+ 1)**4/11
Let l(s) be the third derivative of 19*s**5/90 - 59*s**4/36 + 2*s**3/3 - s**2 - 11*s + 288. Determine y so that l(y) = 0.
2/19, 3
Find l such that 10/7 - 3*l - 1/7*l**3 + 12/7*l**2 = 0.
1, 10
Let j = -1547092/3 + 515810. Solve 455/3*r + 76/3*r**2 + r**3 - j = 0.
-13, 2/3
Let w(t) be the first derivative of -5*t**3 + 285*t**2 + 25401*t + 152. Let b(k) = -2*k**2 + 2*k + 1. Let m(n) = 9*b(n) - w(n). Find a such that m(a) = 0.
-92
Let h(f) = -1303477*f**2 - 121573*f - 2852. Let r(n) = 372420*n**2 + 34735*n + 815. Let u(c) = -5*h(c) - 17*r(c). Determine w so that u(w) = 0.
-9/193
Let h be (9/(-18) + 2)*(208/(-936))/(5/(-2)). Factor 2/5*i**5 + 0*i**3 + 0 + 0*i - h*i**4 + 0*i**2.
2*i**4*(3*i - 1)/15
Let j(d) = -d**3 + d - 2. Let w(p) be the second derivative of 2*p**3/3 + 4*p**2 - 135*p + 1. Let v(l) = -2*j(l) - w(l). Determine g, given that v(g) = 0.
-1, 2
Let h(m) be the first derivative of -m**3/18 - 269*m**2/6 - 72361*m/6 - 1547. Factor h(c).
-(c + 269)**2/6
Let o(t) be the first derivative of 4*t**6/39 - 6*t**5/5 - 55*t**4/13 + 10*t**3/13 + 106*t**2/13 + 48*t/13 + 6343. What is n in o(n) = 0?
-2, -1, -1/4, 1, 12
Find l, given that 5*l**4 - 28*l**2 + 0*l**4 + 41*l**3 + 5*l**4 + 3*l**3 - 588*l - 14*l**4 = 0.
-3, 0, 7
Solve -7/4*j**3 - 27/4*j**2 - 6*j + 1 = 0 for j.
-2, 1/7
Solve -95*m**2 + 15*m**4 - 150*m - 8350*m**5 + 16695*m**5 - 8350*m**5 + 75*m**3 = 0.
-3, -1, 0, 2, 5
Solve -52*z**3 - z**5 - 16*z**2 + 36 + 54*z - 10145*z**4 - z**5 - 10125*z**4 + 20250*z**4 = 0.
-6, -3, -1, 1
Find j such that -j**5 + 0 - 1/2*j + 3/2*j**3 + 1/2*j**2 - 1/2*j**4 = 0.
-1, 0, 1/2, 1
Let n(m) be the third derivative of m**6/480 + 283*m**5/40 + 80089*m**4/8 + 22665187*m**3/3 + m**2 + 29. Find v such that n(v) = 0.
-566
Let n be (-20)/(-60)*18/1348. Let s = 355/4044 - n. Find u such that 1/12*u**5 - s*u**4 - 5/12*u**3 + 1/12*u**2 + 1/3 + 2/3*u = 0.
-1, 2
Suppose -3*h = -3*y, h - 6 = -4. Let v be (-1125)/(-468) + ((-72)/(-39) - y). Let -9*r**2 + 3/8*r**5 + v*r**4 + 3/8*r**3 + 0 + 6*r = 0. What is r?
-4, 0, 1
Let z(f) be the third derivative of 18/35*f**7 - 83/20*f**5 - 21/10*f**6 + 17/4*f**4 - 17*f + f**2 - 3/2*f**3 + 0. Factor z(x).
3*(x - 3)*(x + 1)*(6*x - 1)**2
Suppose 68*f + 50*f = 136*f. Factor -1/4*i**3 - 1/2*i**2 + f + 1/2*i**4 + 0*i + 1/4*i**5.
i**2*(i - 1)*(i + 1)*(i + 2)/4
Let p(i) = -7*i - 37*i - 55 - 4696*i**2 + 4694*i**2 + 11. Let y(x) = 12*x**2 + 221*x + 220. Let s(w) = -11*p(w) - 2*y(w). Factor s(c).
-2*(c - 22)*(c + 1)
Let j(z) be the second derivative of z**4/36 - 5*z**3/9 + 8*z**2/3 - 885*z. Factor j(i).
(i - 8)*(i - 2)/3
Let u be (8/12)/(1/48). Let z = 31 - 27. Factor -40*w + z*w**4 - 48*w - u*w**3 + 92*w**2 + 48 - 24*w.
4*(w - 3)*(w - 2)**2*(w - 1)
Let p be 29/84 - (-46 - (-39688)/861). Factor -p*g**2 - 1/2*g + 0.
-g*(g + 2)/4
Let v be (5/(-15) - 5)*(-12)/16. Factor -61*y**3 + 46*y**3 + 3*y**v - 11*y - 10*y + 27*y**2 + 6.
3*(y - 2)*(y - 1)**3
Suppose 43*t + 87*t + 1345 = 9*t + 3886. Find s, given that t*s**2 + 3/5*s**3 + 102/5*s + 0 = 0.
-34, -1, 0
Let h be (-59)/7 + -19*60/(-2660). Let u be 2*h/60*-3. Find q such that 12/5 + 2*q - 2/5*q**3 - u*q**2 = 0.
-3, -1, 2
Let z = -149 - -152. Let y be (z + -1)/(12/(-3) - -15). Factor -y*v**3 - 18/11 - 6/11*v + 10/11*v**2.
-2*(v - 3)**2*(v + 1)/11
Let m = 246297 + -2216672/9. Let 0 - m*q**2 - 25/9*q = 0. What is q?
-25, 0
Let n(v) be the third derivative of -v**8/112 - 3*v**7/70 + 11*v**6/20 + 6*v**5/5 - 5542*v**2. Suppose n(q) = 0. Calculate q.
-6, -1, 0, 4
Suppose -3*c - 3*i + 93 = 0, -4*i - 149 = -4*c - 3*i. Let s be (3*8/c)/((-4)/(-66)). Factor b**3 - 5*b**3 + 4*b + 16*b**2 - s*b - 9*b.
-4*b*(b - 2)**2
Let g(v) be the third derivative of 15/4*v**4 - 2/3*v**5 - 15/2*v**3 + 0 + 1/42*v**7 + 30*v**2 - 1/12*v**6 - 2*v. Factor g(x).
5*(x - 3)*(x - 1)**2*(x + 3)
Let o(i) be the second derivative of -i**7/63 + 11*i**6/45 - 11*i**5/10 + 5*i**4/18 + 50*i**3/9 + 965*i. Suppose o(c) = 0. Calculate c.
-1, 0, 2, 5
Let y be (-2 + (-4)/(-10))/(57/(-190)). Let i(c) be the first derivative of y*c + 12 + 0*c**2 - 4/9*c**3. Suppose i(t) = 0. What is t?
-2, 2
Let k be 4090/(-3681) + (-31)/45 + 18/10. What is x in -2/3*x**3 + k + 32/3*x + 10*x**2 = 0?
-1, 0, 16
Let l(z) be the first derivative of z**5/5 + 21*z**4/2 + 565*z**3/3 + 1104*z**2 - 2816*z + 8438. Factor l(y).
(y - 1)*(y + 11)*(y + 16)**2
Let v(r) = -2305*r - 5. Let d(s) = s**2 - 2281*s - 4. Let w(a) = -5*d(a) + 4*v(a). Factor w(f).
-5*f*(f - 437)
Let i(j) = 50*j**3 - 5279*j**2 - 12837*j - 4298. Let r(b) = 324*b**3 - 34312*b**2 - 83440*b - 27936. Let a(c) = 32*i(c) - 5*r(c). Factor a(n).
-4*(n - 134)*(n + 2)*(5*n + 2)
Let m(g) = g**2 + 14*g + 14. Let p be m(-13). Suppose -8*c = -41 + p. Let -c - 91*w**2 + 10 + 61*w**2 - 25*w = 0. Calculate w.
-1, 1/6
Find f such that -896/9*f**2 - 34816/9*f + 1064/9*f**3 - 32768/9 + 2/9*f**5 - 86/9*f**4 = 0.
-4, -1, 16
Let i(k) be the second derivative of -k**4/30 + 19*k**3/15 + 216*k**2/5 - 4729*k + 2. Factor i(t).
-2*(t - 27)*(t + 8)/5
Let n(v) be the third derivative of -71/360*v**6 - 6*v**2 + 0 - 1/6*v**4 - 1/252*v**8 + 0*v**3 + 29/630*v**7 + 0*v + 16/45*v**5. Find f, given that n(f) = 0.
0, 1/4, 2, 3
Let y = -352 - -354. Factor -124*a**y - 896*a + 2*a**3 + 588 - 6*a**3 + 436.
-4*(a - 1)*(a + 16)**2
Let h(m) = -2328*m + 267722. Let s be h(115). Find i such that 169/5*i**3 + 2/5 + 312/5*i**s - 51/5*i = 0.
-2, 1/13
Let z(y) be the second derivative of -1/3*y**4 + 8/3*y**3 + 16*y + 3 - 6*y**2. Factor z(a).
-4*(a - 3)*(a - 1)
Let b(y) = -4*y**3 + 4107*y**2 - 1117935*y + 101732084. Let m(d) = -d**3 - 12*d**2 + 1. Let u(g) = b(g) + m(g). Factor u(j).
-5*(j - 273)**3
Let i be 344/12 - 1/(-3). Suppose -5*k + 2*k + 4*m + i = 0, 0 = 5*k - m - 37. Factor -6*d**2 + d + k*d + 387 - 390 + d**4.
(d - 1)**3*(d + 3)
Let o(v) = -2*v**2 - 23*v - 10. Suppose -2 + 17 = 3*r. Suppose -r*k + 6 = 116. Let h(w) = w. Let z(u) = k*h(u) - 2*o(u). Find i, given that z(i) = 0.
-5, -1
Let j(w) be the third derivative of -w**6/24 - 25*w**5/4 - 210*w**4 + 13230*w**3 + 5518*w**2. Find d, given that j(d) = 0.
-42, 9
Let n(v) be the third derivative of 7/80*v**5 + 1029/8*v**3 + 147/32*v**4 + 0*v + 0 - 27*v**2 + 1/1440*v**6. Factor n(g).
(g + 21)**3/12
Let w = 124007/14685 - 1/44055. What is k in 112/9*k - 8/3*k**2 - w*k**3 + 28/9*k**4 + 32/9 = 0?
-1, -2/7, 2
Factor 0 - 26/11*g**3 - 324/11*g**2 - 144/11*g.
-2*g*(g + 12)*(13*g + 6)/11
What is a in 296/7*a**2 - 2/7*a**5 + 310/7*a - 600/7 + 12/7*a**3 - 16/7*a**4 = 0?
-5, -3, 1, 4
Factor 54*b**2 - 7514*b**3 + 317*b**2 - 685 + 314*b**2 - 5*b + 7519*b**3.
5*(b - 1)*(b + 1)*(b + 137)
Let i(c) be the second derivative of c**5/60 + 17*c**4/24 - 3*c**3 - 19*c**2/2 + 3*c + 2. Let o(a) be the first derivative of i(a). Factor o(b).
(b - 1)*(b + 18)
Let x(r) be the first derivative of 1/2*r**3 - 35 + 1/4*r**4 - 3/2*r**2 - 3/20*r**5 - 30*r. Let t(d) be the first derivative of x(d). Factor t(k).
-3*(k - 1)**2*(k + 1)
Let j(a) be the first derivative of 0*a - 26/9*a**3 - 56/45*a**5 + 38/9*a**4 - 2*a**2 - 130. Factor j(q).
-2*q*(2*q - 3)**2*(7*q + 2)/9
Let t(g) be the second derivative of g**5/4 + 15*g**4/4 + 20*g**3 + 40*g**2 - 1097*g. Factor t(w).
5*(w + 1)*(w + 4)**2
Suppose 19/3*j - 1/2*j**2 + 28/3 = 0. Calculate j.
-4/3, 14
Let -36*p - 441/4 + 1/4*p**2 = 0. Calculate p.
-3, 147
Let x(m) = 3*m**3 + 321*m**2 - 2392*m + 230. Let r be x(-114). Factor -14/3 - 2/3*n + 14/3*n**r + 2/3*n**3.
2*(n - 1)*(n + 1)*(n + 7)/3
Factor 0 + 0*a - 1/2*a**4 + 123/2*a**2 - 61*a**3.
-a**2*(a - 1)*(a + 123)/2
Suppose -3*i + 1 = -4*d, -d - 2*i + 4*i - 4 = 0. Factor -25*z**4 - 33*z**d + z**3 - 21*z**3 - 10*z**5 - 28*z**2 + 56*z**2.
-5*z**2*(z + 1)**2*(2*z + 1)
Let s(o) = 5*o**2 + 2*o - 7. Let a = 325 + -331. Let t be (4 - 3)/(1 - 0). Let v(b) = b**2 - 1. Let m(x) = a*v(x) + t*s(x). Suppose m(g) = 0. What is g?
1
Let r be ((-5901)/126 - -41)*96/(-15). Find h such that r*h + 2/3*h**2 + 1568/3 = 0.
-28
Let u = 136 + -125. Suppose 3*l = 0, -5*l = -8*s + u*s. Factor -2/5*i**2 - 4/5*i + 2/5*i**3 + s.
2*i*(i - 2)*(i + 1)/5
Suppose -n = -3*z - 8 - 14, -4*z = 20. Suppose -2*r = -2*k - 7 - n, -2*k = -3*r + 17. Determine j so that -7/4*j**r + 1/2*j + 0 - 5/4*j**2 = 0.
-1, 0, 2/7
Let l(m) be the third derivative of 64/9*m**4 + 8/45*m**5 + 256/9*m**3 + 