h(i) = 7*i**3 + 23*i**2 + 28*i - 306. Suppose 15 + 15 = -6*z. Let x(a) = z*h(a) + 6*y(a). Factor x(c).
(c - 3)*(c + 10)**2
Let n = 603 + -427. Let f be 18 + n - 10/2. Factor 5*s**3 - 174*s + f*s + 4 + 1 + 15*s**2.
5*(s + 1)**3
Let h(t) be the first derivative of t**4/4 + 5*t**3/3 - 5*t**2/2 - 23*t + 155. Let r be h(-5). Find x such that -4/3*x + 0*x**3 - r*x**2 + 0 + 2/3*x**4 = 0.
-1, 0, 2
Let a(t) be the second derivative of -51*t**5/20 + 53*t**4/2 - 177*t**3/2 + 54*t**2 - 574*t. Factor a(u).
-3*(u - 3)**2*(17*u - 4)
Suppose 96*x - 295 = -103. Let 12/11*b + 6/11*b**3 - 2*b**x + 0 + 6/11*b**4 - 2/11*b**5 = 0. Calculate b.
-2, 0, 1, 3
Let a(u) be the first derivative of 1/2*u**6 - 59 + 0*u**2 + 0*u**3 + 18/5*u**5 + 0*u - 12*u**4. Suppose a(d) = 0. Calculate d.
-8, 0, 2
Let c(z) be the first derivative of 1/6*z**6 + 0*z**2 - 168 + 2*z**3 + 0*z + 11/4*z**4 + 6/5*z**5. Determine m, given that c(m) = 0.
-3, -2, -1, 0
Factor -95/3*v - 100 - 5/3*v**2.
-5*(v + 4)*(v + 15)/3
Let h(o) be the third derivative of o**7/70 + 3*o**6/10 + 51*o**5/20 + 23*o**4/2 + 30*o**3 - 2*o**2 - 260. Factor h(f).
3*(f + 2)**2*(f + 3)*(f + 5)
Let j(m) = 2*m**4 - 2*m**3 + 2*m + 1. Suppose 3*o = -s + 2 - 5, -4*o = -s + 4. Let a(g) = g**3 - g + 1. Let y(w) = o*j(w) + 3*a(w). Solve y(i) = 0.
-1, 1/2, 1, 2
Let t(w) be the third derivative of -w**6/24 + 241*w**5/6 - 12200*w**4 + 96000*w**3 + w**2 - 6*w + 14. What is b in t(b) = 0?
2, 240
Let m be (2493/2770)/(3/20). Let k(f) = f**3 + 4*f**2 - f - 2. Let x be k(-4). Factor -12 - m*r + 24*r**2 - 21*r**x - 3*r.
3*(r - 4)*(r + 1)
Let l be 13*(5 - 41100/84). Let i = l + 6326. Determine r so that -6*r**5 - 300/7*r**3 + 120/7*r**2 + i*r**4 - 12/7 + 22/7*r = 0.
-2/7, 1/3, 1, 3
Let r(t) = 9*t**3 + 28*t**2 + 63*t + 27. Let l = -63 - -69. Let p(b) = 3*b**3 + 9*b**2 + 21*b + 9. Let z(i) = l*r(i) - 17*p(i). Find f, given that z(f) = 0.
-3, -1
Suppose 462 = -3*m + 441. Let q be m/28*(-3 + 3)/(-5). Let -2/7*t + 0 + q*t**2 + 2/7*t**3 = 0. Calculate t.
-1, 0, 1
Suppose 4*g - 18*g + 224 = 0. Let h be (-168)/g + 10 - (-9)/2. Solve 0 + 0*n**2 + 3/4*n**h + 0*n - 3*n**3 = 0 for n.
0, 4
Let s(p) = p + 12. Let c be s(-9). Let u be (-155)/(-35) + ((-36)/(-14) - c). Factor -u*g**2 + 2*g**2 - 30*g + 4*g**2 + 24 - 11*g**2.
-3*(g + 4)*(3*g - 2)
Suppose -2*s = -15*s + 624. Suppose -70*f = -s*f - 66. Factor 5/3*n + 5/3*n**f + 10/3*n**2 + 0.
5*n*(n + 1)**2/3
Let l(w) = -w**2 - 16*w + 1561. Let y be l(32). Let s(z) be the third derivative of 0*z + 0 + 0*z**3 + 1/48*z**4 - 1/80*z**5 + 1/480*z**6 - y*z**2. Factor s(c).
c*(c - 2)*(c - 1)/4
Let g(v) be the first derivative of -7*v**6/225 + 2*v**5/25 - v**4/30 - 2*v**3/45 + 2*v - 33. Let u(r) be the first derivative of g(r). Factor u(l).
-2*l*(l - 1)**2*(7*l + 2)/15
Let p be (-8)/(-6)*(-18)/(-12). Suppose 2 = -w, 4*w + 1 = -5*j + 8. Factor f - f**3 - 3*f**p + 13*f**2 - 7 - j*f**2.
-(f - 7)*(f - 1)*(f + 1)
Let y = 21849 - 1114298/51. Let r(u) be the second derivative of 0 - y*u**6 - 21*u + 0*u**3 + 0*u**2 + 2/51*u**4 - 1/170*u**5. Factor r(h).
-2*h**2*(h + 1)*(5*h - 4)/17
Let l(z) be the second derivative of 2/5*z**6 + 1/3*z**4 + 2/21*z**7 + 0 + 15*z + 3/5*z**5 + 0*z**3 + 0*z**2. Factor l(j).
4*j**2*(j + 1)**3
Let 1/5*c**3 + 937/5*c + 468/5 + 94*c**2 = 0. What is c?
-468, -1
Factor 108/5*c**2 - 768/5*c - 2/5*c**3 - 4096.
-2*(c - 32)**2*(c + 10)/5
Suppose 0 = 6*s + 12 + 6. Let a(i) = 7*i**2 - 111*i + 2919. Let f(t) = -12*t**2 + 221*t - 5837. Let g(l) = s*f(l) - 5*a(l). Factor g(b).
(b - 54)**2
Factor 2771*c - 4308*c**3 + c**4 - 302 + 4353*c**3 - 3166 + 651*c**2.
(c - 1)*(c + 12)*(c + 17)**2
Let h(r) be the third derivative of 0 - 13/30*r**4 - 59*r**2 + 31/60*r**5 - 2/15*r**3 - 3*r. Let h(c) = 0. What is c?
-2/31, 2/5
Let t = 14178 - 14165. Let r(a) be the first derivative of t + 2/45*a**3 + 1/30*a**4 - 8/15*a - 4/15*a**2. Suppose r(o) = 0. What is o?
-2, -1, 2
Solve 1076/7*g**2 - 14*g**3 + 22/7*g + 0 = 0 for g.
-1/49, 0, 11
Factor -478*f + 67 - 2383 - 32*f**2 + 391 - 2493 - 274*f.
-2*(4*f + 47)**2
Let t(q) be the second derivative of 1 - 24*q - 112/3*q**3 + 128/3*q**2 + 1/5*q**6 + 74/9*q**4 + 16/5*q**5. Find g such that t(g) = 0.
-8, -4, 2/3
Let d(s) be the third derivative of -s**5/20 + 253*s**4/8 - 126*s**3 + 18*s**2 + 8. Find p, given that d(p) = 0.
1, 252
Let b = 62351/145551 + 4/20793. Factor -6/7*h - 24/7 + b*h**2.
3*(h - 4)*(h + 2)/7
Let r = -243 - -245. Determine k, given that -14*k - 250 - 10*k + 6*k**3 - 2*k**4 + 4*k**r + 266 = 0.
-2, 1, 2
Let n(c) be the third derivative of 0*c + 1/420*c**6 - 1/12*c**4 + 2/7*c**3 + 2 + 0*c**5 - 44*c**2. Find v, given that n(v) = 0.
-3, 1, 2
Suppose 10*u - 7*u = 60. Let z = -15 + u. Determine o, given that -28*o**2 + 8*o - 735*o**z - 6*o**2 - 26*o**2 + 66*o**3 - 130*o**4 + 501*o**4 = 0.
-2/5, 0, 2/7, 1/3
Let z(a) be the second derivative of -17/20*a**4 - 9/100*a**5 - 9/10*a**3 + 3/2*a**2 + 0 + 205*a. Let z(d) = 0. Calculate d.
-5, -1, 1/3
Let c(k) = -21*k**3 + 7*k**2 + 15*k - 8. Let x be c(-4). Let o = x + -4162/3. Factor 1 + o*j - 1/3*j**2.
-(j - 3)*(j + 1)/3
Factor 5808/7 + 264/7*u + 3/7*u**2.
3*(u + 44)**2/7
Let j(o) = -22*o + 4. Let n be j(0). Suppose 240*g**n + 480*g**2 - 142*g**3 - 305*g**3 + 320*g - 25*g**5 - 253*g**3 = 0. Calculate g.
-2/5, 0, 2, 4
Let w(q) be the second derivative of -q**4/66 + 101*q**3/11 - 2236*q. Factor w(n).
-2*n*(n - 303)/11
Let r(v) be the second derivative of 10*v**3 + 29*v + 0 - 1/4*v**5 - 5/3*v**4 + 0*v**2. Factor r(l).
-5*l*(l - 2)*(l + 6)
Let k(n) be the first derivative of 2*n**6/3 - 8*n**5/5 + 2*n**3 - 2*n**2 - 26. Let v(o) = o**2 + o - o. Let f(g) = k(g) + 2*v(g). Factor f(r).
4*r*(r - 1)**3*(r + 1)
Let f(q) be the first derivative of 8/3*q**3 + 1/4*q**4 + 104 + 13/2*q**2 + 6*q. Let f(v) = 0. What is v?
-6, -1
Let y(k) = 12*k**2 - 682*k - 3520. Let m(l) = 19*l**2 - 1022*l - 5281. Let a(i) = 5*m(i) - 8*y(i). Factor a(s).
-(s - 351)*(s + 5)
Let w(g) = 67*g + 400. Let s be w(-6). Let k be (-9 - (-1098)/126) + s/(-7). Solve -2/17*m + 4/17*m**3 + 0 + k*m**2 - 2/17*m**5 + 0*m**4 = 0.
-1, 0, 1
Let v be (26/3)/((-33620)/(-1599)). Let j = v + -1/82. Let 4/5 - 2/5*h - j*h**2 = 0. Calculate h.
-2, 1
Suppose 0 = 4*u - 32*u + 112. Let a(n) be the second derivative of 0 + 3/8*n**2 + 2*n + 1/16*n**u + 1/4*n**3. Factor a(y).
3*(y + 1)**2/4
Factor 22/19*i**2 - 2/19*i**3 - 46/19*i - 70/19.
-2*(i - 7)*(i - 5)*(i + 1)/19
Let y(g) be the third derivative of g**6/2700 - g**5/225 + 17*g**3/3 + 2*g**2. Let i(q) be the first derivative of y(q). Determine z so that i(z) = 0.
0, 4
Let w(q) = q + 141. Let h be w(5). Let x be 61/18*2 - h/(-657). Solve -x*b**3 + 17/3*b**4 + 11/3*b**2 - 2/3*b + 0 - 5/3*b**5 = 0.
0, 2/5, 1
Let u = 43825 - 175297/4. Factor 0 - u*m**2 + 3*m**3 - 3*m + 3/4*m**4.
3*m*(m - 1)*(m + 1)*(m + 4)/4
Let l = -116 + 126. Solve 15*n**2 + 3*n - 3*n**3 + 4*n**3 - l*n**2 - 9 = 0 for n.
-3, 1
Let y(f) be the first derivative of 2*f**3/45 + 7*f**2/15 - 12*f/5 - 262. Factor y(r).
2*(r - 2)*(r + 9)/15
Suppose 57*n + 12*n + 814 - 1159 = 0. Let m(f) be the third derivative of 0*f**3 + 3*f**2 + 1/6*f**4 - 3/5*f**n + 0*f + 0. Factor m(p).
-4*p*(9*p - 1)
Let 0 + 2/9*m**3 + 0*m + 190/3*m**2 = 0. Calculate m.
-285, 0
Let v(c) be the first derivative of 2*c**5/35 - 13*c**4/14 + 106*c**3/21 - 83*c**2/7 + 12*c + 178. Solve v(a) = 0.
1, 2, 3, 7
Let m(w) = -9*w**3 - 21*w**2 - 9*w - 1. Let i(p) = 8*p**3 + 21*p**2 + 9*p + 2. Let a(d) = -2*i(d) - 3*m(d). Find j such that a(j) = 0.
-1, 1/11
Let n = 61 + -57. Find j such that -14*j**3 + 930 - 16*j**2 - j**n - 52*j - 29*j**2 - 490 - 460 = 0.
-10, -2, -1
Let t be (6/4)/(69/644). What is a in -t*a + 4*a + 70*a**2 - 65*a**2 = 0?
0, 2
Suppose -802/3*u - 832/3*u**2 + 76/3 + 46/3*u**3 = 0. What is u?
-1, 2/23, 19
Let o(s) be the first derivative of -3*s**4/20 + 12*s**3/5 - 33*s**2/10 - 120. What is h in o(h) = 0?
0, 1, 11
Let o(i) be the second derivative of -i**6/30 - 9*i**5/10 - 4*i**4 - 23*i**3/3 - 15*i**2/2 - 1502*i. Factor o(j).
-(j + 1)**3*(j + 15)
Let z = -492728 - -492730. Factor 0 - 2/9*m**z + 26/9*m.
-2*m*(m - 13)/9
Let m(f) be the second derivative of -5*f**7/126 + 50*f**6/9 + 215*f**5/12 - 925*f**4/6 - 350*f**3 + 3060*f**2 + 138*f + 2. Solve m(v) = 0 for v.
-3, 2, 102
Let v(a) = -2*a**2 + 57*a - 395. Let w be v(