
Let m(k) be the second derivative of k**7/56 + k**6/8 - 27*k**5/80 - 17*k**4/16 + k**3 + 9*k**2/2 + 4*k - 10. Find l, given that m(l) = 0.
-6, -1, 1, 2
Let r(n) = 138*n**4 - 432*n**3 + 448*n**2 - 191*n + 31. Let b(k) = -k**4 - 2*k**3 + 2*k**2 - k + 1. Let g(h) = -6*b(h) + r(h). Factor g(f).
(f - 1)*(4*f - 1)*(6*f - 5)**2
Suppose -129*r + 23 + 170 = -65. Let f(p) be the first derivative of -1 - 1/5*p**3 - 6/5*p**r - 9/5*p. Factor f(l).
-3*(l + 1)*(l + 3)/5
Let s(i) be the third derivative of 1/20*i**6 - 5/2*i**3 + 9/20*i**5 - 3/4*i**4 + 0 + 0*i + 96*i**2. Let s(g) = 0. Calculate g.
-5, -1/2, 1
Suppose 472 = 11*s + 109. Let m(g) be the first derivative of -s*g**4 + 8/3*g**3 + 8*g**2 + 126/5*g**5 + 6 + 0*g. Factor m(z).
2*z*(3*z - 2)**2*(7*z + 2)
Let n(x) = 2*x**2 + 182*x + 198. Let d(f) = 1. Let k(u) = 36*d(u) - 2*n(u). Factor k(z).
-4*(z + 1)*(z + 90)
Let h(q) be the second derivative of 18*q + 2 + 49*q**2 - 14/3*q**3 + 1/6*q**4. Factor h(v).
2*(v - 7)**2
Let u(p) be the first derivative of p**6/10 + 9*p**5/25 - 3*p**4/2 + 2*p**3/5 + 27*p**2/10 - 3*p - 1268. Determine q so that u(q) = 0.
-5, -1, 1
Let o(x) be the second derivative of 2*x**6/15 + 111*x**5/5 + 1045*x**4 + 6050*x**3/3 + 2*x + 662. Suppose o(u) = 0. What is u?
-55, -1, 0
Let l(q) be the second derivative of -q**7/210 + q**6/30 + 2*q**5/25 - 2*q**4/3 - 8*q**3/15 + 8*q**2 + 2*q + 7. Determine v so that l(v) = 0.
-2, 2, 5
Let -1/5*v**3 + 411/5*v - 206/5 - 204/5*v**2 = 0. Calculate v.
-206, 1
Suppose 0*w - 333 = -s - w, 0 = -2*s + 5*w + 694. Let y = s - 92. Factor 248 - y - p**2 - 2*p**2.
-3*(p - 1)*(p + 1)
Let f = 128392/15 - 8559. Let x(u) be the third derivative of -f*u**6 + 128/3*u**3 + 14*u**2 + 11/5*u**5 + 0 + 2/105*u**7 + 0*u + 56/3*u**4. Solve x(k) = 0.
-1, 8
Factor 12*q - 2/5*q**2 - 112/5.
-2*(q - 28)*(q - 2)/5
Suppose 29 = -6*q + 7*q + 3*y, -2*y + 21 = q. Let w(g) be the third derivative of -2/3*g**3 + 0 - 5/24*g**4 - 1/60*g**q + 0*g - 2*g**2. Factor w(h).
-(h + 1)*(h + 4)
Suppose 5*k - 4*x - 27 = -2*x, 3*k = 4*x + 5. Suppose -u = 4*u - 5, y = 3*u + k. Let y*m**2 - 6*m**3 + 11*m**3 + 4*m - m + 2*m = 0. Calculate m.
-1, 0
Let d be (-6)/(-8) + 2/(-8). Let r = 107314 + -429253/4. Factor -r*c**2 - 3*c**3 + d*c + 0 - 7/4*c**4.
-c*(c + 1)**2*(7*c - 2)/4
Let s be -14 + 3146/110 + 6 - 0. What is v in -17/5*v**4 - 108/5 + 288/5*v + s*v**3 - 267/5*v**2 + 1/5*v**5 = 0?
1, 3, 6
Factor -280/3*s + 1/3*s**4 + 176 - 223/3*s**2 - 26/3*s**3.
(s - 33)*(s - 1)*(s + 4)**2/3
Let p(m) = -6*m - 32. Let g be p(-8). Let n be (1 - (-1)/(-2))*g. Solve -31*y + y**4 - n*y + 19*y + 15*y**3 - 6*y**4 = 0.
-1, 0, 2
Let j(x) = -14*x**3 - 67*x**2 - 12*x - 132. Let g be j(-5). Factor -24/5*z**g + 0*z**4 + 0*z + 6/5*z**5 + 0*z**2 + 0.
6*z**3*(z - 2)*(z + 2)/5
Let h = 612 + -608. Suppose 2 - 5 = -4*j + 5*y, h*j - 10 = -2*y. Find w, given that 3/7*w**j + 60/7*w + 300/7 = 0.
-10
Let u be (-60)/(-36) + (-50)/(-20)*(-4)/6. Let j(h) be the third derivative of 0 + 1/720*h**6 + u*h + 0*h**3 + 0*h**4 + 1/360*h**5 + 42*h**2. Factor j(i).
i**2*(i + 1)/6
Let q(m) = -16*m**2 + 126631*m - 250650699. Let u(s) = -2*s**2 + 15829*s - 31331345. Let p(f) = -6*q(f) + 50*u(f). Factor p(i).
-4*(i - 3958)**2
Let l(f) be the third derivative of -f**7/70 - 3*f**6/40 + 17*f**5/20 + 39*f**4/8 + 10*f**3 + 17*f**2 - 133. Factor l(h).
-3*(h - 4)*(h + 1)**2*(h + 5)
Let a(i) be the third derivative of 0 - 2*i**2 + 18*i**3 + 0*i - 15*i**4 + 37/20*i**5 - 3/40*i**6. Determine z, given that a(z) = 0.
1/3, 6
Let o(d) be the second derivative of 0 - d**2 + 13/12*d**3 + 49*d + 7/48*d**4. Factor o(t).
(t + 4)*(7*t - 2)/4
Let a = 4016912/15 - 267794. Let -a*g**2 + 46/15 + 44/15*g = 0. What is g?
-1, 23
Let u be (-2432)/(-96)*(-570)/(-5). Let l be u/456 - 4*1. Find t, given that -1/3*t**4 + 13/3*t**2 + 5/3*t**3 + l*t + 0 = 0.
-1, 0, 7
Let u be 94/6 + 5/15. Suppose -a + u - 10 = 0. Factor 3*c**2 - a*c**3 + 13*c**3 - 13*c**3 + 3*c**4.
3*c**2*(c - 1)**2
Suppose -2*u + 4*u + 3*c - 52 = 0, 0 = -2*u - c + 60. Let r be ((-24)/u)/((-6)/16). Suppose 18*q**2 + 4*q**3 + 2*q + 2*q - 10*q**r = 0. What is q?
-1, 0
Factor 0 + 0*s**3 - 5*s**4 - 5/2*s**5 + 0*s**2 + 0*s.
-5*s**4*(s + 2)/2
Let x(a) be the first derivative of 50 - 1/25*a**5 + 0*a - 16/15*a**3 + 6/5*a**2 + 7/20*a**4. Suppose x(m) = 0. Calculate m.
0, 2, 3
Let v(t) = 3*t**3 - 2*t**2 + 4*t + 15. Let z be (-2)/(80/15)*(-10 + 2). Let r(f) = 2*f**3 - f**2 + 2*f + 9. Let b(i) = z*v(i) - 5*r(i). Factor b(n).
-n*(n - 1)*(n + 2)
Let q(x) be the second derivative of -5*x**7/42 - 43*x**6/3 - 169*x**5/4 - 35*x**4 + 17*x + 6. What is y in q(y) = 0?
-84, -1, 0
Factor 25 - 801*k**2 - 797*k**2 + 1603*k**2 + 290 + 80*k.
5*(k + 7)*(k + 9)
Let 150*o**3 + 151/3*o + 0 + 148/3*o**4 + 452/3*o**2 - 1/3*o**5 = 0. Calculate o.
-1, 0, 151
Let r be -5*((-76)/40 + 15/(-6) + 4). Factor 1/2*c - 1/10*c**r - 3/5.
-(c - 3)*(c - 2)/10
Let z(i) be the second derivative of -3*i**5/50 - 2*i**4/5 + 7*i**3/5 + 6*i**2 + 14*i + 40. Let z(t) = 0. Calculate t.
-5, -1, 2
Let w = 141480 + -1555604/11. Suppose -1/11*g**2 - 52/11*g - w = 0. What is g?
-26
Let m(v) = v**3 - 2*v**2 + 2*v - 2. Let w(t) = -6*t**3 + 37*t**2 - 454*t - 10150. Let n(g) = -21*m(g) - 3*w(g). Factor n(x).
-3*(x - 21)*(x + 22)**2
Let g be (981/(-7))/((-11620)/98). Let u = g + 3/166. Factor -1/5*d**3 - 8/5 - u*d**2 - 12/5*d.
-(d + 2)**3/5
Let b(m) = -2*m + 16. Let g(v) = -v. Let k be g(-8). Let a be b(k). Solve 4/15*n**4 + 0*n**2 - 2/15*n**5 + 0*n**3 + 0 + a*n = 0 for n.
0, 2
Let m(v) = 172*v - 245. Let q be m(-6). Let b = 1279 + q. Solve y**5 + 0*y**b + 1/2*y**3 - 3/2*y**4 + 0*y + 0 = 0 for y.
0, 1/2, 1
Let q(x) be the second derivative of -x**5/114 - 13*x**4/114 - 5*x**3/57 + 97*x**2/2 - 6*x + 9. Let n(m) be the first derivative of q(m). Factor n(h).
-2*(h + 5)*(5*h + 1)/19
Let l(d) = 20*d**4 - 13*d**3 - 6*d**2 - d + 7. Let q(y) = 34*y**4 - 22*y**3 - 10*y**2 - 2*y + 12. Let u(g) = 12*l(g) - 7*q(g). Find w such that u(w) = 0.
-1, 0, 1
Let p(n) be the second derivative of -11*n**4/9 - 3142*n**3/9 + 572*n**2/3 - 2945*n. Factor p(a).
-4*(a + 143)*(11*a - 2)/3
Let l(h) be the third derivative of -11*h**7/840 + 97*h**6/480 + 83*h**5/80 + 163*h**4/96 + 11*h**3/12 - 52*h**2 + 41. Let l(m) = 0. What is m?
-1, -2/11, 11
Let o = 121 - 122. Let w(f) = -2*f**3 - 3*f**2 + 5*f + 3. Let h(y) = -y. Let r(a) = o*w(a) - 3*h(a). Factor r(n).
(n - 1)*(n + 1)*(2*n + 3)
Let n = 26 - 12. Suppose o = 2*o + 3*j - n, -j + 8 = 2*o. Find z such that 2*z**3 - 3*z**4 - 1 + 2 + 2*z**o - 4*z**5 - 3*z + 0*z**2 + 5*z**5 = 0.
-1, 1
Let t(m) be the first derivative of 1/17*m**2 - 2/17*m**3 + 33 - 1/34*m**4 + 6/17*m. Solve t(b) = 0 for b.
-3, -1, 1
Let o(p) be the first derivative of -4*p**3 - 7 + 0*p - 5/6*p**4 + 17/2*p**2 - 1/15*p**5. Let k(y) be the second derivative of o(y). Factor k(a).
-4*(a + 2)*(a + 3)
Let w(u) be the third derivative of -95/24*u**4 - 10*u**3 + 0 + 0*u + 148*u**2 - 1/24*u**6 - 2/3*u**5. Factor w(a).
-5*(a + 1)*(a + 3)*(a + 4)
Let f = 349 - 615. Let g = 266 + f. Determine m so that 1/5*m**2 + 0 + g*m + 1/5*m**3 = 0.
-1, 0
Let r(l) be the second derivative of -l**7/14 - 119*l**6/10 + 2223*l**5/20 - 1125*l**4/4 + 921*l. Determine x so that r(x) = 0.
-125, 0, 3
Let t(g) be the second derivative of -g**6/75 + 19*g**5/25 - 457*g**4/30 + 608*g**3/5 - 2304*g**2/5 + 7*g - 100. Factor t(p).
-2*(p - 16)**2*(p - 3)**2/5
What is k in -2/3*k**3 - 26*k**2 + 0 + 84*k = 0?
-42, 0, 3
Determine a so that 0 + 6/13*a - 2/13*a**2 = 0.
0, 3
Let p(n) be the first derivative of -26/3*n**3 + 0*n - 199 - 12*n**2 - 1/2*n**4. Solve p(j) = 0 for j.
-12, -1, 0
Let p = -1/523217 + 27207287/1569651. Let -p*u**2 + 0 + 8/3*u = 0. What is u?
0, 2/13
Let x(i) be the first derivative of i**5/240 + 7*i**4/96 - 55*i**2/2 - 84. Let j(l) be the second derivative of x(l). Factor j(o).
o*(o + 7)/4
Let n be (-14*(-66)/1232)/((-8)/(-608)). Factor 457/4*c**2 - 76*c**3 - n*c + 9 + 16*c**4.
(c - 2)**2*(8*c - 3)**2/4
Let l = -18322 + 18325. Let u(f) be the third derivative of -15/8*f**4 + 0*f + 1/12*f**5 + 20/3*f**l + 0 - 21*f**2. Solve u(b) = 0 for b.
1, 8
Let z = -45989/6 - -7665. Let u(k) be the first derivative of 4/27*k**3 + z*k**4 - 2/45*k**5 + 18 - 4/3*k**2 + 16/9*k. Solve u(f) = 0.
-2, 1, 2
Let p(n) be the second derivative of 0 - 