -56*w**2 - 4*w**3 + 2*w**3 + 114919 - 168*w - 114343 = 0.
-24, -6, 2
Let o(v) be the second derivative of -18/7*v**2 - v**3 + 0 - 1/7*v**4 + 22*v. Find n, given that o(n) = 0.
-2, -3/2
Let w(g) be the second derivative of g**6/30 + 27*g**5/5 + 429*g**4/2 - 3078*g**3 + 29241*g**2/2 + 2*g - 284. Factor w(m).
(m - 3)**2*(m + 57)**2
Let i(t) = -532*t**4 + 9082*t**3 - 1571*t**2 + 74*t. Let a(v) = v**4 + v**3 + v**2 - 2*v. Let j(y) = -3*a(y) - i(y). Factor j(f).
f*(f - 17)*(23*f - 2)**2
Let b(f) be the first derivative of 67/5*f**2 + 84/5*f - 2/3*f**3 - 147. Determine a so that b(a) = 0.
-3/5, 14
Let c(h) be the third derivative of -13/21*h**7 - 44/3*h**5 - 35/3*h**3 - 5/48*h**8 + 0 + 445/24*h**4 + 305*h**2 + 67/12*h**6 + 0*h. Find s such that c(s) = 0.
-7, 2/7, 1
Let n(y) be the second derivative of y**7/91 + 28*y**6/195 - 23*y**5/130 - 122*y**4/39 + 380*y**3/39 - 144*y**2/13 + 180*y + 1. Let n(x) = 0. Calculate x.
-9, -4, 2/3, 1, 2
Suppose -14*p + 70 = -7*p. Solve -70*d**2 + 532*d**5 - 3*d**4 + d**2 + 55*d**3 + 30*d - 535*d**5 - p*d**3 = 0 for d.
-5, 0, 1, 2
Suppose -4*l + 308 = 3*f - f, 0 = -3*l - 2*f + 229. Let t = 26983 + -26981. Factor -t*k - 155*k**2 + l*k**2 + 77*k**2.
k*(k - 2)
Let j(t) = -t**3 + 3*t**2 + 2*t - 6. Let y be j(2). Find o, given that 2*o**3 - 8*o + 4*o**3 - 2*o**3 - 4*o**4 + 4*o**y + 4*o**3 = 0.
-1, 0, 1, 2
Let o(w) be the third derivative of -w**5/210 - 7*w**4/12 - 204*w**2 + w. Factor o(x).
-2*x*(x + 49)/7
Determine r, given that -63*r**3 + 72 + 7*r**4 + 197*r**2 - 3*r**4 - 23*r - 187*r = 0.
3/4, 1, 2, 12
Let y(v) = -v**2 + 19*v + 59. Let j(h) = -18*h - 61. Let a(k) = 6*j(k) + 4*y(k). Let r(u) = 9*u**2 + 64*u + 261. Let l(x) = 5*a(x) + 2*r(x). Factor l(t).
-2*(t + 8)**2
Suppose 116*i - 121*i + 4465 = 0. Let d = i - 5357/6. What is s in 0 - 1/2*s**3 - 2/3*s**2 + d*s**5 + 1/3*s**4 + 2/3*s = 0?
-2, 0, 1
Factor -14*x**3 - 140*x - 1712124*x**2 - 2*x**3 + 1712688*x**2.
-4*x*(x - 35)*(4*x - 1)
Let i(x) be the second derivative of -109*x + 11/10*x**4 - 34/15*x**3 + 0 + 1/50*x**5 + 0*x**2. Factor i(b).
2*b*(b - 1)*(b + 34)/5
Let l(f) = 3*f**2 - f. Let r(g) = -37*g - 260. Let z be r(-7). Let n(u) = 22*u**2 - 38*u - 132. Let a(v) = z*n(v) + 6*l(v). Determine m, given that a(m) = 0.
-3, 11
Let j = 805/267 + -3224/1335. Factor 12/5*w - 24/5 - j*w**3 + 6/5*w**2.
-3*(w - 2)**2*(w + 2)/5
Let q(k) be the first derivative of 2*k**5/5 - 9*k**4/2 - 8*k**3/3 - 2*k**2 - 156. Let o(t) = -t**4 + 2*t**3 - t**2 + t. Let h(s) = 4*o(s) + q(s). Factor h(j).
-2*j**2*(j + 2)*(j + 3)
Determine m, given that 380*m**4 + 159*m**3 - m**5 - 515*m**4 + 280*m**2 - 4*m**5 - 9*m**3 = 0.
-28, -1, 0, 2
Let y(z) be the third derivative of -z**6/140 - 2*z**5/7 + z**4/7 + 80*z**3/7 - z**2 + 309*z. Factor y(a).
-6*(a - 2)*(a + 2)*(a + 20)/7
Let r(f) = 2*f**2 - 11305*f + 135375. Let l be r(12). Let 14/3*s**2 + 2/3*s**l + 0 + 20/3*s = 0. Calculate s.
-5, -2, 0
Let o(y) be the second derivative of -y**6/150 - 201*y**5/100 - 133*y**4/20 - 199*y**3/30 + 2165*y. Factor o(q).
-q*(q + 1)**2*(q + 199)/5
Let o(r) be the second derivative of -r**5/130 + 53*r**4/78 + 847*r - 1. Determine s, given that o(s) = 0.
0, 53
Let j(h) = -4*h**4 - 416*h**3 - 22058*h**2 - 6*h + 2. Let o(x) = 13*x**4 + 1246*x**3 + 66178*x**2 + 21*x - 7. Let l(v) = -14*j(v) - 4*o(v). Factor l(z).
4*z**2*(z + 105)**2
Let o = 49 - 43. Suppose 0 = 2*m - 2 - o. Factor -6*j + j + m*j**2 + 5*j.
4*j**2
Suppose 2*m - 7*a = -6*a - 1216, -5*m = -a + 3046. Let y = m - -7966/13. Factor -40/13*w + 2/13*w**4 - 14/13*w**3 + y*w**2 + 16/13.
2*(w - 2)**3*(w - 1)/13
Let j(g) = -2*g**3 - 50*g**2 - 4*g - 95. Let a be j(-25). Let q(f) = -5*f + 25. Let l be q(a). Determine r, given that -3/5*r + 12/5*r**2 + l = 0.
0, 1/4
Let o(g) be the third derivative of -g**5/90 - 497*g**4/18 - 331*g**3/3 + 18*g**2 + 2*g - 55. Determine d, given that o(d) = 0.
-993, -1
Let r = 1913 + -1909. Let c(f) be the first derivative of -8*f**2 + 3/2*f**r + 8*f + 2/3*f**3 + 10. Factor c(g).
2*(g - 1)*(g + 2)*(3*g - 2)
Let c(h) be the third derivative of -h**7/420 - 11*h**6/240 + 13*h**5/60 + 3*h**2 - 110*h. Factor c(s).
-s**2*(s - 2)*(s + 13)/2
Factor -37*g + 84*g - 22*g - 128*g**2 - 3*g**3 + 195 - 67*g**2 - 22*g.
-3*(g - 1)*(g + 1)*(g + 65)
Let c = -6609/70 - -3322/35. Suppose -1/2*s + c*s**3 - 2 + 2*s**2 = 0. Calculate s.
-4, -1, 1
Let t(d) be the second derivative of -19/18*d**3 + 1/60*d**5 + 0 - 7/3*d**2 - 1/9*d**4 + 49*d. Suppose t(s) = 0. Calculate s.
-2, -1, 7
Let w(b) be the first derivative of 3/2*b**2 - 5/3*b**3 + 9*b - 6 + 1/4*b**4. Factor w(p).
(p - 3)**2*(p + 1)
Let l(t) be the third derivative of t**6/360 - t**5/20 - 8*t**4/9 + 26*t**3/3 + 4126*t**2. Factor l(r).
(r - 13)*(r - 2)*(r + 6)/3
Let l be 0/21 - 779/3. Let t = l + 261. Factor t*n**2 - 2*n**3 + 0*n + 0 + 0*n**4 + 2/3*n**5.
2*n**2*(n - 1)**2*(n + 2)/3
Let c(s) be the first derivative of -2*s**3/39 - 139*s**2/13 - 1848*s/13 + 4934. Factor c(n).
-2*(n + 7)*(n + 132)/13
Let i(n) = 3047*n + 39611. Let d be i(-13). Factor 0 + d*h - 9/4*h**2 - 3/8*h**3 + 3/8*h**4.
3*h**2*(h - 3)*(h + 2)/8
Let q = -44645/14 - -3189. Let u(y) be the third derivative of -3/14*y**3 - 1/140*y**5 + 0*y + 0 - 18*y**2 - q*y**4. Factor u(a).
-3*(a + 1)*(a + 3)/7
Let f = 569382 + -569382. Factor 1/10*m**3 - 9/10*m - 1/10*m**4 + f + 9/10*m**2.
-m*(m - 3)*(m - 1)*(m + 3)/10
Let s(h) be the second derivative of -h**6/10 + 69*h**5/10 - 477*h**4/4 - 648*h**3 + 2592*h**2 + 3*h - 1090. Factor s(p).
-3*(p - 24)**2*(p - 1)*(p + 3)
Determine w so that 340/7*w + 9/7*w**3 - 264/7*w**2 - 16 = 0.
2/3, 28
Let y(q) = -q**2 - 7*q - 1. Let n(r) = r**2 + 7*r + 2. Let b(t) = -6*n(t) - 5*y(t). Let f be b(-2). Factor 6*m**4 + 14*m**4 + 15*m**5 - 10*m**3 - 9*m**3 - m**f.
5*m**3*(m + 2)*(3*m - 2)
Let m(w) = 9*w**2 + 4*w - 1. Let o be m(1). Let a be 3*(-28)/o*(-4)/7. Factor 2*x**2 + 20*x**4 - 7*x**a + 5*x**3 - 10*x**4.
x**2*(x + 1)*(3*x + 2)
Solve -7/3*b**3 - 2*b**2 + 0 + b**4 + 0*b = 0.
-2/3, 0, 3
Let w(b) = b**3 + 6*b**2 - 5. Let y be w(-6). Let n be y - -1 - (-3 + -3). What is z in 1/2*z**n - 3/4*z**4 + 0*z + 0 - 5/4*z**3 = 0?
-2, 0, 1/3
Factor 576 + 4769*u**3 + 40*u**2 + 188*u + 160*u - 4773*u**3.
-4*(u - 16)*(u + 3)**2
Let f(c) be the first derivative of -5*c**6/6 + c**5 + 25*c**4/4 - 25*c**3/3 - 10*c**2 + 20*c + 684. Let f(w) = 0. Calculate w.
-2, -1, 1, 2
Let y(t) = 5*t**2 - 98*t - 26. Let q be y(20). Let i(p) be the third derivative of 0 + 0*p**4 - 1/3*p**3 + 1/30*p**5 + 0*p - q*p**2. Find u such that i(u) = 0.
-1, 1
Let h(j) = -2*j**2 - 307*j + 159. Let n be h(-154). Let 5*o - 5/4*o**3 + n - 5/4*o**2 = 0. Calculate o.
-2, -1, 2
Let d(o) be the third derivative of o**5/90 - 289*o**4/18 - 3*o**2 - 13*o. Factor d(c).
2*c*(c - 578)/3
Let -260/7*t + 8*t**4 + 72/7 - 4/7*t**5 - 216/7*t**3 + 352/7*t**2 = 0. Calculate t.
1, 2, 9
Let b = -23734/9 + 2638. Let i(y) be the first derivative of b*y**3 - 4/9*y + 18 - 7/18*y**4 - 1/3*y**2. Factor i(q).
-2*(q - 1)**2*(7*q + 2)/9
Let j(z) = 30*z**3 - 2*z**2 - 2*z + 4. Let l be j(1). Suppose -l = -9*c - c. Solve 4/3 + 4/3*h - 1/3*h**2 - 1/3*h**c = 0.
-2, -1, 2
Let q(k) be the second derivative of -33*k**5/20 - k**4/4 + 110*k**2 - 112*k. Let v(f) be the first derivative of q(f). What is t in v(t) = 0?
-2/33, 0
Solve 100*m**5 + 23*m**3 + 48*m + 24*m**4 - 104*m**5 - 80*m**2 - 42*m**3 + 31*m**3 = 0.
-2, 0, 1, 6
Let x be ((-26)/(-5) - 3)/((-3)/(-75)). What is u in -5*u**2 + 109*u - 180*u - x + 131*u = 0?
1, 11
Let s(r) be the third derivative of -r**8/840 + 17*r**7/525 - 7*r**6/30 - 1023*r**2. Factor s(o).
-2*o**3*(o - 10)*(o - 7)/5
Let y be 396/242*(-44)/(-6). Suppose 0 = 176*t - 172*t - y. Factor 28/3*w + 35/3*w**2 - 25/3*w**t + 4/3.
-(w - 2)*(5*w + 1)*(5*w + 2)/3
Determine r, given that 1/7*r**2 - 611/7 - 34/7*r = 0.
-13, 