).
4*g*(g - 1)
Let h = 393 + -3927/10. Determine g so that -1/10*g - 3/10*g**3 - h*g**2 + 0 - 1/10*g**4 = 0.
-1, 0
Let a(j) be the second derivative of j**9/7056 - j**8/1960 + j**7/1960 + 13*j**3/6 + 12*j. Let w(n) be the second derivative of a(n). Factor w(x).
3*x**3*(x - 1)**2/7
Suppose 7*y + 5*y + 720 = 0. Let t be (-732)/(-70) + (y/25)/4. Factor -90/7*r - 12/7*r**3 - t*r**2 + 27/7.
-3*(r + 3)**2*(4*r - 1)/7
Let x = 60 + 27. Let c = 437/5 - x. Factor q + 1/5*q**3 - 4/5*q**2 - c.
(q - 2)*(q - 1)**2/5
Suppose -2/7*w**3 + 6/7*w**2 + 0 - 4/7*w = 0. Calculate w.
0, 1, 2
Suppose 4*a - 12 = 4, 4*a - 66 = -5*g. Suppose -g + 4 = -2*l. Suppose 3*w**3 - 9*w**2 + 3*w**4 + 0*w**3 + l*w**2 = 0. Calculate w.
-2, 0, 1
Suppose 1 - 2 = t. Let a be (t/2)/(11/(-44)). Find i, given that -4 - 2*i + 12*i - 6*i**2 - 2*i**a + 2*i**3 = 0.
1, 2
Let d = 111 + -84. Suppose 0 = -8*o - 3 + d. Factor 0*a**2 + 2/5*a**o + 0*a + 1/5*a**4 + 0.
a**3*(a + 2)/5
Let -5/4*d**2 + 105/4*d + 115/2 = 0. Calculate d.
-2, 23
Let h(k) be the first derivative of -2/3*k**3 - 50*k - 3 + 10*k**2. Suppose h(z) = 0. What is z?
5
Let o(n) be the third derivative of -n**6/720 - 23*n**5/360 - 37*n**4/48 - 17*n**3/4 + 215*n**2. Factor o(z).
-(z + 3)**2*(z + 17)/6
Let x be (-29 - -14) + (-1020)/(-35). Find i, given that -18/7 + 33/7*i + x*i**2 + 27/7*i**3 - 3*i**4 = 0.
-1, 2/7, 3
Suppose 3294*i**3 + 31*i**5 - 11*i**5 + 582*i**3 + 210*i**4 + 6936*i**2 - 17*i**5 = 0. Calculate i.
-34, -2, 0
Factor 216*j**2 + 5*j**3 + 1520*j + 5325*j + 154*j**2.
5*j*(j + 37)**2
Determine i so that -66 + 36*i - 21 + 9*i + 5*i**2 + 127 = 0.
-8, -1
Suppose 2*c - 214 = -78. Let x = 72 - c. Factor 6/7*t**2 + 0*t - 3/7*t**x + 3/7*t**3 + 0.
-3*t**2*(t - 2)*(t + 1)/7
Suppose 2*p - 4*p + 41 = -3*m, 2*p - 4*m - 42 = 0. Suppose -p + 19 = k. Let 0 + 14/3*h**5 + 0*h**2 + k*h - 10/3*h**4 - 4/3*h**3 = 0. Calculate h.
-2/7, 0, 1
Let n(o) be the third derivative of o**8/10080 - 11*o**7/1260 + 121*o**6/360 + 29*o**5/60 + 13*o**2. Let t(z) be the third derivative of n(z). Factor t(m).
2*(m - 11)**2
Factor -33*d + 15*d**2 + 0 + 3/4*d**3.
3*d*(d - 2)*(d + 22)/4
Suppose -8*a - 2*p = -4*a - 6, 0 = -a + 3*p + 5. Suppose 2*w - 12 = 3*o, -5*w + a*o = -6 - 13. Find u such that 3/5*u**2 - 3/5*u - 1/5*u**w + 1/5 = 0.
1
Let o(z) = 64*z**2 + 434*z - 163. Let p(d) = -96*d**2 - 652*d + 244. Let l(a) = 8*o(a) + 5*p(a). Factor l(b).
4*(b + 7)*(8*b - 3)
Let c be (-7 + 13 - 45)*(-8)/3. Determine r so that 36*r**3 + c*r**2 + 32/3 + 208/3*r = 0.
-2, -2/3, -2/9
Let q(u) be the first derivative of 4*u + 1681/3*u**3 + 24 - 82*u**2. Let q(z) = 0. What is z?
2/41
Let p(s) = 2*s**3 - 2*s**2 + 16*s - 10. Let f(i) = i**2 + i - 1. Let c(g) = -g**3 + 12*g**2 - 11*g + 1. Let l be c(11). Let d(m) = l*p(m) - 6*f(m). Factor d(u).
2*(u - 2)*(u - 1)**2
Suppose 0 = -15*u + 42*u. Suppose g = -g + 4. Factor u - 4/5*x - 2*x**g + 6/5*x**3.
2*x*(x - 2)*(3*x + 1)/5
Determine i, given that -32/9 + 2/9*i**2 - 10/3*i = 0.
-1, 16
Factor -241*c - 8 - 4*c**4 - 11*c**3 + 454*c + 0*c**4 + 3*c**4 - 27*c**2 - 238*c.
-(c + 1)**3*(c + 8)
Let -1690 + 3705/2*v - 5/2*v**4 - 215/2*v**2 - 105/2*v**3 = 0. What is v?
-13, 1, 4
Let t(u) be the third derivative of u**8/120960 - u**6/1080 - 13*u**5/60 - 17*u**2. Let x(o) be the third derivative of t(o). Let x(l) = 0. What is l?
-2, 2
Let l = 2524 + -5045/2. Factor 9/2 + l*j**2 - 1/6*j**3 - 9/2*j.
-(j - 3)**3/6
Let o(x) = 6*x. Let l be o(4). Suppose -l*z + 2*z = -66. Solve -k - 1/3*k**2 + k**z + 2/3*k**4 - 1/3 = 0.
-1, -1/2, 1
Let v(a) = a**2 + a + 1. Let f be 10/(-3)*(-6)/(-5). Let u(b) = b**2 - 3*b - 12*b**3 - 4*b**3 + 15*b**3 + 5*b + 1. Let w(t) = f*v(t) + 4*u(t). Factor w(c).
-4*c*(c - 1)*(c + 1)
Let k(n) = n**5 + n**2 - 2*n - 1. Let g(f) = -6*f**4 + 12*f**3 - 11*f**2 + 5*f + 1. Let r(j) = -3*g(j) - 3*k(j). Factor r(l).
-3*l*(l - 3)*(l - 1)**3
Let s(h) be the first derivative of h**7/42 + h**6/8 + h**5/4 + 5*h**4/24 + h**3/3 - 8. Let x(v) be the third derivative of s(v). Factor x(l).
5*(l + 1)**2*(4*l + 1)
Let i be (2/10 + (-195)/225)*(-16 + 13). Factor -1/2*c**i - 4 - 9/2*c.
-(c + 1)*(c + 8)/2
Let r(k) be the first derivative of -15*k - 17 - 5*k**5 - 5/2*k**4 + 5*k**2 + 40/3*k**3. Find v such that r(v) = 0.
-1, 3/5, 1
Factor 1/4*f**2 + 0 - 1/2*f + 1/2*f**3 - 1/4*f**4.
-f*(f - 2)*(f - 1)*(f + 1)/4
Let k = 4087/730 - -1/730. Let j(q) be the first derivative of -k*q**5 - 16/3*q**3 - 1 + 16*q**4 + 0*q**2 + 0*q. Solve j(v) = 0.
0, 2/7, 2
Let f(w) be the first derivative of w**4/3 + 4*w**3/3 - 6*w**2 - 8*w + 2. Let b(i) be the first derivative of f(i). Determine s so that b(s) = 0.
-3, 1
Let w = 16920 - 50759/3. Factor -w*h**3 + 0 - 1/3*h**2 + 2/3*h.
-h*(h - 1)*(h + 2)/3
Suppose -11*c = -9*c + 2, -3*v - 5*c + 7 = 0. Factor 2/5*n**3 - 1/5 + 3/5*n**v - 3/5*n + 1/5*n**5 - 2/5*n**2.
(n - 1)*(n + 1)**4/5
Let h = 4 + 0. Suppose n = -5*x + 6, 3*x = -0*x + h*n + 22. Factor -4 + 2*q + 2 + x*q**2 - 2.
2*(q - 1)*(q + 2)
Let f(k) be the first derivative of -16*k**6/39 - 336*k**5/65 - 5*k**4/2 + 316*k**3/39 + 81*k**2/13 + 20*k/13 - 102. Suppose f(p) = 0. What is p?
-10, -1, -1/4, 1
Suppose s + 7 + 0 = 0. Let g(l) = -8*l**2 - 3*l + 3. Let n(j) = -7*j**2 - 2*j + 2. Let r(u) = s*n(u) + 6*g(u). Factor r(z).
(z - 2)**2
Let k = 101/11 - 9. Let c = 236 - 234. Suppose 0 + 0*x**c + 0*x**4 + 2/11*x + k*x**5 - 4/11*x**3 = 0. What is x?
-1, 0, 1
Suppose 2*l = 67 - 13. Suppose -l*j = -24*j - 24. Determine i, given that -i**2 - j*i - 4 + 5*i**2 - 8*i**2 = 0.
-1
Let i(p) = 2*p**3 + 100*p**2 - 2*p - 94. Let f(t) = -25*t**3 - 1200*t**2 + 25*t + 1130. Let k(c) = -3*f(c) - 35*i(c). Factor k(j).
5*(j - 1)*(j + 1)*(j + 20)
Let s(o) = o**4 - o**2 + o - 1. Let a(v) = -30*v**5 - 86*v**4 - 86*v**3 - 27*v**2 + 7*v - 2. Let u(t) = a(t) - 3*s(t). Solve u(y) = 0.
-1, -1/6, 1/5
Let k be ((-312)/770)/((-203)/140). Let q = k + 2/319. Suppose 0 + q*c - 2/7*c**3 + 0*c**2 = 0. Calculate c.
-1, 0, 1
Suppose 15*s + 16*s - 62 = 0. Let f(u) be the first derivative of -5*u**2 - s*u - 8 - 8/3*u**3. Factor f(o).
-2*(o + 1)*(4*o + 1)
Let s(x) be the first derivative of 3*x**4/8 - 13*x**3/2 + 105*x**2/4 + 147*x/2 - 202. Determine g, given that s(g) = 0.
-1, 7
Let s(y) be the second derivative of 5*y**4/8 + 41*y**3/4 + 6*y**2 - 119*y. Factor s(j).
3*(j + 8)*(5*j + 1)/2
Let i(j) be the first derivative of -32*j**7/525 - 8*j**6/225 + 2*j**5/75 + j**4/30 + 14*j**3/3 + 17. Let c(z) be the third derivative of i(z). Factor c(w).
-4*(4*w - 1)*(4*w + 1)**2/5
Suppose 0 = m + 4*b - 3*b - 4, 0 = 5*m - 5*b - 10. Let q(w) = -w**2 - 14*w - 4. Let o be q(-3). Solve -11 - o + 0*a**m - a**3 + 10*a**2 + 6*a**3 - 20*a = 0.
-2, 2
Let o(h) be the third derivative of h**6/600 + 3*h**5/100 + h**4/6 + 2*h**3/5 - 2*h**2 + 5*h. Factor o(q).
(q + 1)*(q + 2)*(q + 6)/5
Let t = 0 + 0. Let y(d) be the second derivative of 0*d**2 + 0*d**4 + 1/120*d**6 + 1/40*d**5 + 0 + t*d**3 + 3*d. Factor y(i).
i**3*(i + 2)/4
Let r be 4/14 + (-6 - 10) + (-14674)/(-924). Factor 0*u + r*u**3 + 0 - 1/6*u**5 - 1/6*u**2 + 1/6*u**4.
-u**2*(u - 1)**2*(u + 1)/6
Let w(c) = 21*c**3 + 93*c**2 + 66*c + 12. Let m(i) = 2*i**3 + i**2 - i. Let s(u) = 6*m(u) + 3*w(u). Factor s(n).
3*(n + 3)*(5*n + 2)**2
Let g(h) = -18*h - 13. Let b be g(-3). Find j such that -34*j**2 + 3*j**3 + b*j + 2*j**3 + 4*j**2 + 4*j = 0.
0, 3
Let t = 36773/7 + -5106. Let u = t + -147. Factor 2/7 + 6/7*n + u*n**3 + 6/7*n**2.
2*(n + 1)**3/7
Factor 157*u**3 + 20 - 15*u**2 - 5*u + 5*u - 152*u**3.
5*(u - 2)**2*(u + 1)
Let u be (-40)/(-32) - (-9)/12. What is z in -11*z**3 - 6*z**u - 35*z**4 - 10*z**2 + 36*z**5 + 75*z**3 - 49*z**4 = 0?
0, 2/3, 1
Let b(s) be the second derivative of 0*s**2 + 1/15*s**3 + 0 - 1/50*s**5 - 2*s + 0*s**4. Factor b(y).
-2*y*(y - 1)*(y + 1)/5
Let k = 27513/712 + -309/8. Let g = 2465/1602 + k. Factor -4/9*n**2 + 0*n - g*n**3 + 0.
-2*n**2*(7*n + 2)/9
Let v(g) = 15*g**2 - 252*g + 194. Let u be v(16). Let -8/9*a**3 + 0 + 0*a + 0*a**u + 2/9*a**4 = 0. What is a?
0, 4
Let p(d) be the second derivative of -2*d**6/15 - 3*d**5/5 + 2*d**4 + 16*d**3/3 - 880*d. Solve p(b) = 0 for b.
-4, -1, 0, 2
Factor 6*v**4 - 3*v**4 + v**2 + v + 6 - 7*v**2 - 2*v**3 - 6*v**2 + 3*v**4 + v**5.
(v - 1)**2*(v + 1)**2*(v + 6)
Let r(z) be the first derivative of z**3/2 + 12*z**2 + 117*z/2 + 180. Factor r(o).
3*(