 2
Let s(w) = 12*w**2 + 34*w + 10. Let q(o) = -11*o**2 - 33*o - 11. Let z = 137 + -132. Let i(k) = z*s(k) + 6*q(k). Factor i(t).
-2*(t + 4)*(3*t + 2)
Let l(p) = -9*p**2 - 1791*p + 191779. Let d(g) = -4*g**2 - 894*g + 95892. Let n(v) = -13*d(v) + 6*l(v). Factor n(o).
-2*(o - 219)**2
Factor -36/7 - 13/7*y - 1/7*y**2.
-(y + 4)*(y + 9)/7
Let w(b) = -2*b**2 + 45*b + 1960. Let c be w(-22). Suppose -76/5*n**c + 18/5 + 21*n + 13/5*n**3 = 0. What is n?
-2/13, 3
Let m(s) be the first derivative of -s**4 - 97 - 20/3*s**3 + 12*s**2 + 0*s. Factor m(i).
-4*i*(i - 1)*(i + 6)
Suppose -117*w + 601 = -5*w + 153. Let c(b) be the second derivative of 0 + 1/72*b**w + 14*b + 1/18*b**3 + 0*b**2. Factor c(k).
k*(k + 2)/6
Let k(d) = 2*d**2 - 7*d + 21. Let x be k(3). Suppose g - n - 4 = 0, -2*g + 19*n - x*n + 6 = 0. What is r in 8/5*r + 16/5 - 2*r**3 - 12/5*r**g - 2/5*r**4 = 0?
-2, 1
Factor -49281*r**2 - 130133*r**2 - 3*r**4 - 1380*r**3 + 20714*r**2.
-3*r**2*(r + 230)**2
Let b = 51 + -51. Let l be (b - 84/10)/(44/(-110)). Factor -35*o**2 + 15*o**3 - 12 - l*o**2 + 5*o**2 + 48*o.
3*(o - 2)*(o - 1)*(5*o - 2)
Suppose -79 - 1/6*x**4 + 1033/6*x - 215/2*x**2 + 29/2*x**3 = 0. Calculate x.
1, 6, 79
Let f be 2096/104 + (-14)/91. Suppose -6*q = f*q - 52. Find m, given that -3/2 + q*m - 1/2*m**2 = 0.
1, 3
Factor 207*o**3 - 160*o - 123*o**4 + 168*o**2 + 119*o**4 - 164 - 47*o**3.
-4*(o - 41)*(o - 1)*(o + 1)**2
Let m(j) = -4*j**3 + 5*j**2 - 3*j. Let t be m(1). Let u be (-2)/(-60)*t*55/(-22). Let 1/6*k + 1/6*k**2 - u*k**3 - 1/6 = 0. What is k?
-1, 1
Let f be 339/450 + ((-45)/20)/3. Let s(v) be the third derivative of 0 + 0*v + 0*v**3 + 18*v**2 + f*v**5 - 1/40*v**4. Factor s(q).
q*(q - 3)/5
Let x(d) be the second derivative of -1/20*d**5 - 1/12*d**4 + 5/6*d**3 - d + 12 - 3/2*d**2. What is y in x(y) = 0?
-3, 1
Let b(c) = 2*c**5 - 12*c**2 + 24*c**3 - 37*c**3 + 3 - 7*c - c**4 - 5*c**4. Let x(g) = g**5 - g + 1. Let s(q) = b(q) - 3*x(q). Factor s(z).
-z*(z + 1)**2*(z + 2)**2
Let v(x) be the first derivative of -76 - 15/2*x**2 - 1/3*x**3 + 34*x. Factor v(u).
-(u - 2)*(u + 17)
Let d(a) be the third derivative of a**8/280 + 23*a**7/70 + 242*a**6/25 + 8051*a**5/100 + 1911*a**4/10 - 3042*a**3/5 + 1874*a**2. Solve d(f) = 0 for f.
-26, -3, 1/2
Let l(h) be the first derivative of 0*h + 5/8*h**4 - 169 + 65/6*h**3 + 0*h**2. Suppose l(x) = 0. What is x?
-13, 0
Let r be 8/(160/15) + (-9)/(-4). Factor -4*a - r*a + 11*a**2 - 24*a**2 + 12*a**2 + 2*a**2.
a*(a - 7)
Factor 36*r - 15*r**2 - 9/2*r**3 + 0 + 3/2*r**4.
3*r*(r - 4)*(r - 2)*(r + 3)/2
Factor -1/2*n**2 + 281/2*n + 141.
-(n - 282)*(n + 1)/2
Let u(d) = -5*d + 4*d - 3*d**2 + 5*d**2 - 1 - 3*d**2. Let q(m) = 44*m - 15*m**2 - 13 + 10*m**2 - 29*m. Let l(n) = -q(n) + u(n). Factor l(o).
4*(o - 3)*(o - 1)
Suppose 0 = 4*y + p - 21, 2*y - p - 13 = 2. Let h be 8/2 + y*(-4)/8. Factor 3*l**4 - 9 + 12*l**4 + 55*l**2 - 55*l**3 - h - 5*l + 0.
5*(l - 2)*(l - 1)**2*(3*l + 1)
Let c = -2525 - -2529. Let q(f) be the first derivative of 0*f**5 + 0*f**3 + 0*f - 1/6*f**6 + 7 + 1/4*f**c + 0*f**2. Let q(s) = 0. Calculate s.
-1, 0, 1
Suppose 639*f - 642*f + 24 = 0. Let c = 19 + -13. Factor 2*q + c*q**2 - f*q - 4*q - 9 + 7*q.
3*(q + 1)*(2*q - 3)
Let x = -2860959/11 - -260097. Factor 0 - 2/11*c**2 + x*c.
-2*c*(c - 54)/11
Let j(g) = -g**3 + 6*g**2 + 6*g + 10. Suppose 0*h + 6*h = 42. Let v be j(h). What is d in -156*d**3 - 8*d + 144*d**v - 32*d**2 - 8*d = 0?
-2, -2/3, 0
Let y(s) = -8707 - 11*s + 4351 + 5*s**2 + 4356. Let f be (-1)/((6/(-10))/3). Let b(u) = 14*u**2 - 34*u. Let a(v) = f*b(v) - 16*y(v). Solve a(c) = 0.
0, 3/5
Let u(c) = 9*c - 941. Let n be u(105). Suppose -28/3*h - 104/9*h**3 - 4/9*h**5 - 34/9*h**n - 2 - 140/9*h**2 = 0. Calculate h.
-3, -1, -1/2
Let w = 239122 + -239122. Factor 0*f**3 + 8/5*f + 4/5*f**4 - 12/5*f**2 + w.
4*f*(f - 1)**2*(f + 2)/5
Let m(n) = -4*n**3 + 86*n**2 - 74*n - 52. Let z(i) = 6*i**3 - 86*i**2 + 76*i + 48. Let h(j) = -6*m(j) - 7*z(j). Find s such that h(s) = 0.
-2/9, 2, 3
Let d(f) be the third derivative of f**6/600 - 427*f**5/100 + 3424*f**4 - 40960*f**3/3 + 7151*f**2. Suppose d(a) = 0. What is a?
1, 640
Let l be 275/50 + (2/5)/((-8)/30). Let k(c) be the third derivative of 0*c - 27*c**2 + 25/2*c**3 + 1/20*c**5 + 0 + 5/4*c**l. Factor k(g).
3*(g + 5)**2
Let w(s) be the second derivative of s - 6 + 48*s**2 + 1/18*s**4 + 8/3*s**3. Factor w(i).
2*(i + 12)**2/3
Suppose 49*x = 210 - 91 - 21. Let y(j) be the first derivative of -15 - 15/2*j**x + 10*j + 5/3*j**3. Let y(u) = 0. Calculate u.
1, 2
Let g(c) be the third derivative of c**6/210 - 2*c**4/3 + 32*c**3/7 - 59*c**2 - 4*c. Suppose g(x) = 0. Calculate x.
-6, 2, 4
Let f be 4/9*(-492)/(-656). Factor -14/3*r**2 + 0 + 0*r + f*r**4 + 5/3*r**3.
r**2*(r - 2)*(r + 7)/3
Factor 0 - 8/3*z**2 + 0*z + 4/3*z**3.
4*z**2*(z - 2)/3
Let c(n) = 31*n**2 - 33*n + 7. Let q(g) = -g**2 + g + 1. Let t = 211 - 213. Let r(o) = t*q(o) - 2*c(o). Solve r(u) = 0 for u.
2/5, 2/3
Let k = 209 + -193. What is m in -11*m**2 - k + 18*m - 7*m**2 + 2*m**3 + 8 + 6*m**2 = 0?
1, 4
Suppose 4*f + 9 = -a, a + 19*f = 17*f - 3. Let q(r) be the third derivative of 0*r + 1/60*r**4 + 3*r**2 - 2/75*r**5 + 1/100*r**6 + 0*r**a + 0. Factor q(t).
2*t*(t - 1)*(3*t - 1)/5
Let v(m) be the second derivative of -1/2*m**4 + 0 - 1/10*m**6 + 215*m + 9/20*m**5 + 0*m**2 + 0*m**3. Solve v(y) = 0.
0, 1, 2
Let a be (88/40)/(1221/1110). What is c in -25*c**3 - 80*c - 5/2*c**4 - 145/2*c**a - 30 = 0?
-6, -2, -1
Suppose -3 + 0 = a. Let u be -2 + a - -4 - -3. Factor 2*m**3 + 240*m + 12*m**2 - 72*m**u + 3*m**3 - 502 + 182.
5*(m - 4)**3
Let v(d) = -d**3 - 5*d**2 + 25*d - 1. Let i be v(3). Factor -88/17*m**i + 0 + 48/17*m + 2/17*m**5 + 60/17*m**3 - 18/17*m**4.
2*m*(m - 3)*(m - 2)**3/17
Let j(k) = 10*k - 177. Let f be j(18). Let p(w) = w**3 + 7*w**2 + 6*w + 2. Let t be p(-6). Factor 2*v**f + 624*v + 18*v**t - 50*v**3 + 32*v**4 - 626*v.
2*v*(v - 1)*(4*v - 1)**2
Solve -2167813*z**2 - 3*z**4 + 195*z**3 + 2168134*z**2 - 39*z**3 - 27*z + 97*z + 92*z = 0 for z.
-1, 0, 54
Let z be (9/21)/(276/42 + 130/(-20)). Let -4/5*c - z + 2/5*c**2 = 0. Calculate c.
-3, 5
Factor -14/9*i**3 + 148/9*i + 514/9*i**2 + 0.
-2*i*(i - 37)*(7*i + 2)/9
Suppose 384*y = 751*y - 612*y. Suppose -2/7*r**3 + 0*r + y + 0*r**2 - 6/7*r**4 = 0. Calculate r.
-1/3, 0
Suppose 0 = 3*u + 2*z - 4, -5 = -4*u - 2*z - 1. Suppose -3*q = -5*k - 14, u*q + 3*q = 4*k + 13. Let -3*p**2 - 144*p - 2 + p**q - p**2 + 149*p = 0. What is p?
1, 2
Let p(n) be the second derivative of -n**6/120 - n**5/80 + n**4/48 + n**3/24 + 593*n. Find l, given that p(l) = 0.
-1, 0, 1
Let u = 589 + -589. Let v be 2 + -3 + u + 5. Factor 0*w + 2/17*w**3 - 4/17*w**2 + 0 + 2/17*w**v.
2*w**2*(w - 1)*(w + 2)/17
Solve -28/3 - 20/9*h**2 - 2/9*h**3 + 106/9*h = 0 for h.
-14, 1, 3
Let w(g) be the third derivative of g**7/945 - g**6/135 - 11*g**5/90 + g**4/27 + 32*g**3/27 - g**2 - 8*g - 1. Determine f, given that w(f) = 0.
-4, -1, 1, 8
Let v = -2273/6 - -761/2. Factor 0*d - 5/3 + v*d**2.
5*(d - 1)*(d + 1)/3
Let f be (-2)/(-7) + (0 - (-20)/(-70)). Let p(o) be the third derivative of 4/21*o**3 + f*o + 0 - 29*o**2 + 1/21*o**5 + 1/6*o**4. Factor p(t).
4*(t + 1)*(5*t + 2)/7
Let z(q) = -q**2 - 18*q - 10. Let a(g) be the first derivative of -g**3/3 - 5*g**2 - 6*g - 20. Let b(d) = -5*a(d) + 3*z(d). Let b(u) = 0. Calculate u.
0, 2
Let i(v) = 4*v**4 + 4*v**3 + 3*v**2 + v - 2. Let k = -87 - -92. Let p(u) = u**4 - 1 - 2 + u**3 + 3. Let x(q) = k*p(q) - i(q). Suppose x(d) = 0. Calculate d.
-2, -1, 1
Let l be (-1 - 16/(-10)) + (-4 - (-23316)/(-335) - -76). Factor -2/7*c**l + 2/7*c**2 + 2/7*c - 2/7.
-2*(c - 1)**2*(c + 1)/7
Let h = -51/2225 + 36059/20025. Let -122/9*n**3 - 4/3*n + h - 2*n**4 + 14/9*n**5 - 118/9*n**2 = 0. Calculate n.
-1, 2/7, 4
Let w be ((-2088)/(-870))/(6/5). Solve 0*t**w - 24 - 9/2*t**5 + 48*t + 51/2*t**4 - 42*t**3 = 0.
-1, 2/3, 2
Let l(f) = f**3 + 35*f**2 - 44*f - 1537. Let v be l(-35). Let -44/5*p - 4/5*p**v + 4 + 28/5*p**2 = 0. What is p?
1, 5
Factor 159/4*o**2 + 309/4*o + 153/4 + 3/4*o**3.
3*(o + 1)**2*(o + 51)/4
Let t be ((-2745)/162)/((-8)/(-120)*-5). Determine u, given that 150*u - 5/6*u**4 - 250/3 - 15*u**3 - t*u**2 = 0.
-10, 1
Suppose -c + 4*c = 4*p + 28091, 28103 = 3*c - p. Factor -9359*f + c*f + 37*f**2 + f**5 + 33*f**3 - 6*f**2 + 13*f**4.
f*(f + 1)*