*2
Let x(f) be the third derivative of 0*f**3 + 1/150*f**5 + 0 - 224*f**2 - 71/60*f**4 + 0*f. Factor x(r).
2*r*(r - 71)/5
Let k(w) = -5*w + 105 - 103 + 10*w - 4*w + 2*w**2. Let n(v) = 15*v**2 - 75*v + 90. Let b(s) = -6*k(s) + n(s). Solve b(f) = 0 for f.
1, 26
Suppose -2*d + 51 = 5*t, -3*t - 58*d = -62*d - 15. Suppose 0 = 4*g - t*g - 4*c, 4*g = -4*c. Factor -3/8*x**3 + g*x**2 + 0*x + 0 - 9/8*x**4.
-3*x**3*(3*x + 1)/8
Let c be 7/(-14) - (-10)/12. Let r be (130/(-78))/(5/(-2)). Let -2/3*h**3 + r*h - 1/3*h**4 + c + 0*h**2 = 0. Calculate h.
-1, 1
Let v(w) = -w**2 + 754*w + 9197. Let u be v(-12). Factor 0 + 0*h - 2/3*h**u - 6*h**2 - 2*h**3 + 10/3*h**4.
-2*h**2*(h - 3)**2*(h + 1)/3
Suppose -59/4*x + x**4 - 157/4*x**2 + 119/4*x**3 + 93/4 = 0. Calculate x.
-31, -3/4, 1
Let x(u) be the second derivative of u**4/24 - 13*u**3/4 + 35*u**2 + 1352*u. Factor x(g).
(g - 35)*(g - 4)/2
Let x be (-2)/8 + 18/(-24). Let h(k) = 7*k**3 + 2*k**2 - 6. Let t be (1/2)/((-2)/24). Let d(z) = -z**3 - z**2 + 1. Let n(r) = t*d(r) + x*h(r). Factor n(q).
-q**2*(q - 4)
Let d(g) be the first derivative of -3*g**4/22 + 46*g**3/33 - 28*g**2/11 - 24*g/11 + 710. Let d(k) = 0. What is k?
-1/3, 2, 6
Let l = -47051/14 - -23550/7. Factor -l*v + 1/2*v**2 + 3.
(v - 6)*(v - 1)/2
Let h(z) = 40*z**3 + 872*z**2 + 1128*z + 140. Let y(f) = -f**3 - f + 4. Let g(m) = -2*h(m) - 52*y(m). Factor g(b).
-4*(b + 1)*(b + 61)*(7*b + 2)
Let r(l) be the first derivative of 676*l + 26*l**2 + 1/3*l**3 + 75. Factor r(b).
(b + 26)**2
Let g(u) = 2*u**4 + 3*u**3 + u**2 - 2. Let l(c) = 3*c**4 - 105*c**3 + 2*c**2 - 4. Let t(q) = 2*g(q) - l(q). Factor t(a).
a**3*(a + 111)
Find i, given that -445*i + 583*i + 80089 + i**2 + 428*i = 0.
-283
Suppose -2 = 49*m - 50*m. Factor -52*t - 21*t**2 - 34 + 710 + 43*t**m - 21*t**2.
(t - 26)**2
Let d be (-4)/5 - (-3)/(-60)*184. Let n be ((-2)/(-20))/((-5)/d + 0). Let 0 + 0*w**2 - 3/5*w**3 + 4/5*w - n*w**4 = 0. What is w?
-2, 0, 1
Let s be 0 - 1 - (-8080)/(-3030)*(-33)/40. Factor 0 + 224*p**2 + 166/5*p**3 - 392/5*p + s*p**4.
2*p*(p + 14)**2*(3*p - 1)/5
Let a(z) be the third derivative of z**7/630 - z**6/180 - z**5/60 + z**4/9 - 2*z**3/9 - 77*z**2 - 13*z. Suppose a(n) = 0. What is n?
-2, 1, 2
Let c(l) be the third derivative of l**5/60 + l**4/8 - 9*l**3 - 16*l**2 + 3*l. Let c(o) = 0. Calculate o.
-9, 6
Let g be 15/(-105) + (-138)/(-182). Factor -56/13*v + g*v**2 + 64/13 + 2/13*v**3.
2*(v - 2)**2*(v + 8)/13
Let w be (64/(-4))/4 + 0. Let h be 1/((-5)/(80/w)). Find s such that 87*s**4 + 132*s - 83*s**h + 32*s**3 + 96*s**2 - 4*s + 64 = 0.
-2
Let d = 222684 + -1118328/5. Let z = d + 982. Suppose -4/5*u**3 + 0*u**2 + 2/5*u**5 - z*u**4 + 0*u + 0 = 0. What is u?
-1, 0, 2
Suppose -3*z + 10 + 1 = -1. Let g(q) be the third derivative of -16*q**2 + 0*q + 3/10*q**3 - 1/40*q**z + 0 - 1/60*q**5 - 1/600*q**6. Factor g(w).
-(w - 1)*(w + 3)**2/5
Suppose 2*j = -9*j + 17 - 5 + 10. Solve -3/2*x**j - 15 + 33/2*x = 0 for x.
1, 10
Suppose -3*l + 184 = 2*x, -135 = 3*l - 3*x - 309. Let w be (-1 + 65/l)/(14/42). Factor -1/2*r**2 + 1/4*r + 0 + w*r**3.
r*(r - 1)**2/4
Let c(b) be the second derivative of b**7/70 + 3*b**6/8 + 7*b**5/10 + 69*b**2/2 + 2*b + 9. Let y(a) be the first derivative of c(a). Factor y(p).
3*p**2*(p + 1)*(p + 14)
Let f = 2376/65 + -1916/65. Determine v, given that -f*v + 2/13*v**2 + 1058/13 = 0.
23
Let g(l) = -l - 1. Let c(z) = z**2 - 12*z + 26. Let y be c(8). Let u(x) = 2*x**2 + 102*x + 1452. Let w(m) = y*g(m) + u(m). Let w(k) = 0. Calculate k.
-27
Factor -31303*h**3 - 31305*h**3 + 62606*h**3 + 148*h**2 - 288*h.
-2*h*(h - 72)*(h - 2)
Let a = -23 + 16. Let o be (a - -11) + (-56)/(-2). Factor s**2 - 31*s - 27*s + 22*s + 3*s**2 + o.
4*(s - 8)*(s - 1)
Let n(m) be the first derivative of 5/2*m**3 - 13*m - 38 + 5/12*m**4 + 0*m**2. Let b(h) be the first derivative of n(h). Factor b(c).
5*c*(c + 3)
What is w in -33*w**2 - 156*w**3 - 902*w**4 - 4*w**5 - 79*w**2 + 854*w**4 = 0?
-7, -4, -1, 0
Let w(f) be the first derivative of 1/8*f**4 + 3/2*f**2 + 22*f - 3/4*f**3 - 19. Let s(z) be the first derivative of w(z). Factor s(a).
3*(a - 2)*(a - 1)/2
Let j be 9010/(-5406)*(1 - 101/95). Suppose -5*p = 4 - 29. Solve 2/19*s**p + 0 + 8/19*s**4 + 8/19*s**2 + j*s + 12/19*s**3 = 0.
-1, 0
Suppose 5*x - 1859 + 1839 = 0. Suppose x*w = -4*a + 24, 2*w + 4 = w + 4*a. Factor 2/17*o**w + 0*o - 2/17*o**3 - 12/17*o**2 + 0.
2*o**2*(o - 3)*(o + 2)/17
Let i = 2016 + -1414. Let x = i - 1189/2. Determine y so that -33/2*y - 21/2*y**2 - 3/2*y**3 - x = 0.
-5, -1
Suppose 0 = -327079*n + 327109*n - 60. Let 2/21*s**n + 8/21 + 10/21*s = 0. What is s?
-4, -1
Let y(p) = 12*p**2 + 680*p - 4008. Let k(d) = 8*d**2 + 450*d - 2673. Let n(a) = -8*k(a) + 5*y(a). Factor n(o).
-4*(o - 6)*(o + 56)
Let g(a) = -a**3 + 7*a**2 - 9*a + 1. Let c be g(5). Suppose -1 = u - c. Let -2 - 2*n**2 + 4 - n - n**u - 2*n + 4*n**3 = 0. What is n?
-2, -1, 1
Suppose 0 = -8*s + 639 - 599. Let 2*a**3 - 4*a**3 - a**4 - s*a + 4*a**3 + 8*a**2 + 0*a**2 - 13*a + 9 = 0. What is a?
-3, 1, 3
Let g(i) = -i**4 + 57*i**3 + 108*i**2 + 53*i - 9. Let q(r) = 58*r**3 + 110*r**2 + 54*r - 6. Let b(l) = 2*g(l) - 3*q(l). Find d such that b(d) = 0.
-28, -1, 0
Let f(j) = -j**3 - 8*j**2 + 7*j - 7. Let d be f(-9). Suppose y + 2*y - 21 = 0. Find o, given that 20*o**2 + 15 + d*o**2 + 36*o - y*o**2 + 4*o**3 + 1 = 0.
-4, -1
Let s be 5 - ((-282)/27 + (-20)/(-45)). Suppose 8 = -0*n + 4*n. Factor -1 + 17*u**n + 4*u - s*u**2 + 1.
2*u*(u + 2)
Suppose -42/5*b**2 - 12/5 - 254/5*b = 0. What is b?
-6, -1/21
Let s(b) = 5*b**4 + 35*b**3 - 445*b**2 + 225*b. Let r(n) = 6*n**4 + 35*n**3 - 476*n**2 + 225*n. Let f(g) = 6*r(g) - 7*s(g). Factor f(c).
c*(c - 25)*(c - 9)*(c - 1)
Let h be 58/116 + (-2)/4. Let c(l) be the first derivative of -1/3*l**3 + 0*l**2 - 1/8*l**4 - 10 + h*l. Factor c(x).
-x**2*(x + 2)/2
Let f(t) be the second derivative of -t**4/12 + 7*t**3/3 - 188*t + 11. Factor f(k).
-k*(k - 14)
Let d(r) be the second derivative of -r**4/60 - 59*r**3/15 - 69*r**2/2 - 1486*r - 2. Factor d(v).
-(v + 3)*(v + 115)/5
Let h(b) be the first derivative of 2*b**7/105 + 11*b**6/30 + 8*b**5/5 - 6*b**4 + b**2 + 5*b - 156. Let z(v) be the second derivative of h(v). Factor z(u).
4*u*(u - 1)*(u + 6)**2
Factor -32768/5 - 2306/5*v**2 + 9/5*v**3 + 147968/5*v.
(v - 128)**2*(9*v - 2)/5
Suppose 6 = -188252*f + 188254*f. Suppose -14/9*g - 4/9*g**2 - 8/9 + 2/9*g**f = 0. What is g?
-1, 4
Find u, given that 975 - 330*u**2 - 1285/2*u - 5/2*u**3 = 0.
-130, -3, 1
Suppose -4*g + 36 = 7*h - 6*h, 4*h - 40 = -3*g. Let q be (88/(-396))/(g/(-42)). Factor l - 1/6*l**2 + q.
-(l - 7)*(l + 1)/6
Let r(i) be the third derivative of i**6/200 - 99*i**5/100 + 48*i**4/5 - 38*i**3 + 1455*i**2. Factor r(g).
3*(g - 95)*(g - 2)**2/5
Let m(n) be the third derivative of -3*n**7/280 - 79*n**6/160 - 1207*n**5/240 + 295*n**4/32 - 19*n**3/3 - 2483*n**2. Determine w so that m(w) = 0.
-19, -8, 1/3
What is s in -10560*s - 243/4*s**3 + 3779*s**2 - 14400 + 1/4*s**4 = 0?
-1, 4, 120
Let j be (-45 - 4732/(-105))*30. Solve 24/7 + 16/7*k + 2/7*k**j = 0.
-6, -2
Suppose 5*q = -12*z + 13*z + 8, 3*z = -3*q + 12. Let m(o) be the third derivative of -1/420*o**5 + 0*o + 0*o**3 - 1/168*o**4 + 0 + 13*o**q. Factor m(k).
-k*(k + 1)/7
Let -50*d**2 - 27 - 14*d**4 + 5*d**4 + 8*d**4 - 15*d**3 + 27 = 0. Calculate d.
-10, -5, 0
Let t(u) = 4*u**3 + 164*u**2 + 152*u + 8. Let r(x) = 8*x**3 + 327*x**2 + 305*x + 14. Let g(s) = 4*r(s) - 7*t(s). Factor g(j).
4*j*(j + 1)*(j + 39)
Let g(w) be the third derivative of -w**5/60 + 229*w**4/6 - 104882*w**3/3 - 5*w**2 + 3*w. Let g(i) = 0. What is i?
458
Let i(h) be the first derivative of -5*h**6/3 + 42*h**5/5 + 323*h**4/5 + 344*h**3/3 + 408*h**2/5 + 128*h/5 + 1805. Suppose i(r) = 0. Calculate r.
-2, -1, -2/5, 8
Let p be (-4)/(-8) - 11787/(-6). Let 1960*d**2 - 80 - p*d**2 - 33*d + 83*d = 0. Calculate d.
2, 8
Let y(o) be the second derivative of -o**4/72 + 5*o**3/6 + 34*o**2/3 - 4*o + 6. Factor y(k).
-(k - 34)*(k + 4)/6
Factor 187*w - 1/2*w**2 + 376.
-(w - 376)*(w + 2)/2
Let y be 2910/9 - 46/(-69). Let p = y - 4210/13. Determine m, given that 2/13*m**2 + 4/13*m**3 - 4/13*m + 0 - p*m**4 = 0.
-1, 0, 1, 2
Suppose 102*b**3 + 1160*b**4 - 590*b**4 - 5408*b - 569*b**4 + 2496*b**2 = 0. What is b?
-52, 0, 2
Let h = -20420 - -20423. Let z(b) be the third de