et p = -31697/3 - -10566. Let s(o) be the third derivative of p*o**3 - 1/120*o**5 - 4*o**2 + 0*o + 0 + 1/16*o**4. Determine g, given that s(g) = 0.
-1, 4
Let h(g) be the third derivative of -g**7/420 + g**6/16 - 17*g**5/30 + 7*g**4/4 - 14*g**2 + g + 4. Factor h(z).
-z*(z - 7)*(z - 6)*(z - 2)/2
Let m(q) be the third derivative of 0 - 193*q**2 + 19/24*q**4 + 1/120*q**5 + 37/12*q**3 + 0*q. Factor m(u).
(u + 1)*(u + 37)/2
Let z(o) = 17*o**2 + 5525*o + 3803273. Let i(d) = 12*d**2 + 5522*d + 3803276. Let a(r) = -3*i(r) + 2*z(r). Suppose a(n) = 0. What is n?
-1379
Let d(s) be the third derivative of 13*s**4/24 + 5*s**3/3 + 4*s**2. Let l be d(3). Solve -l*n + 3 - 10*n**3 - 6*n**2 + 51*n - 1 - 4*n**4 = 0.
-1, 1/2
Suppose -100*x + 99*x + 8 = 0. Factor -r - r + 2 - r**2 - r + x.
-(r - 2)*(r + 5)
Suppose -148*g**3 + 123*g**3 - 4880*g - 86 + 2263 + 1083 - 8165*g**2 = 0. Calculate g.
-326, -1, 2/5
Let q(l) be the second derivative of -4/21*l**7 - 5/3*l**4 - 16/3*l**3 - 15*l + 2*l**5 + 2/15*l**6 + 0 + 8*l**2. What is n in q(n) = 0?
-2, -1, 1/2, 1, 2
Let q = 74740 - 74738. Find x, given that -1/2*x + 0 - 9/4*x**4 + 4*x**3 - 5/4*x**q = 0.
-2/9, 0, 1
Let h(w) = 4*w**2 - 84*w - 3*w**2 - 5*w**2 + 5 + 83*w. Let u(c) = 3*c**2 + c - 1. Let r(v) = -h(v) - u(v). Factor r(q).
(q - 2)*(q + 2)
Suppose 9*r**4 + 3*r**5 + 118 - 303*r**3 - 996*r + 21*r**4 - 79 + 71 + 298 + 858*r**2 = 0. Calculate r.
-17, 1, 2
Let l(g) be the third derivative of -g**6/150 + g**5/3 + 41*g**4/15 + 112*g**3/15 - 1198*g**2. Factor l(b).
-4*(b - 28)*(b + 1)*(b + 2)/5
Let d(i) = -i**3 - 21*i**2 + 21*i - 9. Let v be d(-22). Suppose 0 = -0*o - v*o + 3*o. Factor o + 1/7*n**5 + 0*n + 2/7*n**3 + 0*n**2 + 3/7*n**4.
n**3*(n + 1)*(n + 2)/7
Let k be 2 + 2 + 15 - 50/(-10). Let t(u) be the second derivative of 1/42*u**7 + 0*u**2 + 1/6*u**3 - 1/10*u**5 + 0 + 0*u**4 - k*u + 0*u**6. Factor t(x).
x*(x - 1)**2*(x + 1)**2
Let n = -895309/4 + 223838. Factor 11/2 + 1/4*x**3 - n*x + 5*x**2.
(x - 1)**2*(x + 22)/4
Let u(y) be the second derivative of -163*y - 65/3*y**3 + 15/4*y**4 + 50*y**2 + 1/8*y**5 - 1/12*y**6 + 0. Suppose u(f) = 0. Calculate f.
-5, 2
Let q(i) be the first derivative of -i**5/10 - 83*i**4/8 - 307*i**3 - 1240*i**2 - 1600*i - 3231. Factor q(m).
-(m + 1)*(m + 2)*(m + 40)**2/2
Let p(x) be the second derivative of 103*x + 2/21*x**7 + 0 - 3/5*x**5 + 0*x**2 + 2/5*x**6 - 4*x**3 - 11/3*x**4. Factor p(h).
4*h*(h - 2)*(h + 1)**2*(h + 3)
Suppose 28*i = -179 + 879. Suppose 50*k + i*k = 225. Factor -18/11*d**4 + 96/11*d + 2/11*d**5 - 32/11 + 64/11*d**k - 112/11*d**2.
2*(d - 2)**4*(d - 1)/11
Factor 57/2 - 89/4*d - 6*d**2 - 1/4*d**3.
-(d - 1)*(d + 6)*(d + 19)/4
Suppose 5*f - 261 = 4*i, -4*i + 163 = -f + 4*f. Let s = f - 48. Factor -s*q**2 - 17 - 20*q + 3*q**2 - 6 - 27.
-2*(q + 5)**2
Suppose 0 = 4*o + 2*x - x - 125, 2*o - 40 = 4*x. Factor -58*m**5 + 30*m**5 + 2*m**4 + o*m**5.
2*m**4*(m + 1)
Let z(c) be the first derivative of c**3 - 105*c**2/2 - 468*c - 2228. Factor z(s).
3*(s - 39)*(s + 4)
Let j(v) = 267*v - 4806. Let s be j(18). Let b(l) be the third derivative of 0*l**3 + s*l + 0*l**4 + 0 + 1/90*l**5 + 45*l**2 + 1/36*l**6. Solve b(q) = 0 for q.
-1/5, 0
Let n(k) = 64*k**3 - 152*k**2 - 16*k. Let o(m) = -m**4 - m**3 - 4*m. Let x(f) = -n(f) + 4*o(f). Suppose x(b) = 0. Calculate b.
-19, 0, 2
Let z = 3509 - 10525/3. Let s(y) be the first derivative of 0*y + z*y**3 - 2/5*y**5 - 1/6*y**6 + 1/4*y**4 + 19 + 0*y**2. Determine t so that s(t) = 0.
-2, -1, 0, 1
Let i(b) be the third derivative of 2*b**2 + 35 + 7*b**3 + 1/30*b**5 + 5/6*b**4 + 0*b. Let i(d) = 0. Calculate d.
-7, -3
Let b = 819498 - 819496. Suppose 74/5*d + 88/5*d**b - 28/5 - 14/5*d**3 = 0. What is d?
-1, 2/7, 7
Let h be (105/245)/((-2120)/(-525) - 4). Suppose h*u**3 + 225/4*u**2 + 0 + 375/4*u + 3/4*u**4 = 0. Calculate u.
-5, 0
Let h(m) be the second derivative of m**4/3 + 98*m**3/3 + 2376*m. Factor h(j).
4*j*(j + 49)
Let i = 20861 + -145120/7. Let j = i - 129. Factor -1/7*k**3 - j*k**2 - 2/7 - 5/7*k.
-(k + 1)**2*(k + 2)/7
Suppose -4*t**5 - 44401441*t - 544 - 668*t**2 + 44402425*t + 5*t**5 - 27*t**4 + 206*t**3 = 0. Calculate t.
2, 4, 17
Let b(c) be the first derivative of c**6/39 + 6*c**5/65 - 5*c**4/13 - 8*c**3/3 - 72*c**2/13 - 64*c/13 + 1553. Determine u, given that b(u) = 0.
-2, -1, 4
Let s(v) be the third derivative of -v**7/1260 - 11*v**6/720 - v**5/40 + 11*v**4/144 + 5*v**3/18 - 10*v**2 - 14*v. Factor s(g).
-(g - 1)*(g + 1)**2*(g + 10)/6
Let -512/7*z**3 + 6/7*z**5 + 148/7 - 208/7*z**4 + 218/7*z - 228/7*z**2 = 0. Calculate z.
-1, 2/3, 37
Determine x so that 2/7*x**2 - 9724/7*x + 11819522/7 = 0.
2431
Let a(u) be the second derivative of u**6/120 - u**5/5 - 7*u**4/6 + 16*u**3 - 54*u**2 - 1774*u. What is t in a(t) = 0?
-6, 2, 18
Suppose -20402/15 + 404/15*d - 2/15*d**2 = 0. Calculate d.
101
Let h(n) = 4*n**3 + n**2 - 6*n. Let j(l) = -l**4 + 7*l**3 + 9*l**2 + 17*l + 34. Let o(u) = 6*h(u) - j(u). Suppose o(w) = 0. What is w?
-17, -1, 2
Let q(l) = -5*l**2 + 11*l + 13. Let i(z) = -11*z**2 - 3 + 18 - 97*z + 118*z + 10. Let k(y) = -3*i(y) + 7*q(y). Factor k(n).
-2*(n - 8)*(n + 1)
Let u(v) be the third derivative of -245*v**6/36 - 2933*v**5/9 + 1679*v**4/36 - 8*v**3/3 + 65*v**2 + 2*v + 8. Find i such that u(i) = 0.
-24, 1/35
Let h be 11 + 37/(-3) + 10/3. Factor -j**h + 8*j + 7*j**2 - 2*j + 10*j + 2*j**3 + 6*j**2.
2*j*(j + 2)*(j + 4)
Let b be 4 + 3 + -3 + -2. Let v(i) = 2 - 1 - i + i**3 - b. Let n(w) = 2*w**4 + 8*w**3 + 18*w**2 + 16*w + 6. Let m(k) = n(k) + 2*v(k). Let m(q) = 0. What is q?
-2, -1
Let p(y) be the third derivative of 11/114*y**4 + 0*y - 3*y**2 - 1/570*y**5 - 7/19*y**3 - 3. Factor p(j).
-2*(j - 21)*(j - 1)/19
Let j(z) = z**3 - 2*z**2 + z - 3. Let y(r) = 27*r**2 - 21*r - 69. Let n(q) = -3*j(q) + y(q). Factor n(x).
-3*(x - 10)*(x - 2)*(x + 1)
Let z(w) be the second derivative of -1/30*w**6 + 1/2*w**4 + 3 + 2/3*w**3 + 30*w - 1/20*w**5 - 4*w**2. Factor z(r).
-(r - 2)*(r - 1)*(r + 2)**2
Let b be (-2*1*-1)/(-30 - -32). Let f(r) = -r**3 - 4*r - 4. Let x(w) = w**2 - 1. Let z(j) = b*f(j) - 4*x(j). Factor z(a).
-a*(a + 2)**2
Let x(t) be the second derivative of 2*t**6/15 + 4*t**5/5 + t**4 - 8*t**3/3 - 8*t**2 + 807*t. Determine m so that x(m) = 0.
-2, -1, 1
Let a(d) be the first derivative of -112*d**2 - 13/2*d**4 + 128*d + 28 + 40*d**3 + 2/5*d**5. Factor a(s).
2*(s - 4)**3*(s - 1)
Let o(d) be the first derivative of -18*d**5/5 + 21*d**4/2 + 2344*d**3/3 - 1580*d**2 + 1056*d + 1054. What is x in o(x) = 0?
-11, 2/3, 12
Suppose 5*h + 2 = -4*z, -40 = -5*z + 3*h - 24. Suppose 0 + 4*j**z - 16/5*j + 4/5*j**5 + 12/5*j**3 - 4*j**4 = 0. Calculate j.
-1, 0, 1, 4
Let q = -5993/66120 + 8/87. Let t = q + 301/2280. Factor t*z**2 - 8/15*z + 2/5.
2*(z - 3)*(z - 1)/15
Let o(b) be the third derivative of -b**7/1260 - b**6/5 + 37*b**5/45 + 4*b**4 - 292*b**3/9 - b**2 - 2*b + 16. What is s in o(s) = 0?
-146, -2, 2
Let o(k) = 42*k**2 + 28*k - 42. Let y be o(8). Let g be 1 - (-6)/(-10) - y/(-700). Determine v so that -3 - 75/4*v**2 + 21*v + g*v**3 = 0.
1/6, 2
Let c(n) be the third derivative of 0*n - 2*n**2 - 7/100*n**5 - 21 - 1/200*n**6 + 8/5*n**3 - 1/5*n**4. Factor c(r).
-3*(r - 1)*(r + 4)**2/5
Let c(z) be the third derivative of -19*z**7/3360 - 3*z**6/160 + z**5/160 + 17*z**4/24 - 83*z**2. Let a(u) be the second derivative of c(u). Factor a(t).
-3*(t + 1)*(19*t - 1)/4
Let h(c) = 12*c - 217. Let u be h(16). Let v be ((-5)/u)/((-2)/(-6)). Determine n so that 0*n - v*n**2 + 4/5 + 1/5*n**3 = 0.
-1, 2
Factor -67712/3 - 2/3*o**2 - 736/3*o.
-2*(o + 184)**2/3
Let d(r) = -r**2 + r + 1. Let c(m) = m + 16. Let n be c(-14). Suppose -n*z = 10 - 14. Let l(q) = 6*q - 10. Let g(b) = z*l(b) + 4*d(b). Factor g(s).
-4*(s - 2)**2
Let d(w) be the third derivative of w**10/378000 + 13*w**9/151200 - w**8/3600 + 11*w**5/20 - 71*w**2. Let g(b) be the third derivative of d(b). Factor g(p).
2*p**2*(p - 1)*(p + 14)/5
Let s(f) be the second derivative of -f**5/90 + 19*f**4/27 - 37*f**3/27 - 240*f - 1. Factor s(p).
-2*p*(p - 37)*(p - 1)/9
Let x(k) be the second derivative of -2*k**6/15 - 294*k**5/5 - 7491*k**4 - 84672*k**3 - 373248*k**2 + 21*k + 85. Factor x(s).
-4*(s + 3)**2*(s + 144)**2
Let u(i) = -2*i**3 + 120*i**2 - 793*i - 1953. Let f be u(52). Find p such that f + 3/4*p**3 + 90*p + 63/4*p**2 = 0.
-10, -1
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