Let p(n) = -n**3 + 36*n**2 - n + 35. Let o be p(36). Let m be 44/(-110) + (o - (-161)/15). Find a such that -12*a - m*a**2 - 8/3 = 0.
-1, -2/7
Let i(z) = -13*z + 49. Let r be i(-7). Let o be 75/r + 3/(-12). Factor -8/7*v - 6/7 - o*v**2.
-2*(v + 1)*(v + 3)/7
Suppose -3*t + 15 = 0, -5*y - t = -12 - 23. Suppose 0*c = 4*c - 8. Find z, given that -3*z**4 + 9*z**3 - 3*z**3 - 9*z**c + y*z**2 + 0*z**2 = 0.
0, 1
Let s(a) be the third derivative of a**6/660 - 26*a**5/55 + 7*a**4/3 - 3*a**2 - 11*a. Factor s(w).
2*w*(w - 154)*(w - 2)/11
Suppose -t + 18 = -34*v + 36*v, -v = -t - 9. Factor 1/2*i**3 + 5/2*i**2 + 3*i + t.
i*(i + 2)*(i + 3)/2
Let 0*v + 6*v**4 + 2/3*v**5 - 40/3*v**2 - 8*v**3 + 0 = 0. What is v?
-10, -1, 0, 2
Suppose -90 = 5*w + 5*f, f = -2*w - 2*f - 34. Let x be w/(-35)*14/4. Factor 4*d**3 + d**2 + d**2 + d - 3*d**2 + 6*d**x.
d*(d + 1)*(4*d + 1)
Find i, given that 24336/7 - 932/7*i**3 + 71761/7*i**2 + 97032/7*i + 3/7*i**4 = 0.
-1, -1/3, 156
Let x(v) be the first derivative of 45064/9*v**3 + 17677/6*v**4 + 7396/3*v**2 - 112 + 0*v + 524/5*v**5 + v**6. Find d, given that x(d) = 0.
-43, -2/3, 0
Let x(y) be the first derivative of 2*y**5/5 + 3*y**4 - 32*y**2 - 393. Factor x(z).
2*z*(z - 2)*(z + 4)**2
Let -202/7*d + 12/7 - 36/7*d**3 - 250/7*d**2 = 0. Calculate d.
-6, -1, 1/18
Let r(j) be the first derivative of j**7/420 - 7*j**6/540 + j**5/90 + 11*j**3 - j**2/2 - 2. Let z(p) be the third derivative of r(p). Factor z(t).
2*t*(t - 2)*(3*t - 1)/3
Suppose 75*y**3 - 300*y - 39*y**5 + 228*y**2 - 150*y - 228*y**4 + 414*y = 0. What is y?
-6, -1, 0, 2/13, 1
Let q(o) = -19*o - 323. Let s(r) = -r**2 - 10*r + 127. Let b be s(-18). Let z be q(b). Factor z + 1/7*g**2 + 2/7*g.
g*(g + 2)/7
Suppose 1504293*t**2 - 1014*t**5 - 1046919/2*t**3 + 42666*t**4 + 2166 - 226803/2*t = 0. What is t?
1/26, 4, 19
Suppose 10 = -120*i + 125*i. Determine l, given that -3 - 2*l**i - 2*l**5 - 5*l**4 + 10*l**4 + 5*l**5 + 6*l**3 - 7*l - 2*l**5 = 0.
-3, -1, 1
Let 8800/3*l**2 - 1/6*l**5 + 0 + 34/3*l**4 - 280*l**3 - 32000/3*l = 0. Calculate l.
0, 8, 20
Let k(n) be the first derivative of -n**4/6 + 2*n**3/3 + 8*n**2 + 82*n - 8. Let w(p) be the first derivative of k(p). Determine y, given that w(y) = 0.
-2, 4
Let q be (5/38)/((-380)/(-304)) - (-14)/(-133). Factor q*z + 0 - 7/8*z**2 + 1/8*z**3.
z**2*(z - 7)/8
Let y be (0 + -7)/(7/14) - 732/(-51). Factor y*v - 36/17 + 2/17*v**2.
2*(v - 3)*(v + 6)/17
Let g = -645 + 3218/5. Let z = -13/20 - g. Factor z - 3/4*k**2 - 3/2*k**3 + 3/2*k.
-3*(k - 1)*(k + 1)*(2*k + 1)/4
Let q(k) = -12*k**3 - 677*k**2 + 1322*k - 701. Let a(y) = 4*y**3 + 226*y**2 - 440*y + 234. Let o(f) = -17*a(f) - 6*q(f). Determine h, given that o(h) = 0.
-57, 1
Determine g, given that 76/5*g**2 - 22/5*g**4 - 536/5*g + 48/5 + 134/5*g**3 = 0.
-2, 1/11, 2, 6
Let b(z) = -z + 5. Let i be b(6). Let o be ((-25)/(-5) - 16)*i. Factor o*k**3 + 7*k**3 - 17*k**3 + 4*k**3.
5*k**3
Let t(x) be the second derivative of 3 + 9/2*x**2 - 21*x + 17/2*x**3 + 11/16*x**4. Factor t(b).
3*(b + 6)*(11*b + 2)/4
Let m be (-171)/(-27) - (92 - 92). Find w, given that -2/3*w**2 - 5/3*w**3 + m*w - 4 = 0.
-12/5, 1
Let p = 1384113 - 9688677/7. Let 0 - 3/7*y**5 - 1188/7*y**3 + p*y**4 + 1944/7*y**2 + 0*y = 0. What is y?
0, 2, 18
Let t(u) = u**4 - 58*u**3 + 1512*u**2 - 13230*u + 27791. Let b(q) = -2*q**3 - 2. Let l(y) = -12*b(y) - 3*t(y). Factor l(x).
-3*(x - 21)**3*(x - 3)
Let k(q) be the third derivative of q**6/360 + 31*q**5/36 + 6083*q**4/72 + 5929*q**3/18 + 3272*q**2 - 1. Factor k(v).
(v + 1)*(v + 77)**2/3
Let v = 906713/4 + -226678. Solve -1/4*o**4 + 13/4*o**2 + v*o**5 - 7/4*o**3 + 0 - 3/2*o = 0 for o.
-3, 0, 1, 2
Let j be 144/(-504) + 18/14. Let q be (4/j)/(-72)*-4. Factor 128/9 + q*b**2 + 32/9*b.
2*(b + 8)**2/9
Suppose -30*m + 193 = -317. Suppose 0 = 3*q - 5*q + m*q. Let 1/4*j**2 + 3/2*j + q = 0. What is j?
-6, 0
Let w = -636 + 631. Let b be w - (-23 + -5)/4. Find v, given that 0 + 8/7*v**b + 8/7*v + 2/7*v**3 = 0.
-2, 0
Let v(p) = 2*p**2 - 9*p - 22. Let f be v(-2). Solve 8*k - 44*k**3 + 2*k**4 + 0*k**4 + 38*k**3 - 4*k**f = 0 for k.
-2, 0, 1
Let b be ((-14)/(-756)*24)/((-40)/9900*-25). Factor -8/5*l**2 - 12/5 - b*l.
-2*(l + 2)*(4*l + 3)/5
Let h(p) be the first derivative of 3*p**5/40 - 27*p**4/32 + 7*p**3/2 - 27*p**2/4 + 6*p - 1814. Factor h(t).
3*(t - 4)*(t - 2)**2*(t - 1)/8
Let a(g) be the first derivative of 11*g**4/4 - 16*g**3/3 - 23*g**2 - 70. Let i(b) = 32*b**3 - 47*b**2 - 137*b. Let l(t) = 17*a(t) - 6*i(t). Factor l(r).
-5*r*(r - 4)*(r + 2)
Let -10135*c**2 + 123*c + 101*c + 3246*c**2 - 1 - 41*c - 17*c = 0. Calculate c.
1/83
Let x(d) be the third derivative of -d**5/690 + 79*d**4/92 + 195*d**2. Factor x(r).
-2*r*(r - 237)/23
Factor 2/9*a**2 - 34/3 + 100/9*a.
2*(a - 1)*(a + 51)/9
Find k, given that 259081/4 + 1/4*k**2 - 509/2*k = 0.
509
Let g = -159 + 157. Let w be (2 + g - 5) + (-66)/(-12). Factor -1/2 + 0*l**2 - l + w*l**4 + l**3.
(l - 1)*(l + 1)**3/2
Let i = 16 - 9. Let j be (-55)/(-825) - 29/(-15). Factor 0 + j*c**2 - 4*c**2 + i*c**4 - 6*c**4 + 1.
(c - 1)**2*(c + 1)**2
Let n(k) be the second derivative of 79 + 50*k**2 - k + 10*k**3 + 5/12*k**4. Let n(x) = 0. Calculate x.
-10, -2
Let g(l) be the second derivative of -3/2*l**2 + 1/4*l**4 + 0*l**3 + 0 - 52*l. Determine y, given that g(y) = 0.
-1, 1
Suppose -4*f = 8*r - 152, 977*f - 978*f + 3*r = 52. Factor 1/5*h**3 + 88*h - 43/5*h**f + 484/5.
(h - 22)**2*(h + 1)/5
Factor 327/2*m + 93/4 + 21/4*m**2.
3*(m + 31)*(7*m + 1)/4
Let r(l) be the second derivative of 0 - 96*l + 0*l**2 + 1/10*l**5 + 3/8*l**4 + 1/6*l**3. Let r(v) = 0. Calculate v.
-2, -1/4, 0
Let h(v) = -1643*v**2 + 1581*v + 2. Let p(g) = -1633*g**2 + 1581*g + 2. Let c(o) = 5*h(o) - 6*p(o). Let c(l) = 0. What is l?
-2/1583, 1
Let i(y) be the second derivative of y**6/75 - 4*y**5/5 - 41*y**4/30 - 2*y - 96. Factor i(n).
2*n**2*(n - 41)*(n + 1)/5
Let o(v) be the second derivative of 2/7*v**7 + 5/2*v**3 + 8*v + 0*v**2 + 11/4*v**4 - 3 + 13/10*v**6 - 99/20*v**5. Suppose o(f) = 0. Calculate f.
-5, -1/4, 0, 1
Suppose 4*n - 8 = 4*t, -56*t + 4*n = -t - 196. Determine y so that -4/5*y**t + 4/5*y**3 + 0 - 16/5*y + 16/5*y**2 = 0.
-2, 0, 1, 2
Let s(t) be the third derivative of 1/6*t**3 - 7/480*t**6 + 0 - 1/60*t**5 + 7/96*t**4 - t**2 - 13*t. Solve s(l) = 0.
-1, -4/7, 1
Factor 38124 + 5166*x**2 + 7434*x**2 - 160102*x**4 + 160098*x**4 - 1376*x**3 - 38016*x.
-4*(x - 3)**3*(x + 353)
Let a = 5950 + -89249/15. Let m(y) be the third derivative of -32/3*y**3 + 0*y + 4/3*y**4 + y**2 - a*y**5 + 0. Factor m(u).
-4*(u - 4)**2
Let o = -492 - -526. Suppose -36*t + o*t**4 - 27*t**5 - 17*t**4 - 89*t**4 + 60*t**2 + 51*t**3 = 0. Calculate t.
-3, -1, 0, 2/3
Suppose -19*m + 23*m = -4*w + 116, 4*m = w - 54. Let c be (-40)/(-70) - w/(-14). Find g such that 0 + 0*g - 1/2*g**c + 1/2*g**5 + g**2 - g**4 = 0.
-1, 0, 1, 2
Let z = 2671/17 + -155. Let r(p) = -12*p + 5. Let t be r(0). Determine x so that 2/17*x**t - 16/17*x**4 + 0 + 42/17*x**3 + 0*x - z*x**2 = 0.
0, 2, 3
Let p(x) be the second derivative of 0 + 15*x**3 + 1/4*x**4 + 11*x + 675/2*x**2. Factor p(r).
3*(r + 15)**2
Suppose 4*q + n + 45 = 0, -5*q = 5*n + 41 + 19. Let m = q + 14. Factor 3*g**3 - 5*g + 2*g**3 + 0*g**m + 0*g**3.
5*g*(g - 1)*(g + 1)
Let m(l) be the second derivative of l**6/15 + 3*l**5/2 - l**4/2 - 47*l**3/3 - 30*l**2 + 21*l - 14. Factor m(z).
2*(z - 2)*(z + 1)**2*(z + 15)
Let d(c) be the third derivative of 82*c**2 + 0 - 1/32*c**4 + 1/240*c**5 + 0*c - 1/6*c**3. Suppose d(w) = 0. Calculate w.
-1, 4
Let l be (-6)/(-14)*(-7 - -14). Let i be (-72)/48 + (l/(-3) - -3). Factor -1/2*o**2 + 0 + o + i*o**4 - o**3.
o*(o - 2)*(o - 1)*(o + 1)/2
Factor -3576/5*q + 716 - 4/5*q**2.
-4*(q - 1)*(q + 895)/5
Suppose 1888/5*n + 14/5*n**3 - 512/5 - 68*n**2 = 0. Calculate n.
2/7, 8, 16
Suppose 6*r - 123*r + 352 = 53*r + 6*r. Determine n, given that 1/4*n**4 - 7/2*n**r + 0*n + 0 + 13/4*n**3 = 0.
-14, 0, 1
Let v(c) be the third derivative of -c**6/4500 + c**5/500 + c**4/30 - 25*c**3/3 + 5*c**2. Let i(z) be the first derivative of v(z). Let i(p) = 0. What is p?
-2, 5
Let h(k) = -10 - 10*k + 1 - 3 + 56*k**2 - 55*k**2. Let c(r) = -6*r**2 + 51*r + 60. Let x(v) = 6*c(v) + 33*h(v). Factor x(d).
-3*(d + 2)*(d + 6)
Let u(k) be the first derivative of 10181645*k**3/3 - 14270*k**2 + 20*k - 1022. Factor u