= 2*h + 60, 3*h + 198 = 4*c. Let x(k) = -12*k + 3. Let r be x(-3). Find m, given that -27*m**2 + c*m**2 + 42*m - r - 27*m**2 = 0.
1, 13
Let p be 24/(-78)*(4 + (-84)/8). Let c(r) be the second derivative of 0*r**p + 10*r - 1/36*r**4 + 0*r**3 - 1/60*r**5 + 0. Suppose c(g) = 0. What is g?
-1, 0
Let o be (36 - 32) + 3514/10. Let d = o + -355. Factor 0 - 2/5*h**2 + d*h**4 - 4/5*h + 4/5*h**3.
2*h*(h - 1)*(h + 1)*(h + 2)/5
Suppose 45 = 9*u - 45. Suppose 8*q - u*q = -4. Determine z so that z**2 + 44*z - 34*z - 6*z**q = 0.
0, 2
Let k(x) be the first derivative of 4*x**3/3 - 12*x**2 - 28*x - 1142. Factor k(a).
4*(a - 7)*(a + 1)
Let n(b) = -3*b**3 + b**2 - 2*b - 2. Let q be n(-1). Suppose 5*z - 29 = -q. Factor 4*s**3 - 5*s**5 + 0*s**3 + s**z + 0*s**5.
-4*s**3*(s - 1)*(s + 1)
Let f(s) = -6*s**3 - 99*s**2 - 18*s + 18. Let i(o) = -3*o**3 - 49*o**2 - 8*o + 8. Let j(k) = -4*f(k) + 9*i(k). Let j(g) = 0. What is g?
-15, 0
Let w(n) be the second derivative of -n**6/90 + 28*n**5/5 - 3136*n**4/3 + 702464*n**3/9 + 1342*n. Factor w(i).
-i*(i - 112)**3/3
Let c(r) = r**3 - 13*r**2 - 37*r - 1. Let n(p) = -2*p**3 + p + 1. Suppose -229*l + 231*l = 2. Let q(s) = l*n(s) + c(s). Factor q(z).
-z*(z + 4)*(z + 9)
Let w(v) = -3*v**3 - 39*v**2 + 71*v - 41. Let q(z) = 7*z**3 + 119*z**2 - 215*z + 122. Let y(n) = 8*q(n) + 22*w(n). Factor y(h).
-2*(h - 1)**2*(5*h - 37)
Let l(u) be the second derivative of 21/50*u**5 - 71 - 3/5*u**4 + 6/25*u**6 + 0*u**2 - 1/70*u**7 + 2*u - 13/10*u**3. Determine a so that l(a) = 0.
-1, 0, 1, 13
Let z(i) be the third derivative of i**7/1260 - i**6/120 - 5*i**4/3 + 2*i**2 + 2. Let x(f) be the second derivative of z(f). Suppose x(y) = 0. Calculate y.
0, 3
Let h(g) be the third derivative of -1/1344*g**8 + 83*g**2 + 0*g + 0 - 5/48*g**5 - 1/6*g**4 - 1/120*g**7 - 1/6*g**3 - 19/480*g**6. Factor h(m).
-(m + 1)**3*(m + 2)**2/4
Suppose -16*h - 12*h + 112 = 0. Suppose 3*x = p + 14, 0 = -x - h*p + 3 + 6. Factor 3/5*t + 3/5*t**x + 0*t**2 + 0 + 0*t**4 - 6/5*t**3.
3*t*(t - 1)**2*(t + 1)**2/5
Let o = -805682/155 + 5198. Let j = 1462/1705 + o. Factor 0 + j*y**3 - 16/11*y**2 + 8/11*y - 2/11*y**4.
-2*y*(y - 2)**2*(y - 1)/11
Let q be -2*(-6)/(-180)*-12. Let y = -15/329 - -2049/1645. Factor y*o + q + 2/5*o**2.
2*(o + 1)*(o + 2)/5
Let a(d) = -d**2 + d + 7. Let u(h) = -4*h**3 - 44*h**2 - 4*h + 156. Let n(q) = 24*a(q) - u(q). What is j in n(j) = 0?
-3, -1
Let c(q) be the second derivative of -2*q**7/21 + 2*q**6/3 + 69*q**5/5 + 57*q**4 + 72*q**3 + q + 123. Solve c(d) = 0 for d.
-3, -1, 0, 12
Solve 74/11*k**2 - 212/11*k + 48/11 + 26/11*k**3 - 8/11*k**4 = 0 for k.
-3, 1/4, 2, 4
Let y(i) = i**2 + 2. Let a(s) = -8*s**2 - 1314*s + 1304. Let x(u) = -a(u) - 6*y(u). Determine h, given that x(h) = 0.
-658, 1
Let v(g) be the first derivative of 5*g**4/12 + 100*g**3/3 - 205*g**2/2 + 93*g - 15. Let x(y) be the first derivative of v(y). Factor x(a).
5*(a - 1)*(a + 41)
Let p = -80 - -88. Let i(h) = h**3 - 8*h**2 - h + 10. Let k be i(p). Solve 0 - 1/4*y**4 + 0*y - 5/4*y**3 + 1/4*y**5 - 3/4*y**k = 0 for y.
-1, 0, 3
Let j(k) = 6*k**2 - k. Let m(x) = 34*x**2 - 1938*x. Let v(r) = 6*j(r) - m(r). Let v(g) = 0. Calculate g.
-966, 0
Let z(h) be the third derivative of 1/9*h**4 - 1/45*h**5 + 0*h - 53*h**2 + 0 + 0*h**3. What is w in z(w) = 0?
0, 2
Factor -33600/17*o**2 - 460/17*o**3 - 640000/17*o + 10240000/17 - 2/17*o**4.
-2*(o - 10)*(o + 80)**3/17
Determine g so that -41 + 115*g**2 + 42*g - 5*g**4 - 222 + 3*g - 45*g**3 + 153 = 0.
-11, -1, 1, 2
Let z(r) = -r. Let p(s) = -54*s**3 - 54*s**2 - 22*s - 2. Let k(l) = l. Let q be k(0). Suppose q = -m + 8*m - 28. Let b(u) = m*z(u) - p(u). Factor b(i).
2*(3*i + 1)**3
Let q(i) be the first derivative of 6 - 3*i**4 + 1/15*i**5 - 21*i**2 + 54*i**3 + 0*i. Let o(y) be the second derivative of q(y). Factor o(r).
4*(r - 9)**2
Factor 287*m**2 - 294*m + 1656 - 184*m**2 + 82*m**2 - 182*m**2.
3*(m - 92)*(m - 6)
Suppose -6*m - 16 = 2*m. Let j = 4 + m. Factor -3*l**3 + 4*l**3 + l**3 - 4*l + l**3 + 4*l**j - 2*l**4 - l**5.
-l*(l - 1)**2*(l + 2)**2
Suppose k - 114 - 1 = 0. Let u = 691 - k. Factor -578*o**3 - 4 - 2*o**4 + 6*o**2 + 0*o**2 + u*o**3 + 2*o.
-2*(o - 1)**2*(o + 1)*(o + 2)
Solve 162256 + 106*z**2 - 101*z**2 + 326942 + 307206 + 4320*z + 136716 = 0 for z.
-432
Let k(z) = -3*z - 76. Let h be k(-26). Solve -2 + 17 - 4*w**h + 8*w - 9 - 10 = 0 for w.
1
Let d(w) be the second derivative of -w**4/27 + 40*w**3/27 - 8*w**2 - 73*w - 2. Factor d(b).
-4*(b - 18)*(b - 2)/9
Let v(w) be the third derivative of w**9/362880 + w**8/24192 + w**7/7560 + 5*w**5/4 + 15*w**2. Let i(k) be the third derivative of v(k). Factor i(o).
o*(o + 1)*(o + 4)/6
Let g = -4685981/599 + 7823. Let t = g - -619/2995. Factor 49/5 + 14/5*j + t*j**2.
(j + 7)**2/5
Let b(n) = n**5 - 33*n**4 + 44*n**3 - 6*n**2 - 6*n. Let w(m) = 2*m**5 - 36*m**4 + 43*m**3 - 7*m**2 - 7*m. Let k(z) = 7*b(z) - 6*w(z). Factor k(g).
-5*g**3*(g - 2)*(g + 5)
Suppose 15*m + 360 = -21*m. Let h be (8/10)/(m - 583/(-55)). Factor 1/3*p**2 + 4/3*p + h.
(p + 2)**2/3
Let a(l) be the third derivative of 19*l**5/20 - 47*l**4/20 - l**3/10 - 4*l**2 - 6*l. Factor a(x).
3*(x - 1)*(95*x + 1)/5
Let w(o) = -8*o**2 - 21*o - 1. Let r(p) = 3*p. Let t(i) = -i**3 - 8*i**2 - 14*i - 108. Let u be t(-8). Let a(z) = u*r(z) + w(z). What is n in a(n) = 0?
-1, -1/8
Let a(g) = -21*g**3 - 2*g**2 + 42*g**3 - 20*g**3 + 6*g**2 + 3*g + 1. Let t be a(-2). Let 2*i - 6/5 - 2/5*i**2 - 2/5*i**t = 0. What is i?
-3, 1
Suppose 4*s - 7*s + 12 = 0. Let x be (-8)/(-14) + (-20309)/(-805) + (9 - 32). Find l, given that -2/5*l**2 + x*l**3 + 6/5 - 14/5*l - 4/5*l**s = 0.
-1, 1/2, 1, 3
Let g(y) be the third derivative of y**8/13440 - y**7/840 + y**6/288 + y**5/20 + 71*y**4/24 + 63*y**2. Let v(q) be the second derivative of g(q). Factor v(n).
(n - 4)*(n - 3)*(n + 1)/2
Let w be (-31 - 1) + 26068/784. Factor 1/2*m - 2 + 1/4*m**3 + w*m**2.
(m - 1)*(m + 2)*(m + 4)/4
Let y(l) be the first derivative of -2*l**5 - 123*l**4/2 - 584*l**3/3 - 132*l**2 + 7053. Suppose y(f) = 0. What is f?
-22, -2, -3/5, 0
Let r(c) be the second derivative of -c**7/42 + 2*c**6/15 - c**5/20 - c**4/2 - 599*c. Factor r(h).
-h**2*(h - 3)*(h - 2)*(h + 1)
Let q be 5/25 - (1074/120 + -9). Solve q*z**2 + 1/2 + 3/4*z = 0 for z.
-2, -1
Let -476*m**2 + 475*m**2 + 131*m - 114*m + 578 = 0. What is m?
-17, 34
Let v(f) be the first derivative of -162*f**2 + 120*f**3 - 2/3*f**6 + 44/5*f**5 - 46*f**4 + 108*f - 60. Solve v(r) = 0.
1, 3
Let k(f) be the first derivative of 0*f**2 + 5 + 1/3*f**3 + 1/3*f**4 + 1/10*f**5 + 17*f. Let g(z) be the first derivative of k(z). Suppose g(q) = 0. What is q?
-1, 0
Factor -2/5*g**3 - 534/5*g**2 - 106 - 1062/5*g.
-2*(g + 1)**2*(g + 265)/5
Let m be 1*(-54)/(-30) + 2/10. Let r(s) = -s + 25. Let j be r(11). Factor -m*u**2 + 17*u**3 + 4 - j*u + 14*u**3 - 17*u**3 - 2*u**2.
2*(u - 1)*(u + 1)*(7*u - 2)
Let t(q) be the first derivative of -q**5/5 + 97*q**4 + 390*q**3 + 586*q**2 + 391*q + 2523. Factor t(h).
-(h - 391)*(h + 1)**3
Factor -2/7*t**2 - 1640/7*t + 1642/7.
-2*(t - 1)*(t + 821)/7
Let i(p) = -4*p**2 + 6*p - 11. Let q be i(6). Let a = 122 + q. Solve 3*t**5 - 60*t**4 + 12*t**2 + 24*t - 18*t**a + 115*t**4 - 58*t**4 = 0.
-2, -1, 0, 2
Let u be 2/(-2) + 45 - -3. Suppose -u + 38 = -3*f. Factor -1/3*j**4 + 0*j**2 + 2/3*j**f + 0*j + 0.
-j**3*(j - 2)/3
Let b(n) be the third derivative of n**5/210 + 20*n**4/21 + 372*n**3/7 - 11*n**2 + 461*n. Factor b(p).
2*(p + 18)*(p + 62)/7
Let x(u) be the third derivative of u**7/105 - 11*u**6/120 - u**5/20 + 11*u**4/6 - 10*u**3/3 - u**2 - 2204. Solve x(f) = 0.
-2, 1/2, 2, 5
Suppose -26*i - 18 = 21*i - 159. Let h = 5388 + -1601. Factor -h + 3*f + i*f**2 + 3787.
3*f*(f + 1)
Suppose 55*k + 25 = 60*k. What is m in 1346*m - 4*m**5 - 76*m**4 + 0*m**k - 522*m**3 - 400 - 1026*m + 206*m**3 + 476*m**2 = 0?
-10, -1, 1
Let i(a) be the third derivative of -121/150*a**5 + 0 + 0*a**4 - 1/525*a**7 + 29*a**2 + 0*a**3 + 0*a - 11/150*a**6. Find j such that i(j) = 0.
-11, 0
Let b = -6 + 4. Let t be b/10*-5 + 9. Find s, given that -4*s**2 - 105 - 4*s + t*s**3 + 109 - 6*s + 0*s = 0.
-1, 2/5, 1
Suppose -75 = 5*a - 8*a. Let u(d) = 20*d**4 + 5*d**2. Suppose 22 = -202*g + 180*g. Let p(w) = w**4. Let x(q) = a*p(q) + g*u(q). Suppose x(b) = 0. Calculate b.
-1, 0, 1
Let p(i) be the first derivative o