).
2*(l - 362)*(l + 1)*(l + 2)/3
Suppose 8*s + 29*s - 111 = 0. Find h, given that 42*h**s + h - 49*h**2 + 11*h**2 - 2*h**4 - h - 2*h**2 = 0.
0, 1, 20
Let n be 40/6 + -7 - (-4)/(-6). Let p(x) = 4*x**3 - 22*x**2 + 71*x - 48. Let z(w) = -2*w**2 + w. Let s(g) = n*p(g) - 5*z(g). Factor s(c).
-4*(c - 4)*(c - 3)*(c - 1)
Suppose 0 - 205/2*t - 5/2*t**2 = 0. What is t?
-41, 0
Suppose -4*i = 3*i - 343. Let q = 54 - i. Determine u so that 49*u**4 - 10*u**2 + 16*u**5 - 39*u**4 - 25*u**3 + 9*u**q = 0.
-1, -2/5, 0, 1
Let m(k) be the second derivative of 24*k - 20/27*k**3 + 0*k**2 + 2 - 41/54*k**4 - 1/45*k**5. Suppose m(z) = 0. Calculate z.
-20, -1/2, 0
Let b(i) be the first derivative of i**6/75 + i**5/50 - i**4/15 - 24*i - 61. Let f(k) be the first derivative of b(k). Factor f(o).
2*o**2*(o - 1)*(o + 2)/5
Let y(u) be the second derivative of -u**7/210 - u**6/30 + 9*u**5/100 + 3*u**4/4 + 973*u. Let y(s) = 0. Calculate s.
-5, -3, 0, 3
Let z be 24/(-28) - (-2340)/182. Suppose 3*y - 16 = 5*m, 2*y - 18*m + 14*m - z = 0. Let 0 - 1/4*o**y - 1/4*o = 0. What is o?
-1, 0
Factor -4*x**3 - 33*x + 2*x**3 + 0*x**3 - 192 + x + 493*x**2 - 465*x**2.
-2*(x - 12)*(x - 4)*(x + 2)
Suppose -262*x + 281*x = -21 + 97. Factor -1/8*b**5 + 0 - 9/2*b**2 + 0*b - 13/8*b**x - 6*b**3.
-b**2*(b + 1)*(b + 6)**2/8
Factor 207/2 + 15/4*j**3 - 627/4*j - 513/2*j**2.
3*(j - 69)*(j + 1)*(5*j - 2)/4
Let c(m) be the first derivative of 9*m**5/5 - 15*m**4/8 - m**3/2 - 1193. Factor c(q).
3*q**2*(q - 1)*(6*q + 1)/2
Let z(i) = -2*i**2 + 15*i - 10. Let l be z(8). Let q be -2 + (-327)/l + 1/(-6). Solve 2*f**2 - q*f + 3*f**2 - f**2 + 48 - 32 = 0.
2
Let p(r) = 5*r + 32. Let d be p(-4). Factor -8*t**2 + 7*t**2 + 5*t**2 + 16*t - d + 4*t**4 - 16*t**3 + 4*t**2.
4*(t - 3)*(t - 1)**2*(t + 1)
Let h(x) = 12*x**2 + 11*x - 14. Let z(v) = -2*v**2 - 2. Let c(b) = h(b) + 3*z(b). Let j(k) = k**2 - k - 4. Let q(t) = -2*c(t) + 10*j(t). Factor q(m).
-2*m*(m + 16)
Let r(y) = 72*y**2 + 355*y - 4022. Let m(l) = -172*l**2 - 888*l + 10056. Let o(x) = -5*m(x) - 12*r(x). Factor o(v).
-4*(v - 24)*(v - 21)
Let h be (-9)/((-135)/500)*(6 + -9). Let y be (-10)/8*160/h. Factor p**y - p - 1/2*p**4 - 1/4*p**5 + 0 + 3/4*p**3.
-p*(p - 1)**2*(p + 2)**2/4
Let h(b) = -16*b**2 + 34*b - 3. Let q(s) = 5*s**2 - s + 1. Let m(v) = 37*v + 219. Let l be m(-6). Let a(n) = l*q(n) - h(n). Factor a(j).
j*(j - 31)
Factor -1/5*v**2 + 24/5*v + 5.
-(v - 25)*(v + 1)/5
Let w(z) be the first derivative of -z**4/4 - 4*z**3/3 + 45*z**2/2 + 6740. Factor w(h).
-h*(h - 5)*(h + 9)
Let b = 2593/58680 - -1/3912. Let s(u) be the second derivative of 0 - 5/27*u**3 + b*u**5 - 1/27*u**4 + 1/189*u**7 - 14*u + 4/135*u**6 - 2/9*u**2. Factor s(i).
2*(i - 1)*(i + 1)**3*(i + 2)/9
Factor -x**3 + 1484*x**2 - 71*x + 128 - 1492*x**2 + 87*x.
-(x - 4)*(x + 4)*(x + 8)
Let f(p) = -20*p + 80. Let w(a) = -59*a + 236. Let t(q) = -8*f(q) + 3*w(q). Let b be t(4). Factor 1/5*v**3 + b + 1/5*v**4 + 0*v - 1/5*v**2 - 1/5*v**5.
-v**2*(v - 1)**2*(v + 1)/5
Let r be -2 - (13/(2080/640))/((-1 - 0) + 0). Factor 1/5*u**r + 3/5*u - 4/5.
(u - 1)*(u + 4)/5
Suppose 759 + 681 = 3*t. Factor 142 + 30*u**3 + 3*u**4 + 434 + 52*u**2 - 10*u**3 - 2*u**4 - t*u.
(u - 2)**2*(u + 12)**2
Let h(k) = 10*k**3 - 800*k**2 - 2*k + 162. Let f be h(80). Factor -68/9*b - 578/9 - 2/9*b**f.
-2*(b + 17)**2/9
Let m(b) be the first derivative of -2*b**3/3 + 48*b**2 - 1134*b + 4208. Factor m(l).
-2*(l - 27)*(l - 21)
Let q(z) be the third derivative of -z**8/50400 + z**7/1575 + z**5/10 + z**3/3 + 50*z**2. Let a(h) be the third derivative of q(h). Find n such that a(n) = 0.
0, 8
Let s = 178 + -167. Let o be (4/22)/1 - (-31)/s. Factor -2/3*g**4 + 0*g + 0*g**o - 2/3 + 4/3*g**2.
-2*(g - 1)**2*(g + 1)**2/3
Find o, given that 176/5*o**2 - 40*o**3 + 52/5*o**4 + 32/5*o + 0 = 0.
-2/13, 0, 2
Let m(h) = 4*h**2 + 12*h + 4. Let j(y) = 2*y**2 + 3*y + 2. Let s be j(-2). Let x(g) = s + 0 - 2 - 3. Let b(z) = m(z) - 4*x(z). Determine n, given that b(n) = 0.
-2, -1
Let h = 6/287 + 496/3731. Let t be ((-240)/(-1820))/(4/14). Let -t*u + 8/13*u**2 - h*u**3 + 0 = 0. Calculate u.
0, 1, 3
Let u be ((-9)/15)/(-1) - (-666)/15. Let h = u - 43. Suppose -26 - h*l**2 - 27 + 53 - 8*l = 0. What is l?
-4, 0
Let r(p) be the first derivative of p**4/8 + 95*p**3/6 - 98*p**2 + 198*p - 490. Factor r(j).
(j - 2)**2*(j + 99)/2
Let a(i) be the first derivative of -i**5/15 + 17*i**4/3 + 716*i**3/9 - 10608*i**2 - 292032*i + 7590. Find c such that a(c) = 0.
-18, 52
Let s(k) be the third derivative of -15*k**2 + 4 - 5/6*k**3 - 47/24*k**4 + 0*k - 91/300*k**5 - 3/200*k**6. Factor s(p).
-(p + 5)**2*(9*p + 1)/5
Suppose 0*z - 2*z = 3*f + 2, 2*f = -2*z. Let n be 18 + -18 + 0*f/4. Factor -1/4*i**2 + 1/4 + n*i.
-(i - 1)*(i + 1)/4
Let f(v) be the first derivative of -v**6/9 + 32*v**5/15 - 2*v**4 - 92*v**3/9 + 13*v**2/3 + 20*v + 6. Determine k so that f(k) = 0.
-1, 1, 2, 15
Let x be 126/((-294)/14) + (-2 - -11). Let z(m) be the second derivative of -27*m + 0*m**x + 1/54*m**4 + 0 + 0*m**2. Factor z(y).
2*y**2/9
Let f(r) = -17*r**4 - 11*r**3 + 49*r**2 - 15*r - 12. Let h(q) = 70*q**4 + 45*q**3 - 200*q**2 + 60*q + 50. Let z(d) = 25*f(d) + 6*h(d). Factor z(w).
-5*w*(w - 1)**2*(w + 3)
Let -38*o**2 - 2*o**3 - 195223*o + 98066*o + 97589*o = 0. Calculate o.
-27, 0, 8
Let r = 1924 - 1924. Suppose 0 = 4*b + s, -2*b + 160*s - 164*s = r. Factor 0 + 0*w**4 + b*w**2 + 2/11*w + 2/11*w**5 - 4/11*w**3.
2*w*(w - 1)**2*(w + 1)**2/11
Let h(k) be the third derivative of -2/3*k**3 - 1/105*k**7 + 1/10*k**5 + 0*k + 0 - 1/12*k**4 + 1/60*k**6 - 112*k**2. Determine y, given that h(y) = 0.
-1, 1, 2
Find n such that 139*n**3 + 11760*n + 4760*n**2 + 205*n**3 + 7*n**4 + 33*n**3 - 82*n**3 - 2*n**4 = 0.
-28, -3, 0
Let 2*r**2 - 19075 - 48*r - 36*r + 18535 - 5*r**2 = 0. Calculate r.
-18, -10
Let q(c) be the first derivative of c**4/8 + 47*c**3/6 - 12*c**2 + 6655. What is x in q(x) = 0?
-48, 0, 1
Let v(n) be the second derivative of -1/54*n**4 + 205*n + 13/27*n**3 + 0*n**2 + 0. Factor v(f).
-2*f*(f - 13)/9
Let m(x) be the second derivative of x**7/70 - 323*x**6/50 - 1953*x**5/50 - 979*x**4/10 - 1307*x**3/10 - 981*x**2/10 + 14299*x. Solve m(i) = 0.
-1, 327
Suppose -103 = -5*o - 2*c + 3*c, -3*c + 69 = 3*o. Let h = o - 17. Suppose -15*b**h + 20*b**5 - 2*b**2 + 3*b**3 + 2*b**2 - 8*b**3 = 0. Calculate b.
-1/4, 0, 1
Let k(j) be the first derivative of -5*j**3 - 273*j**2/2 - 306*j - 2175. What is t in k(t) = 0?
-17, -6/5
Let c(r) be the second derivative of -6*r**5/5 + 91*r**4/3 + 54*r**3 - 32*r**2 - 140*r. Factor c(u).
-4*(u - 16)*(u + 1)*(6*u - 1)
Suppose 0 = -3*o + 3*p - 0 + 18, -o + 5*p - 14 = 0. Let g be -6 + 0 + o + -3. Factor -2/11*z**g + 4/11*z + 0.
-2*z*(z - 2)/11
Let s(t) be the first derivative of t**4/4 + 20*t**3/3 + 2*t**2 + 81*t + 58. Let m be s(-20). Find y such that -1/3*y**2 + 2/3*y + m = 0.
-1, 3
Suppose -3*z = -4*y + 3*y - 7, -3*z = -4*y - 1. Let f = 12 - 6. Factor -2*x + f*x**4 + 4*x**y - 5*x**4 - 7*x**2.
x*(x - 2)*(x + 1)**2
Let y(r) = -2*r**2 - 1553*r + 1660. Let g(t) = t**2 + 776*t - 822. Let s(n) = -7*g(n) - 3*y(n). Determine f, given that s(f) = 0.
-774, 1
Let m(u) be the second derivative of u**6/420 - u**5/42 - 6*u**2 - u - 5. Let n(f) be the first derivative of m(f). Factor n(b).
2*b**2*(b - 5)/7
Let a(n) be the second derivative of -2/3*n**3 - 1 + 21/2*n**2 + 25*n - 1/12*n**4. Factor a(u).
-(u - 3)*(u + 7)
Let l(k) be the first derivative of -9*k**2 - 15*k**3 + 8 + 21*k - 3/2*k**4. What is u in l(u) = 0?
-7, -1, 1/2
Let s(d) be the first derivative of 13/3*d - 49 - 41/9*d**3 + 1/4*d**4 + 25/6*d**2. Let s(g) = 0. Calculate g.
-1/3, 1, 13
Let x = 16 + -8. Let s be (-1*0/(7 - x))/(-1). Solve 0*u - 1/2*u**5 + 4/3*u**4 + s + 1/3*u**2 - 7/6*u**3 = 0 for u.
0, 2/3, 1
Factor -247828 - 227*g**3 + 247828 - 73983*g**2 - 318*g**3 - g**4 + 74529*g.
-g*(g - 1)*(g + 273)**2
Let c(o) be the first derivative of -49*o**4 + 195916*o**3/3 - 55952*o**2 + 15984*o - 8835. Factor c(n).
-4*(n - 999)*(7*n - 2)**2
Let j be 142/46 + 114/(-1311). Factor 0 + 0*m + 0*m**j - 3/2*m**2 + 3/2*m**4.
3*m**2*(m - 1)*(m + 1)/2
Let m = -54 + 52. Let r be (m - -3)/(330/(-336) - -1). What is d in -r*d**4 + 0*d**5 - 3*d**5 - 30*d**4 - 3375*d + 23*d**4 - 1875 - 510*d**3 - 1950*d**2 = 0?
-5, -1
Let w(p) = -4*p**3 + 6*p**2 + 292*p + 438. Let m(y)