
Let a(w) be the second derivative of w**5/90 - 7*w**4/36 - 10*w**3/3 + 49*w**2/2 - 2*w - 166. Let h(j) be the first derivative of a(j). Factor h(u).
2*(u - 10)*(u + 3)/3
Suppose 2*q = -1434 - 666. Let c be 834/q*-5 + (-2)/5. Let 0 + 0*u + c*u**4 + 20/7*u**3 + 4/7*u**2 = 0. What is u?
-2/5, 0
Let p(a) be the second derivative of 2*a**3 - 51*a + 1/8*a**4 + 9*a**2 - 1. Let p(f) = 0. What is f?
-6, -2
Let p be ((-2 + 3)/22)/((-12150)/330 - -37). Suppose -p*j**2 + 21/4*j - 5 = 0. What is j?
1, 20
Let o(j) be the first derivative of j**6/12 + 11*j**5/2 + 881*j**4/8 + 3425*j**3/6 + 1875*j**2/2 + 3180. Find w, given that o(w) = 0.
-25, -3, -2, 0
Let r(g) = 144*g**2 + 158*g - 306. Let k(t) = t**3 + 142*t**2 + 160*t - 309. Let m(l) = 2*k(l) - 3*r(l). Solve m(y) = 0 for y.
-2, 1, 75
Let q(h) be the third derivative of -h**6/120 + 31*h**5/20 + 63*h**4/8 + 95*h**3/6 + 1359*h**2. Determine a so that q(a) = 0.
-1, 95
Let z(r) = -15*r - 212. Let l be z(-14). Let t be 45/60 + l - (-6)/4. Factor -3/4*k**2 - t + k.
-(k - 1)*(3*k - 1)/4
Let v = 66763/77889 - 1/77889. Factor 3/7*a**2 + 9/7*a + v.
3*(a + 1)*(a + 2)/7
Let l = 409 + -405. Suppose 2*z = -2*o, l*o = -2*z + z. Factor 2/9*t**3 - 8/9*t**2 + 8/9*t + o.
2*t*(t - 2)**2/9
Determine n so that 18*n**2 + 7*n - 2*n + 78*n**2 - n - 4*n**3 - 96 = 0.
-1, 1, 24
Let g = 782 - 784. Let l be (g/(-4))/(77/5346). Factor 54/7*j - l - 3/7*j**2.
-3*(j - 9)**2/7
Let g(l) = -4*l**2 + 1218*l - 91199. Let a(u) = -8*u**2 + 2434*u - 182399. Let t(n) = 5*a(n) - 9*g(n). Factor t(w).
-4*(w - 151)**2
Let v(w) be the third derivative of -w**7/1680 + 63*w**6/40 - 71063*w**5/60 - 23877*w**4/2 - 143641*w**3/3 - 3316*w**2. Factor v(o).
-(o - 758)**2*(o + 2)**2/8
Find i such that -1814/5*i**2 + 2/5*i**3 - 3634/5*i - 1818/5 = 0.
-1, 909
Let a(y) be the second derivative of -3/20*y**5 + 0 + 11/2*y**4 + 7*y - 121/2*y**3 + 0*y**2. What is c in a(c) = 0?
0, 11
Let r be 8/(-332) + (-8904)/(-4399). Find n such that -1/2*n + 0 - 1/6*n**r = 0.
-3, 0
Let b(x) be the second derivative of -3*x**5/20 + 33*x**4 + 823*x**3/2 + 1035*x**2 + 99*x. Solve b(s) = 0 for s.
-5, -1, 138
Let -5 + 5 - 722*r - 3*r**2 - 703*r = 0. What is r?
-475, 0
Let i = -97057 + 97061. Let 36/13*z**i + 66/13*z**3 + 22/13*z**2 - 2/13 - 10/13*z = 0. What is z?
-1, -1/6, 1/3
Let q(y) be the second derivative of y**6/210 + 11*y**5/140 + 8*y**4/21 + 2*y**3/3 + 326*y + 4. Factor q(x).
x*(x + 2)**2*(x + 7)/7
Factor 240*p - 81 - 36 + 3*p**2 - 12 - 93 - 21.
3*(p - 1)*(p + 81)
Factor 11 + 45*n**4 - 50*n**4 - 3745*n**3 - 3740*n**2 - 11.
-5*n**2*(n + 1)*(n + 748)
Let n be (28 + (-1254)/44)*(-4)/10. Find m, given that -6/5 - m + n*m**2 = 0.
-1, 6
Let w = 200366/60135 - -28/20045. Suppose -3*o + 12 = o. Let 2/9 + 14/9*r + w*r**2 + 2*r**o = 0. What is r?
-1, -1/3
Let j(z) be the third derivative of -z**7/84 + 109*z**6/48 + 111*z**5/8 + 1675*z**4/48 + 140*z**3/3 - 43*z**2 - 35. What is c in j(c) = 0?
-1, 112
Let q(w) = 3*w**2 + 56*w - 725. Let z(s) = 5*s**2 + 57*s - 723. Let d(c) = -3*c**3 - c**2 + 4*c - 3. Let p be d(1). Let y(l) = p*q(l) + 2*z(l). Factor y(t).
(t - 27)**2
Factor -1833*o**2 - 672 - 656*o + 912*o**2 + 917*o**2 + 2000.
-4*(o - 2)*(o + 166)
Determine u so that -14/13*u**2 - 2*u**3 + 0 + 2/13*u**5 - 10/13*u**4 + 0*u = 0.
-1, 0, 7
Let g(b) be the second derivative of 11*b + 0*b**2 + 0 + 7/24*b**3 - 1/48*b**4. Solve g(c) = 0 for c.
0, 7
Let h(f) = -69*f**2 - 16470*f - 13563053. Let x(w) = 260*w**2 + 65880*w + 54252210. Let t(c) = 15*h(c) + 4*x(c). Factor t(j).
5*(j + 1647)**2
Let z = 87 + 69. Let x be z/32 - (-1)/8. Factor 3*v - 8 + x*v**3 + 0*v - 8*v + 20*v**2 - 12.
5*(v - 1)*(v + 1)*(v + 4)
Suppose 51*u - 3000 = 26*u. Suppose 308*q = 278*q + u. Factor 12*m**2 - 25/2 + 1/2*m**q + 5*m - 5*m**3.
(m - 5)**2*(m - 1)*(m + 1)/2
Let h(n) be the third derivative of n**8/1176 + n**7/7 + 213*n**6/28 + 1557*n**5/14 + 5400*n**4/7 + 20736*n**3/7 + 2*n**2 + 141. Find l such that h(l) = 0.
-48, -3
Factor 2/7*n**2 - 350*n - 2452/7.
2*(n - 1226)*(n + 1)/7
Let v be 24/(-3) - (-13 + -150). Let h be 6/(-1) + v/25. Factor -4/5*p**2 - h*p**3 + 0 - 4/5*p.
-p*(p + 2)**2/5
Let q = -451 - -457. Suppose -24*c - q = -26*c. Factor -2 - 2/3*x**2 - 2/3*x**c + 10/3*x.
-2*(x - 1)**2*(x + 3)/3
Let h(v) be the second derivative of 5*v**4/16 - 37*v**3/8 + 81*v**2/4 + 60*v. Determine g so that h(g) = 0.
2, 27/5
Let y be -20 + (-23 - -4) + 39. Let o(z) be the second derivative of -3/20*z**5 - z + y*z**2 + 0 + 1/90*z**6 - 7/18*z**3 + 5/12*z**4. Let o(x) = 0. Calculate x.
0, 1, 7
Factor -868*x + 1882*x - 4*x**2 - 806*x + 212.
-4*(x - 53)*(x + 1)
Let j(f) = -f**2 + 13*f + 90. Let w be j(-5). Factor w*b**2 - 6*b**2 + 3*b**4 + 121 - 118.
3*(b - 1)**2*(b + 1)**2
Solve 48/7*w**3 + 464/7*w - 300/7*w**2 - 30 - 2/7*w**4 = 0 for w.
1, 7, 15
Determine r, given that -240/11 - 2/11*r**2 - 22*r = 0.
-120, -1
Let i(s) = -26*s**2 + 72*s - 2. Let w(k) = -k**3 - 131*k**2 + 364*k - 11. Let o(d) = 22*i(d) - 4*w(d). Factor o(g).
4*g*(g - 8)*(g - 4)
Let f = 4786 - 4786. Let u(z) be the first derivative of 0*z + f*z**2 - 1/10*z**5 - 7 + 1/2*z**4 - 1/3*z**6 + 1/6*z**3. Find m, given that u(m) = 0.
-1, -1/4, 0, 1
Let g(x) be the first derivative of -x**6/24 - 267*x**5/20 - 18219*x**4/16 - 53065*x**3/12 - 6567*x**2 - 4356*x - 670. Factor g(w).
-(w + 1)**3*(w + 132)**2/4
Let j(q) be the second derivative of 37*q**5/6 - 41*q**4 - 8*q**3/9 + 3063*q - 2. Factor j(l).
2*l*(l - 4)*(185*l + 2)/3
Let d be (-1288)/(-90) - (-420)/350. Let w = -136/9 + d. Let w*x**4 + 6/5*x**2 + 8/5*x**3 - 8/5*x - 8/5 = 0. Calculate x.
-2, -1, 1
Determine i, given that 8/3*i + 2/9*i**2 + 64/9 = 0.
-8, -4
Let g(c) = 10*c**2 + 82*c + 48. Let b(p) = 4*p**2 + 33*p + 19. Suppose 60 = 4*f - 3*d, -5*f = -d - 46 - 18. Let u(j) = f*b(j) - 5*g(j). Factor u(m).
-2*(m + 1)*(m + 6)
Let c be (2 + -3)*-1*43. Suppose c*m = 55*m. Find d, given that m + 0*d - 14/9*d**3 + 4/9*d**2 + 10/9*d**4 = 0.
0, 2/5, 1
Let f(w) = w**3 + 26*w**2 + 254*w + 7589. Let g be f(-27). Factor -10/7*z**g + 0 - 1/7*z**3 - 16/7*z.
-z*(z + 2)*(z + 8)/7
Let b be (414/186 + -3)*4/(-6). Let r = b - -89/248. Let r*n**3 + 1/4*n**2 + 0*n + 0 + 5/8*n**4 = 0. What is n?
-1, -2/5, 0
Let n be 24/42 - 20/35. Let t(r) be the second derivative of 0*r**2 - 1/4*r**4 - r**3 + 5*r + n. Let t(s) = 0. What is s?
-2, 0
Let p(i) = -11*i**2 + 26*i - 14. Let f(l) = 56*l**2 - 131*l + 71. Suppose -3*a + 22 + 26 = 3*q, q = 3*a - 4. Let j(y) = q*p(y) + 2*f(y). Factor j(r).
-3*(r - 2)*(3*r - 2)
Suppose 0 = 31*f - 34*f + 12. Factor -346*b**4 + 1 - 30*b**2 + b**5 - 6*b**3 - 1 - 5*b**3 + 350*b**f.
b**2*(b - 3)*(b + 2)*(b + 5)
Let r(k) be the third derivative of k**5/100 + 15*k**4/4 - 152*k**3/5 + 11*k**2 + 389. Let r(p) = 0. What is p?
-152, 2
Let j(t) be the third derivative of -t**5/90 + 41*t**4/4 - 9085*t**2. Suppose j(i) = 0. Calculate i.
0, 369
Let b be 4/8*(-18)/(-3). Let -3/7*u**3 - 15/7*u**2 - b + 39/7*u = 0. What is u?
-7, 1
Factor 258*w**2 - 11*w**3 - 6*w**4 + 468 + 2*w**4 - 14*w**3 + 46*w**2 - 744*w + w**3.
-4*(w - 3)**2*(w - 1)*(w + 13)
Suppose -6625 + 9*d**2 - 8*d**2 + 64*d + 7453 = 0. Calculate d.
-46, -18
Let b(r) be the first derivative of 31/8*r**2 + 13 + 3/2*r - 9/16*r**4 + 4/3*r**3. Find w, given that b(w) = 0.
-1, -2/9, 3
Let k(v) be the second derivative of v**5/100 + v**4/60 - 16*v**3/15 - 6*v**2 - 17*v + 13. Determine y so that k(y) = 0.
-5, -2, 6
Let i be ((0 - -1) + 24/(-40))*921/614. Factor -i*f + 1/5*f**3 + 0 - 2/5*f**2.
f*(f - 3)*(f + 1)/5
Let c = 5185/3 + -1727. Let k(t) be the first derivative of -c*t**3 + 4*t + 15 + 0*t**2. Factor k(r).
-4*(r - 1)*(r + 1)
Let w = 392 - 389. Factor 72 + 233*i + 24*i**w + 229*i - 93*i**3 + 680*i**2 - 131*i**3.
-2*(i - 4)*(10*i + 3)**2
Suppose -226*j - 1836 = -838*j. Factor -18 - 15/2*s**j - 9/2*s**2 + 48*s.
-3*(s - 2)*(s + 3)*(5*s - 2)/2
Suppose 5272 = -18308*o + 18967*o. Let -30*n + 51/2*n**3 - 34*n**2 + o + 9/2*n**5 + 26*n**4 = 0. What is n?
-4, -2, -1, 2/9, 1
Solve -71 - 9*j + 6*j**2 + 3*j**3 + 99 - 28 = 0.
-3, 0, 1
Suppose 2*v + 10 = n, 10 = 5*n - 4*n - 4*v. Let u be (16 - n)*1/2. Find d, given that 65*d**3 - 38*d**3 - 37*d**u + 5*d + 5*d**2 = 0.
-1/2, 0, 1
Let v(k) be the second derivative of 0 - 214*k + 5/14*k**3 - 1/6*k**4 - 1/140*k**5 + 0*k**2. Find a such that v(a) = 0.
-