alculate h.
0, 1, 2, 4
Let h(a) be the third derivative of -a**6/240 + 2*a**5 - 713*a**4/48 + 79*a**3/2 - 10683*a**2. Factor h(t).
-(t - 237)*(t - 2)*(t - 1)/2
Factor 1/3*v**3 - 13/3*v**2 + 88 - 2/3*v.
(v - 11)*(v - 6)*(v + 4)/3
Let f be (-4 + 34747 - -4)/(-21). Let n = f - -1655. Factor -2/21*r**2 - 8/21*r - n.
-2*(r + 2)**2/21
Determine g, given that -69*g + 0 + 139/2*g**2 - 1/2*g**3 = 0.
0, 1, 138
Let q(y) = 6*y**2 - 112*y + 16. Let n(j) = j**2 - 2*j - 1. Let z(v) = 5*v**2 - 43*v + 3. Let o(m) = 3*n(m) - z(m). Let c(k) = -8*o(k) - 3*q(k). Factor c(l).
-2*l*(l - 20)
Let s(p) be the second derivative of p**6/240 - p**5/60 - p**4/16 + 33*p**2/2 - 84*p. Let n(z) be the first derivative of s(z). Factor n(a).
a*(a - 3)*(a + 1)/2
Let g(v) be the third derivative of 28/5*v**5 - 5/7*v**7 + 0*v + 2/3*v**6 + 8*v**4 + 16/3*v**3 + 0 + 122*v**2. Suppose g(o) = 0. What is o?
-2/3, -2/5, 2
Let g(b) = -14*b**3 - 355*b**2 - 831*b - 246. Let y(z) = 27*z**3 + 710*z**2 + 1663*z + 513. Let w(h) = 7*g(h) + 4*y(h). Factor w(o).
5*(o + 2)*(o + 33)*(2*o + 1)
Let d be ((-111)/(-629))/((-639)/(-2414)). What is m in -8/3*m**2 - 2/3*m**3 + 8/3 + d*m = 0?
-4, -1, 1
Let s(f) be the first derivative of 2*f**5/65 + 11*f**4/26 + 28*f**3/39 - 44*f**2/13 - 144*f/13 - 8061. Solve s(o) = 0.
-9, -2, 2
Let x(n) be the third derivative of -2/105*n**7 + 0*n**4 - 1/120*n**5 + 0 + 0*n**3 - 1/42*n**8 + 7/240*n**6 + 11*n**2 + 5*n. Determine f, given that x(f) = 0.
-1, 0, 1/4
Solve -504 - 3/4*k**3 - 48*k + 33/2*k**2 = 0.
-4, 12, 14
Let o be -4*((-108)/(-126) + -1). Let u = -30 + 214/7. Factor o*z - u*z**3 + 4/7*z**2 - 4/7.
-4*(z - 1)**2*(z + 1)/7
Let i(z) be the second derivative of z**9/1008 - z**7/140 + z**5/40 - 85*z**3/3 + 250*z. Let g(w) be the second derivative of i(w). Factor g(h).
3*h*(h - 1)**2*(h + 1)**2
Let y(r) be the third derivative of -1/105*r**7 - 32*r**2 + 0*r**3 + 2 + 0*r + 7/60*r**6 + 5/12*r**4 - 11/30*r**5. Factor y(g).
-2*g*(g - 5)*(g - 1)**2
Let l be 5 + 0 + (-2)/(-2). Let k = -4 + l. Determine m, given that -k*m**2 + m**2 + 2*m**5 - 9*m**3 + 9*m**4 + 2*m**5 + 3*m - 6*m**5 = 0.
-1/2, 0, 1, 3
Let j = 23 + -24. Let r be (1/5 - j)/((-36)/(-90)). Find x such that -2*x - 2*x**r + x - 5*x**2 - x + x**4 - x**3 + x**5 = 0.
-1, 0, 2
Let b = 3928 + -7851/2. Let i(s) be the second derivative of 11*s + 0*s**2 - b*s**3 + 0 - 5/12*s**4. Factor i(n).
-5*n*(n + 3)
Suppose -49*l - 23458 + 23458 = 0. Factor -4/3*t**3 + l - 16/3*t**2 + 20/3*t.
-4*t*(t - 1)*(t + 5)/3
Factor 368*x**2 + 4016*x - 4377*x**3 - 1243 - 421 + 4357*x**3.
-4*(x - 26)*(x + 8)*(5*x - 2)
Let s(t) = 93*t**2 - 4788*t - 1905627. Let w(u) = 263*u**2 - 14363*u - 5716881. Let p(o) = -17*s(o) + 6*w(o). Suppose p(j) = 0. What is j?
-797
Let m be (-5)/(-22) + (-1)/((-440)/120). Let n(q) be the first derivative of m*q**3 + 150*q - 42 - 15*q**2. Factor n(a).
3*(a - 10)**2/2
Let c(f) be the third derivative of -1/12*f**4 + f + 0 - 1/360*f**6 + 1/36*f**5 + 303*f**2 + 0*f**3. Factor c(g).
-g*(g - 3)*(g - 2)/3
Let b = -118/4519 + 85640749/45190. Let y = b - 1895. Determine x so that -y*x**4 + 4/5*x**2 + 0 + 6/5*x - 1/10*x**3 = 0.
-2, 0, 3
Let h = -29797 - -29800. Determine t, given that -328/9*t - 50/9*t**h + 64/9 + 440/9*t**2 = 0.
2/5, 8
Let i(c) = -3*c**4 - 43*c**3 + 174*c**2 - 294*c + 144. Let j(a) = -5*a**4 - 44*a**3 + 167*a**2 - 295*a + 144. Let x(m) = 3*i(m) - 2*j(m). Factor x(s).
(s - 36)*(s - 2)**2*(s - 1)
Let k(w) be the first derivative of -6*w**2 - 3/5*w**5 + 3*w**4 + 0*w + w**3 - 32. Suppose k(c) = 0. Calculate c.
-1, 0, 1, 4
Find o, given that 8/11*o + 94/11*o**3 - 24/11*o**5 + 14/11*o**4 - 56/11*o**2 + 0 = 0.
-2, 0, 1/4, 1/3, 2
Let d(b) be the second derivative of 1/72*b**4 + 9 + 2*b**2 - 10*b + 7/18*b**3. Factor d(x).
(x + 2)*(x + 12)/6
Let k(d) = 446*d - 4456. Let f be k(10). Let c(q) be the first derivative of -16/3*q**3 + 16*q**2 - 2*q**f + 4/5*q**5 + 0*q - 25. Factor c(u).
4*u*(u - 2)**2*(u + 2)
Suppose 7*d - 3*d - 2*t + 3934 = 0, -2*d + 4*t - 1976 = 0. Let q = -504 - d. Factor -24 + i**3 - q*i + 458*i - 2*i**2 + 0*i**3.
(i - 6)*(i + 2)**2
Factor 18*p**4 - 4219*p**3 - 30*p - 6*p + 3*p**5 - 60*p**2 + 4210*p**3.
3*p*(p - 2)*(p + 1)**2*(p + 6)
Let m = -756 - -761. Factor -3*p**3 + 79*p**2 - 141*p**2 + 60*p**2 + 56*p**2 - m + 3*p - 49.
-3*(p - 18)*(p - 1)*(p + 1)
Let n be 2/(-6) - 281/(-6) - (-148 + -72 + 225). Factor -1763/2*x - 1/2*x**3 - n*x**2 - 1681/2.
-(x + 1)*(x + 41)**2/2
Find x, given that -52080*x - 1608*x**2 - 5*x**4 - 2383*x**2 - 2494*x**2 - 141120 - 310*x**3 = 0.
-24, -7
Suppose -103119 = -741*l + 3585. Factor -59*v**3 - 5/2*v**4 + l*v - 336*v**2 + 0.
-v*(v + 12)**2*(5*v - 2)/2
Let i = -289 - -291. Determine n so that -60*n**i - 15*n**2 - 36*n - 34*n**3 - 3*n**4 - 8*n**3 = 0.
-12, -1, 0
Let z = -1103 + 13237/12. Let s(a) be the first derivative of -9 - 5/6*a**2 + 2/3*a + 4/9*a**3 - z*a**4. Solve s(f) = 0.
1, 2
Let q(s) = -6*s - 85. Let k be q(-13). Let m(z) = 42*z + 297. Let f be m(k). Determine n, given that -6/5*n - 18/5 - 2/5*n**f + 2*n**2 = 0.
-1, 3
Suppose -4*y - 180 = a - 191, 5*y - 5 = 0. Let b(f) be the second derivative of 0*f**2 + 0 + 0*f**3 + 1/27*f**4 - 1/90*f**5 - a*f. Factor b(l).
-2*l**2*(l - 2)/9
Let x(n) = -44*n + 179. Let t(g) = g**2 + 11*g - 308. Let o be t(-24). Let k be x(o). Let 2/9*r - 2/9*r**k - 2/3 + 2/3*r**2 = 0. Calculate r.
-1, 1, 3
Let i be 1/1 + (-5 - 1725/(-420)). Let s(v) be the third derivative of 15*v**2 + 1/420*v**6 + i*v**4 - 4/21*v**3 + 0 + 0*v - 1/35*v**5. Factor s(p).
2*(p - 4)*(p - 1)**2/7
Let o(x) be the second derivative of -2*x**7/105 + 19*x**6/75 + 22*x**5/25 - 23*x**4/6 - 22*x**3/5 + 423*x - 5. Determine d, given that o(d) = 0.
-3, -1/2, 0, 2, 11
Solve -4/7*q**3 - 2960/7 + 2944/7*q - 724/7*q**2 = 0 for q.
-185, 2
Let a(w) be the first derivative of w**6/540 - w**5/270 - 2*w**4/27 + 4*w**3/9 + 30*w**2 + 16. Let d(y) be the second derivative of a(y). Factor d(r).
2*(r - 2)**2*(r + 3)/9
Suppose 5*c = 23*c - 13626. Solve 1508*l**2 - 752*l**2 - c*l**2 + 1 = 0 for l.
-1, 1
Let q(h) be the first derivative of h**4/4 - h + 121. Let o(x) = -4*x**2 - 8*x + 12. Let p(d) = -o(d) - 8*q(d). Suppose p(s) = 0. Calculate s.
-1, 1/2, 1
Let u(g) be the first derivative of g**5/15 - 2*g**4 - 731. Factor u(r).
r**3*(r - 24)/3
Let o be 1248/(-48) + (-1 - -2)*-3. Let g be -1*(o - 2 - -4). Find k, given that -19*k**2 - 3*k - g*k**2 + 43*k**2 = 0.
-1, 0
Let p(v) be the second derivative of 10*v + 4/3*v**2 + 7/9*v**3 - 1/30*v**5 + 1/9*v**4 + 1. Find h such that p(h) = 0.
-1, 4
Let w(g) be the first derivative of 0*g - g**4 - 1/20*g**5 - 9*g**2 + 31 - 8*g**3. Let v(a) be the second derivative of w(a). Factor v(s).
-3*(s + 4)**2
Let p(u) be the first derivative of u**3/6 + 23*u**2/2 + 45*u/2 + 1327. Suppose p(l) = 0. What is l?
-45, -1
Let f(p) = -2*p**3 + 92*p**2 - 1225*p + 3549. Let g(m) = -m**3 + 46*m**2 - 612*m + 1773. Let l(u) = -3*f(u) + 7*g(u). Factor l(x).
-(x - 21)**2*(x - 4)
Solve 397/3*n**3 - 133/3*n + n**4 - 262/3 + 523/3*n**2 = 0.
-131, -1, 2/3
Suppose 3*c = -9*c + 48. Solve -77*r - 15*r**3 + 75*r**2 + 7 - 5*r**c + 13*r - 21*r + 23 = 0.
-6, 1
Let h(i) = -i**3 + 6*i**2 + i - 4. Let c be h(6). Let o = -333 + 335. Factor -44*a**2 + 26*a**c + 15*a + 20*a**o - a.
2*a*(a + 7)
Let j = 613/259 - 3/37. Let l = 422090/7 - 60298. Suppose j - 16/7*t - 4/7*t**2 + l*t**3 = 0. What is t?
-2, 1, 2
Factor 34 + 508/3*k - 10/3*k**2.
-2*(k - 51)*(5*k + 1)/3
Let l(v) be the third derivative of 5/4*v**4 - 1/20*v**6 + v**2 + 1/105*v**7 + 0*v**3 + 0 - 13/30*v**5 - 57*v. Factor l(z).
2*z*(z - 5)*(z - 1)*(z + 3)
Factor -197/4*o - 15 - 58*o**2 - 5*o**4 - 1/4*o**5 - 57/2*o**3.
-(o + 1)**3*(o + 5)*(o + 12)/4
Let x = 1578/5 - 1576/5. Let w = 879/5 - 175. Determine n so that -w + x*n**2 + 2/5*n = 0.
-2, 1
Find i such that -1394/15*i**2 + 2/15*i**3 + 0*i + 0 = 0.
0, 697
Let h = -14264 - -27817/2. Let r = 356 + h. Factor -r*s**2 + 1/2*s + 0.
-s*(s - 1)/2
Let g(h) be the first derivative of 13*h**5/15 - 67*h**4/12 + 101*h**3/9 - 53*h**2/6 + 2*h + 3207. Let g(s) = 0. What is s?
2/13, 1, 3
Let m(c) be the first derivative of c**6/1440 - c**4/24 + 68*c**3/3 - 39. Let f(o) be the third derivative of m(o). Factor f(l).
(l - 2)*(l + 2)/4
Factor -94/3*f**2 - 30 + 182/3*f + 2/3*f**3.
2*(f - 45)*(f - 1)**2/3
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