-u**4/3 + 18*u**3 - 2*u + 13. Factor m(s).
-4*s*(s - 27)
Suppose -32*y = -26*y - 264. Let c(w) = w**3 - w**2 + w - 1. Let g(q) = 12*q**3 - 23*q**2 + 22*q - 11. Let v(u) = y*c(u) - 4*g(u). Solve v(d) = 0.
0, 1, 11
Let p(z) be the first derivative of 21 + 2/3*z**3 - z**2 - 1/5*z**5 - 1/12*z**6 + 3/8*z**4 + 0*z. Let p(b) = 0. Calculate b.
-2, 0, 1
Let x be (-85)/5*(-6 + 5). Find n such that -25*n**2 + 40 + 5*n**3 + 5*n - 7*n + x*n - 5*n = 0.
-1, 2, 4
Let d(r) = -4*r + 1. Let y be d(-2). Suppose 3*g = y*g - 24. Determine t, given that -8*t + 2*t**4 + 12*t + 8*t**3 + 10*t**2 + 0*t**g = 0.
-2, -1, 0
Let i(l) be the second derivative of l**8/1344 - l**7/630 + l**6/900 + l**4/4 - 11*l. Let j(g) be the third derivative of i(g). Suppose j(p) = 0. What is p?
0, 2/5
Let k(i) = -10*i**3 + 30*i**2 + 5*i - 5. Let t(r) = 17*r**3 - 3*r**2 - 8*r**3 - 4*r**3 - 12*r**2 - 2*r + 2. Let c(d) = 2*k(d) + 5*t(d). Factor c(h).
5*h**2*(h - 3)
Factor -123*o**3 + 3*o**2 + 1498*o - o**4 - 2*o**4 - 1375*o.
-3*o*(o - 1)*(o + 1)*(o + 41)
Factor -27*o + 26 - 95*o**2 - 18 + 38 + 20 + 92*o**2.
-3*(o - 2)*(o + 11)
Let k = 3/131 + 107/1048. Let r(v) be the second derivative of v**2 + 5*v - k*v**4 + 0 - 1/40*v**5 + 0*v**3. Determine m so that r(m) = 0.
-2, 1
Let m(w) be the second derivative of 5/8*w**3 - 1/6*w**6 - 1/8*w**5 - 5/168*w**7 + 4*w + 0*w**2 + 5/12*w**4 + 0. Suppose m(l) = 0. Calculate l.
-3, -1, 0, 1
Let f(t) be the second derivative of t**5/100 + 3*t**4/20 + 9*t**3/10 + 27*t**2/10 - 96*t. Find c, given that f(c) = 0.
-3
Let l be (-7)/(-2)*10/(-5). Let o = -4 - l. Factor o - 3 + 3*k - 5*k**2 - 4*k**2.
-3*k*(3*k - 1)
Let h(l) be the second derivative of -l**6/30 + l**5/20 + l**4/12 - l**3/6 - 30*l + 2. Factor h(r).
-r*(r - 1)**2*(r + 1)
Suppose 192*n + 127*n + 52 - 18*n**2 - 89*n = 0. What is n?
-2/9, 13
Let b(u) be the second derivative of u**5/180 - 43*u**4/108 + 220*u**3/27 + 242*u**2/9 + 100*u. Suppose b(k) = 0. Calculate k.
-1, 22
Let f(j) = -40*j**3 - 295*j**2 + 40*j + 345. Let t(q) = 5*q**3 + 37*q**2 - 5*q - 43. Let y(b) = 3*f(b) + 25*t(b). Let y(i) = 0. Calculate i.
-8, -1, 1
Let b(s) be the second derivative of 0 - 5/18*s**3 + 1/90*s**6 + 1/60*s**5 - 1/3*s**2 - 1/12*s**4 + 15*s. Suppose b(h) = 0. What is h?
-1, 2
Let s(c) = 10*c**3 + 6*c**2 + 12*c - 16. Let k(r) = -8*r**3 - 6*r**2 - 12*r + 16. Let h(g) = 6*k(g) + 5*s(g). Let h(b) = 0. Calculate b.
-2, 1, 4
Let v(g) = 9*g**2 + 164*g + 304. Let h(b) = -17*b**2 - 327*b - 607. Let x(l) = 4*h(l) + 7*v(l). Factor x(f).
-5*(f + 2)*(f + 30)
Solve 16/7*g**2 + 0*g + 36/7*g**3 - 10/7*g**4 + 0 = 0 for g.
-2/5, 0, 4
Suppose 0 = -a - 12 + 17. Let n(f) be the third derivative of 0*f**3 + 5*f**2 - 1/36*f**a + 0*f + 1/72*f**4 + 0 + 1/90*f**6. Let n(p) = 0. Calculate p.
0, 1/4, 1
Let c(a) be the second derivative of -a**5/40 - a**4/12 + 5*a**3/12 + 3*a**2/2 + 40*a. Solve c(s) = 0 for s.
-3, -1, 2
Let n(f) be the second derivative of f**8/11760 - f**6/420 + f**5/105 - f**4/6 - 18*f. Let o(g) be the third derivative of n(g). Suppose o(p) = 0. Calculate p.
-2, 1
Let v(d) be the second derivative of -1/4*d**4 + 0*d**2 - 2*d - 36 + 1/2*d**3. Suppose v(q) = 0. What is q?
0, 1
Let h(t) be the third derivative of t**5/150 + 31*t**4/60 - 22*t**3/5 + 431*t**2. Factor h(y).
2*(y - 2)*(y + 33)/5
Let w(y) = -y**2 + y - 1. Let q(o) = -o**3 + 4*o**2 - 12*o - 8. Let m(x) = 3*q(x) - 24*w(x). Determine a so that m(a) = 0.
0, 2, 10
Let u = 33 + -21. Factor -u*y**3 + 3*y**3 + 4*y**3 + 60*y + 80.
-5*(y - 4)*(y + 2)**2
Let p = 8515 - 42571/5. Solve -p*j**5 - 16/5*j**2 + 0 - 24/5*j**3 - 4/5*j - 16/5*j**4 = 0 for j.
-1, 0
Factor 2*z + 0*z + z + 10 - 9*z + 3*z - z**2.
-(z - 2)*(z + 5)
Factor 4/5*g**2 + 824/5*g + 42436/5.
4*(g + 103)**2/5
Let v be (-8)/6*225/(-60). Suppose 13 = 3*b - j, 8 - 9 = v*b + 4*j. Factor 0*m - 2/15*m**b + 0 + 4/15*m**2.
-2*m**2*(m - 2)/15
Let w(j) = 36*j**3 + 104*j**2 - 20*j + 4. Let m(k) = -72*k**3 - 208*k**2 + 42*k - 9. Let n(h) = -4*m(h) - 9*w(h). Determine d, given that n(d) = 0.
-3, 0, 1/9
Let r(h) = 8*h**2 - 36*h + 28. Let a(v) = 7*v**2 - 36*v + 29. Let f(p) = 5*a(p) - 4*r(p). Suppose f(k) = 0. Calculate k.
1, 11
Suppose 7485*z**3 + 154*z**4 - 36670*z**2 + 2154*z - 43560 + 3484*z + 5*z**5 + 62342*z - 186*z**4 - 328*z**4 = 0. Calculate z.
2, 33
Let c(j) = 3*j**3 - 2*j**2 + 3*j - 2. Let t(b) = b**2 + 2*b - 23. Let l be t(-6). Let d be c(l). Factor 0*z**d - 2/5*z**3 + 2/5*z**4 + 0 + 0*z.
2*z**3*(z - 1)/5
Let a(y) be the first derivative of y**3/15 - 29*y**2/5 + 841*y/5 + 399. Solve a(m) = 0 for m.
29
Let t(j) be the first derivative of -j**6/840 + j**5/140 - 2*j**3/21 + 9*j**2/2 - 13. Let r(s) be the second derivative of t(s). Solve r(k) = 0.
-1, 2
Factor 3*u**2 + 28 - 4 + 26*u - 2*u**2 - 3*u**2 + 4.
-2*(u - 14)*(u + 1)
Suppose 147 + 173 = 4*k. Suppose 0 = -4*o + k - 32. Determine f so that 3*f - 3*f**2 + o - 12 = 0.
0, 1
Let v(y) be the first derivative of 1/3*y**3 - 2*y**2 + 8 + 3*y. Find g, given that v(g) = 0.
1, 3
Let s = -64028/5 + 12806. Factor -12/5*q**2 - s*q**3 + 2/5*q + 12/5.
-2*(q - 1)*(q + 1)*(q + 6)/5
Let x be 3/(-15) + (-2255)/(-25). Let g = 96 - x. Solve -8*a - 8/3 - g*a**3 + 50/3*a**2 = 0 for a.
-2/9, 1, 2
Let b(i) be the third derivative of -i**7/315 + i**5/90 - 60*i**2. Suppose b(t) = 0. Calculate t.
-1, 0, 1
Let c(o) be the third derivative of -o**7/735 + 8*o**5/105 - 160*o**2. Factor c(m).
-2*m**2*(m - 4)*(m + 4)/7
Suppose -3*z = 2*o + 280, -3*z - 3*o - 295 = 2*o. Let d be (z/75)/(4/(-10)). Factor 5/3*g**d - g**2 - 2/3*g + 0.
g*(g - 1)*(5*g + 2)/3
Let p(c) = -c**2 + 8*c + 3. Let z be p(6). Suppose 2*w = -3*w + z. Factor 2*t**2 - 6*t**3 - 3*t**2 - 2*t**2 - w*t**4.
-3*t**2*(t + 1)**2
Suppose 61*a + 21 - 9*a**2 + 46*a - 47*a = 0. Calculate a.
-1/3, 7
Let h be (8 + (-276)/30)/(-7 - 320/(-50)). Let 34/11 - 36/11*q + 2/11*q**h = 0. What is q?
1, 17
Let k be (-28)/196*(-14)/(-8)*-6. Find l, given that -1/4*l**3 + k*l**2 + 7/4*l + 0 = 0.
-1, 0, 7
Let l = 2542 + -2542. Determine b, given that -2/3*b**2 + 1/3*b**3 + 1/3*b + l = 0.
0, 1
Factor 79*c**2 + 9*c - 82*c**2 + c**4 - 7*c.
c*(c - 1)**2*(c + 2)
Let z(l) be the second derivative of -1/14*l**7 + 0*l**2 - 1/10*l**6 - 41*l - 1/8*l**4 + 21/80*l**5 + 0 + 0*l**3. Factor z(o).
-3*o**2*(o + 2)*(2*o - 1)**2/4
Suppose -3*q - 45/4 + 1/4*q**2 = 0. What is q?
-3, 15
Let q be (4/(-30))/((54/5)/(-3)). Let o(g) be the second derivative of 0*g**2 - 2*g - q*g**3 - 1/135*g**6 + 0 + 1/90*g**5 + 1/54*g**4. Factor o(l).
-2*l*(l - 1)**2*(l + 1)/9
Factor -12/13*q**2 + 0 + 0*q + 10/13*q**4 + 2*q**3.
2*q**2*(q + 3)*(5*q - 2)/13
Solve -2*c**2 + 0 + 4/5*c**3 + 4/5*c = 0 for c.
0, 1/2, 2
Let u be 2/10 - (-603)/60. Let d = u - 279/28. Factor -2/7*i**2 - 2/7*i**3 + d*i + 2/7.
-2*(i - 1)*(i + 1)**2/7
Let c(d) be the second derivative of 5/6*d**4 - 1/2*d**5 + 1/6*d**6 - 16*d + 1/2*d**2 - 5/6*d**3 + 0 - 1/42*d**7. Suppose c(y) = 0. What is y?
1
Determine s, given that 16*s**4 - 28*s + 12*s**2 - 32 + 0*s**2 - 12*s + 38*s**3 + s**2 + 3*s**2 + 2*s**5 = 0.
-4, -2, -1, 1
Let z be 4 + -3 - (0 - -1). Suppose -4*n = -s + 19, z*s + n = s - 7. Factor -3*c**4 - 6*c - 3*c**s + 6*c + 6*c**2.
-3*c**2*(c - 1)*(c + 2)
Let 75*t**2 + 2*t + 40*t**3 - 18*t**3 - 2*t + 2*t**4 - 99*t**2 = 0. What is t?
-12, 0, 1
Let o(y) be the second derivative of y**5/100 - y**4/10 + 4*y**3/15 - 3*y - 226. Find a such that o(a) = 0.
0, 2, 4
Determine f, given that -3410 - 67*f**2 - 32046 + 1008*f + 63*f**2 - 28048 = 0.
126
Let u(m) be the second derivative of -5*m**4/36 - 23*m**3/9 - 8*m**2 + 279*m. Suppose u(o) = 0. Calculate o.
-8, -6/5
Suppose 11*y - 53 - 24 = 0. Let q(s) be the second derivative of 1/27*s**4 - 1/9*s**2 - 1/27*s**3 + 0 - 1/135*s**6 - 1/189*s**y + 8*s + 1/45*s**5. Factor q(k).
-2*(k - 1)**2*(k + 1)**3/9
Suppose s + 0 + 8 = 0. Let x be 1/(1 - s/(-12)). Factor -4*r**4 - r**3 + r**2 + 8*r + 4*r**5 - 11*r**3 + x*r**2.
4*r*(r - 2)*(r - 1)*(r + 1)**2
Let c(w) be the first derivative of w**5/20 - w**4/4 - 3*w**3/2 - 5*w**2/2 + 34*w + 11. Let g(j) be the first derivative of c(j). Factor g(k).
(k - 5)*(k + 1)**2
Let o(n) = n - 6. Let w be o(6). Suppose w = -3*y + 23 - 17. Factor -m**2 + m + 3*m**4 - y*m**2 - 3*m**3 + 2*m.
3*m*(m - 1)**2*(m + 1)
Let 6/5 + 4/5*a + 2/15*a**2 = 0. What is a?
-3
Factor 31/6*q - 1/6*q**2 + 1