= -d**2 + 21*d + 12. Let r(y) = -y**2 + y. Let u(g) = c*p(g) - 5*r(g). Factor u(z).
4*(z + 1)*(z + 3)
Factor 0*i**3 + 0 + 10*i - 21/2*i**2 + 1/2*i**4.
i*(i - 4)*(i - 1)*(i + 5)/2
Let t be 0 + 185/225 + (16/36)/(-2). Find d, given that -33/5 + 6*d + t*d**2 = 0.
-11, 1
Suppose 5*j = t + 18, 0 = -t - t + j. Let l = t - 0. Factor l*p**4 + 11*p**4 - 3*p**4 + 14*p**3 + 2*p**5 + 25*p**2 - 19*p**2.
2*p**2*(p + 1)**2*(p + 3)
Let i be 136/(-374)*22/(-5). What is z in 2/5*z**2 + i*z + 8/15 - 2/3*z**3 = 0?
-1, -2/5, 2
Let p(y) = y**5 - y**4 - y**2 + 2*y. Let b(r) = 6*r**5 - 24*r**4 - 30*r**3 - 7*r**2 + 14*r. Let x(i) = -3*b(i) + 21*p(i). Factor x(d).
3*d**3*(d + 2)*(d + 15)
Let u(v) = 2715*v**2 - 208*v + 26. Let i(g) = -82*g + 19 - 15 + 1358*g**2 - 22*g + 10. Let p(j) = 11*i(j) - 6*u(j). Factor p(a).
-2*(26*a - 1)**2
Let b = 1010 - 994. Suppose 88 = b*d + 40. Factor 0 - 2/7*n**d - 6/7*n**2 + 8/7*n.
-2*n*(n - 1)*(n + 4)/7
Let l(r) be the first derivative of 4*r**6/3 - 124*r**5 - 84*r**4 + 1844*r**3/3 + 1088*r**2 + 624*r + 4173. Let l(g) = 0. What is g?
-1, -1/2, 2, 78
Let p(x) = -x**2 - 15*x - 11. Let r(v) = -v**3 + 9*v**2 - 22*v + 3. Let o be r(4). Let c(l) = 7*l + 6. Let i(h) = o*c(h) - 3*p(h). Factor i(s).
(s + 3)*(3*s + 1)
Let d be (-56)/36 + 2 - (2366/(-117))/13. Factor 2/5*i**d + 0 + 28/5*i.
2*i*(i + 14)/5
Solve 50/3*f**4 + 1920 + 2440/3*f**2 + 496/3*f**3 + 1984*f + 2/3*f**5 = 0 for f.
-6, -5, -4
Let f(d) be the third derivative of -d**8/2940 + d**7/630 + d**6/630 + 7*d**4/24 - d**3/6 - 73*d**2. Let o(a) be the second derivative of f(a). Factor o(c).
-4*c*(c - 2)*(4*c + 1)/7
Solve -3/5*i**3 + 16875 - 2925*i - 87*i**2 = 0.
-75, 5
Let h(f) = -2*f**5 + 8*f**4 - 13*f**3 + 10*f**2 + 3. Let y(c) = c**5 - 2*c**4 - 1. Let x(d) = 2*h(d) + 6*y(d). Factor x(p).
2*p**2*(p - 2)*(p - 1)*(p + 5)
Let q(l) be the second derivative of -4*l**4 - 72*l**2 - 26*l**3 - 344*l + 0 - 3/20*l**5. Factor q(r).
-3*(r + 2)**2*(r + 12)
Let h(w) be the second derivative of w**8/5040 - w**6/120 - w**5/90 + w**4/6 + 19*w**3/3 + 46*w. Let x(v) be the second derivative of h(v). Factor x(g).
(g - 3)*(g - 1)*(g + 2)**2/3
Factor -4*x**4 + 44571*x**3 + 16*x - 430 + 564*x**2 - 322 - 44395*x**3.
-4*(x - 47)*(x - 1)*(x + 2)**2
Factor -5/3*v**3 - 3982/3*v**2 - 316808/3 - 793612/3*v.
-(v + 398)**2*(5*v + 2)/3
What is z in -26/11*z**4 + 2/11*z**5 - 46/11*z + 4*z**3 + 2 + 4/11*z**2 = 0?
-1, 1, 11
Let 2/17*m**4 + 5136/17*m**2 + 26880/17 - 444/17*m**3 - 20288/17*m = 0. Calculate m.
4, 210
Let k(x) be the third derivative of 845*x**7/1512 - 13*x**6/108 + x**5/90 - 5*x**4/12 - 23*x**2. Let t(h) be the second derivative of k(h). Factor t(c).
(65*c - 2)**2/3
Let w(h) = 29*h**2 + 7792*h + 3049805. Let x(v) = 170*v**2 + 46755*v + 18298830. Let z(y) = 35*w(y) - 6*x(y). Factor z(a).
-5*(a + 781)**2
Let r(l) = -l**3 - 2*l + 1. Let m(z) = -2*z**5 - 14*z**4 + 10*z**3 + 38*z**2 - 20*z - 4. Let h(p) = m(p) + 4*r(p). What is u in h(u) = 0?
-7, -2, 0, 1
Suppose 0 = -l - 5*k + 25, 9*k = -l + 6*k + 21. Factor -l*s + 10*s**3 + 206*s**2 - 2*s**4 - 204*s**2 + 5*s.
-2*s*(s - 5)*(s - 1)*(s + 1)
Let l(g) = 48*g**2 + 1867*g - 1036. Let x(f) = -6*f**2 - 233*f + 128. Let v(w) = 6*l(w) + 46*x(w). Let v(t) = 0. Calculate t.
-41, 2/3
Let d(b) be the second derivative of b**4/6 + 43*b**3/3 - 294*b**2 - 5809*b. Factor d(g).
2*(g - 6)*(g + 49)
Let x(d) be the second derivative of d**6/540 + 7*d**5/45 + 49*d**4/9 - d**3/6 - 53*d**2/2 + 141*d. Let p(n) be the second derivative of x(n). Factor p(i).
2*(i + 14)**2/3
Let h(w) be the second derivative of -w**4/90 + 1108*w**3/45 + 1109*w**2/15 - 16130*w. Factor h(r).
-2*(r - 1109)*(r + 1)/15
Suppose 4*k + 16 = 5*d + 3*k, 3*d + 5*k = 32. Suppose -8*x + 116 = -d. Factor 85 + x*r**3 - 12*r - 61 - 6*r**2 - 3*r**4 - 12*r**2.
-3*(r - 2)**3*(r + 1)
Suppose -144 = 16*i - 4*i. Let u be (i/15)/((-14)/(-105)*-3). Factor -3/2*o**3 - o**u + 0*o + 0*o**4 + 0 + 1/2*o**5.
o**2*(o - 2)*(o + 1)**2/2
Let z(v) be the third derivative of -192*v**7/35 + 188*v**6/3 - 1314*v**5/5 + 1539*v**4/4 + 486*v**3 - 75*v**2 + 2*v - 7. Factor z(r).
-2*(4*r - 9)**3*(9*r + 2)
Let d be -1*5/(-4 - (-9 - -4)). Let j be (-5 - d)/(-4 - 12/(-4)). What is o in j*o - 2/13*o**2 - 4/13*o**3 + 0 - 2/13*o**4 = 0?
-1, 0
Let f(y) be the first derivative of 15*y**4/4 + 25*y**3/3 - 170*y**2 - 800*y - 2603. Factor f(j).
5*(j - 5)*(j + 4)*(3*j + 8)
Let j(w) be the first derivative of w**7/1365 + w**6/780 - 68*w**2 - 29. Let b(x) be the second derivative of j(x). Solve b(i) = 0.
-1, 0
Let y(c) be the first derivative of 14/5*c**2 + 1/25*c**5 - 24/5*c + 33 - 3/20*c**4 - 2/5*c**3. Factor y(x).
(x - 2)**3*(x + 3)/5
Let g be ((-24)/(-14))/(((-24)/(-35))/12). Suppose -3*d = -5*n + g, 9*d = -3*n + 14*d + 34. Determine f, given that 4/9*f**2 - 4/9 + 16/9*f**n - 16/9*f = 0.
-1, -1/4, 1
Let y(h) = -10*h**3 + 3*h**2 + h - 10. Let g be y(-2). Suppose 27 - 1607 = -5*q. Factor 203 + v**2 - g*v - q - 5*v**2 - 287.
-4*(v + 10)**2
Let v = 726470/7 - 103780. Suppose -48/7*n + 88/7*n**2 - v*n**5 + 0 + 100/7*n**3 - 46/7*n**4 = 0. What is n?
-6, -1, 0, 2/5, 2
Let c(s) be the third derivative of 1/840*s**7 + 1/8*s**4 - 1/160*s**6 + 3*s**2 + 0*s - 1/120*s**5 - 1/3*s**3 - 16. Find h, given that c(h) = 0.
-2, 1, 2
Let r(b) be the third derivative of -1/780*b**6 + 7/390*b**5 + 0*b**3 + 0 - 3*b**2 - 1/26*b**4 - 23*b. Find v such that r(v) = 0.
0, 1, 6
Let t be 496/80*(-1)/((-2)/(-6)). Let o = 661/35 + t. Solve 1/7 + 0*d + 1/7*d**4 - o*d**2 + 0*d**3 = 0.
-1, 1
Suppose 3*o - t = -6, 16*o - 48 = 10*o - 3*t. Factor -1/6*z**2 + 13/6 - o*z.
-(z - 1)*(z + 13)/6
Factor 0 + 1/2*d**4 + d**2 + 1/4*d**5 + 5*d - 15/4*d**3.
d*(d - 2)**2*(d + 1)*(d + 5)/4
Let v(h) be the first derivative of -h**3/3 - 10*h**2 + 69*h - 660. Factor v(n).
-(n - 3)*(n + 23)
Suppose -2 = 2*k, 3 = 5*g + 5*k - 17. Factor g*n - n + 4 - 32*n**2 + 28*n**2 + 4.
-4*(n - 2)*(n + 1)
Let s(a) be the second derivative of a**6/60 - a**5/10 - 11*a**4/24 - a**3/2 + 61*a + 4. Factor s(w).
w*(w - 6)*(w + 1)**2/2
Suppose 368 = 3*j + 53. What is v in -168*v - j - 3*v**3 + 101 + 39*v**2 + 9 + 123 + 112 = 0?
4, 5
Suppose 3*h - 4*h + 2*b + 51 = 0, -2*h = 3*b - 130. Let q = -57 + h. Factor 30*n**2 - 6*n**3 + 31*n**2 - 59*n**2 - 4 + q*n**4 + 6*n.
2*(n - 2)*(n - 1)**2*(n + 1)
Let a(z) = -32*z**4 + 144*z**3 - 84*z**2 - 204*z - 56. Let v(g) = -g**4 + g**3 - g. Let k be (-2)/(-6) + (-123)/(-9) + 2. Let x(y) = k*v(y) - a(y). Factor x(n).
4*(n - 7)*(n - 2)*(2*n + 1)**2
Let b = 3670 + -3661. Let t(h) be the second derivative of 5/4*h**3 + b*h**2 - 1/12*h**4 - 1/40*h**5 + 18*h + 0. Suppose t(p) = 0. Calculate p.
-3, 4
Let v(x) = -x + 3. Suppose -16*h = -19*h. Let u be v(h). Suppose 8*d**2 - d**2 + 9*d**u + 6*d + 8*d**2 = 0. Calculate d.
-1, -2/3, 0
Let p(x) be the first derivative of -6*x**5/5 - 1437*x**4/8 + 60*x**3 + 1799. Find i such that p(i) = 0.
-120, 0, 1/4
Let x(r) be the second derivative of -1/12*r**4 - 1/40*r**5 + 0 - 180*r + 3*r**2 + 11/12*r**3. Determine j so that x(j) = 0.
-4, -1, 3
Factor 40/3 - 10/9*r**2 - 598/9*r.
-2*(r + 60)*(5*r - 1)/9
Let n(r) be the first derivative of 4*r**5/15 - 4*r**4/3 - 28*r**3/9 + 20*r**2/3 + 9. Factor n(b).
4*b*(b - 5)*(b - 1)*(b + 2)/3
Let x(u) be the third derivative of -u**9/302400 - u**8/8400 + 17*u**5/10 + u**2 + 12*u. Let r(a) be the third derivative of x(a). Factor r(w).
-w**2*(w + 12)/5
Suppose -6 + 27 = 7*f. Suppose -f*n = -8 + 2. Factor 127*o**3 - 10 + 65*o - 12*o**3 - 35*o**4 + 3*o**2 - 138*o**n.
-5*(o - 1)**3*(7*o - 2)
Let o(z) = 3*z**2 - 18*z + 64. Let b be o(6). Factor -b*x**2 + 141*x**2 + 376*x - 2161 + 10997 - 73*x**2.
4*(x + 47)**2
Let l(v) be the second derivative of 7/24*v**4 + 1/16*v**5 + 0*v**2 + 0*v**3 - 1/120*v**6 + 0 + 110*v. Factor l(w).
-w**2*(w - 7)*(w + 2)/4
Let j(d) be the second derivative of -23*d + 20/3*d**3 + 0*d**2 - 5/12*d**4 - 2. Determine b so that j(b) = 0.
0, 8
Let j(m) be the third derivative of -16/63*m**3 + 2 + 1/630*m**5 + 9*m**2 + 0*m - 1/42*m**4. Factor j(r).
2*(r - 8)*(r + 2)/21
Let a = 164/91 - 16/13. Let r be 108/(-21) + ((-940)/(-160) - (-14)/112). Let r*f**3 - 2/7*f + 8/7*f**2 - a = 0. What is f?
-1, 2/3
Suppose -4*u - 15 + 23 = 0. Let o = 740/2211 - 1/737. Find s, given that -u*s**2 + 0 - 3/2*s - 1/6*s**5 + 2/3*s**4 + o*s**3 = 0.
-1, 0,