 p so that 0*p**2 - 4/9*p**3 + 0*p + t - 2/9*p**x = 0.
-2, 0
Let k = -184 + 509. Let m = 325 - k. Determine t, given that 0*t**2 + 0*t + m - 2/5*t**3 = 0.
0
Let r(x) be the second derivative of -3*x**5/20 - 51*x**4/4 + 105*x**3/2 - 159*x**2/2 + 1621*x - 1. What is z in r(z) = 0?
-53, 1
Let x(o) = 2 + 10 + 7 - 2*o - 6. Let s be x(5). Factor -3*i**2 + 5*i - s*i**2 + 7*i - 4*i + 8.
-2*(i - 2)*(3*i + 2)
Let a be (-446)/(-132) - 23/506. Let t(y) be the first derivative of -5 + 0*y - 4/9*y**3 - a*y**2. Factor t(l).
-4*l*(l + 5)/3
Suppose -5*o + 5*d + 15 = 0, 5*o - 20 = 3*d - 7. Let 9*q + 9567*q**o - 2*q**3 + 35*q**3 - 9534*q**2 - 6*q**5 + 3*q**4 = 0. What is q?
-1, -1/2, 0, 3
Let n(l) be the third derivative of -l**6/40 + 19*l**5/20 - 55*l**4/8 - 363*l**3/2 + 1395*l**2. Factor n(j).
-3*(j - 11)**2*(j + 3)
Let i(u) = 2*u - 52. Let k be (-52)/(2*7/(-7)). Let h be i(k). Factor 0*p + 4/13*p**3 + h*p**2 + 2/13*p**4 + 0.
2*p**3*(p + 2)/13
Let a(z) = 179*z**2 + 16*z + 4. Let o(d) = 347*d**2 + 33*d + 7. Let x(c) = -7*a(c) + 4*o(c). Factor x(u).
5*u*(27*u + 4)
Let n(x) be the second derivative of -x**5/70 + 19*x**4/42 + 781*x**3/21 + 4961*x**2/7 - 2555*x. Factor n(w).
-2*(w - 41)*(w + 11)**2/7
Suppose 2*w = 5*h + 36, -12 = 4*w - 86*h + 90*h. Let o(g) be the first derivative of -2*g**2 - 1/3*g**w - 4*g - 47. Factor o(k).
-(k + 2)**2
Find h such that 24*h**3 - 2873664*h**4 + 2873663*h**4 + 8*h**3 - 31*h**2 = 0.
0, 1, 31
Suppose 13*c - 37 = 28. Factor 0*i**2 + 63*i - 59*i - i**3 + 2*i**c - 2*i**2 + 2*i**4 - 5*i**3.
2*i*(i - 1)**2*(i + 1)*(i + 2)
Let d(j) be the third derivative of -5*j**8/336 + 11*j**7/14 - 115*j**6/24 - 11*j**5/4 + 145*j**4/6 + 20*j**2 + 3*j + 10. Determine l, given that d(l) = 0.
-1, 0, 1, 4, 29
Let g = -1/1872 + -26203/9360. Let v = g - -103/35. Factor -25/7 + 10/7*k - v*k**2.
-(k - 5)**2/7
Let f be (1 - 2)/(-1) + 1. Let l(b) = b**3 + 17*b**2 + 28*b - 224. Let i be l(-6). Solve 3*x + 17/2*x**2 - f*x**3 - 3/2*x**i + 0 = 0.
-3, -1/3, 0, 2
Let g(p) be the second derivative of p**6/135 + 71*p**5/90 - 4*p**4/3 - 992*p. Determine m, given that g(m) = 0.
-72, 0, 1
Factor -2/7*c**2 - 242/7*c + 244/7.
-2*(c - 1)*(c + 122)/7
Let f(l) be the third derivative of 0*l + 7/4*l**4 - 3*l**3 + 7/120*l**6 + 0 - 61/120*l**5 - 1/420*l**7 - 8*l**2. Factor f(s).
-(s - 6)**2*(s - 1)**2/2
Determine r so that 9764/15*r - 2/15*r**2 - 11916962/15 = 0.
2441
Let r(t) = 1167*t + 5837. Let b be r(-5). Find p, given that 0*p + 5/2*p**b + 0 + 11/4*p**3 + 1/4*p**4 = 0.
-10, -1, 0
Let q(l) be the first derivative of l**5/5 + 17*l**4/4 + 41*l**3/3 - 137*l**2/2 + 78*l + 1878. Factor q(z).
(z - 1)**2*(z + 6)*(z + 13)
Suppose 36*p - 121*p + 510 = 0. Let m(q) = 6*q**2 + q - 1. Let r be m(1). Factor -p*s**2 - 15*s + 48*s - r*s**2 - 18 - 3*s**3.
-3*(s - 1)**2*(s + 6)
Suppose -3*x**4 + 90*x**4 - 154*x - 170*x + 448*x**3 - 102*x**2 - 122*x**3 - 2*x**5 + 15*x**4 = 0. What is x?
-3, -1, 0, 1, 54
Let f(p) be the first derivative of p**4/9 + p**3 + 4*p**2/3 + 4*p + 164. Let h(t) be the first derivative of f(t). Determine b so that h(b) = 0.
-4, -1/2
Let k(v) be the second derivative of v**4/3 - 3344*v**3/3 + 1397792*v**2 - v - 1979. Factor k(f).
4*(f - 836)**2
Factor 392/5 - 4/5*r**2 + 188/5*r.
-4*(r - 49)*(r + 2)/5
Let n be ((-272)/(-156))/(1416/9204). Find b such that -12*b - 2/3*b**2 - n = 0.
-17, -1
Let z(m) = 21*m**2 + 36*m + 24. Let l be ((-19)/(-57))/((-1)/(-6)). Let b = -2 + 11. Let p(h) = -5*h**2 - 9*h - 6. Let y(v) = b*p(v) + l*z(v). Factor y(u).
-3*(u + 1)*(u + 2)
What is g in -2*g**4 + 107/2*g**3 + 507/2*g**2 + 308*g + 62 = 0?
-2, -1/4, 31
Let l = 756 + -973. Let w be (-6)/(-21) + (-589)/l. Factor -32/3*t + 52/9*t**w - 20/3*t**2 + 16/9.
4*(t - 2)*(t + 1)*(13*t - 2)/9
Let a(z) be the third derivative of z**7/2520 - z**6/30 + 6*z**5/5 - z**4/8 - z**3/3 + 62*z**2. Let t(w) be the second derivative of a(w). Solve t(c) = 0.
12
Let t(s) be the second derivative of 23*s**4/6 + 18*s**3 + 16*s**2 - 406*s + 7. Factor t(r).
2*(r + 2)*(23*r + 8)
Suppose -2*g**3 + 164*g + g**2 + 149*g + g**4 - 2*g**4 - 311*g = 0. Calculate g.
-2, -1, 0, 1
Let i be -3*((-4)/(-10) + (-240)/225). Suppose 5*u = v - 8, i*u - 13 = -3*v + 6*u. Suppose 0 + 3*a**v + 4*a**3 + 56*a - 31*a**2 + 16 - 3*a**3 = 0. Calculate a.
-1/4, 4
Let m(t) = 3*t - 74. Let c(a) = a - 74. Let k(w) = -4*c(w) + 5*m(w). Let d be k(7). Factor 18*f**2 + 1/2*f**4 + 5*f**d + 28*f + 16.
(f + 2)**3*(f + 4)/2
Let a(r) be the first derivative of 81*r**5/5 + 2781*r**4/2 + 3039*r**3 + 2418*r**2 + 804*r - 2077. Let a(g) = 0. Calculate g.
-67, -2/3, -1/3
Factor -230/11 + 232/11*w - 2/11*w**2.
-2*(w - 115)*(w - 1)/11
Let w = 192 - 187. Find t, given that -25 - 10*t - 24 + 64 - w*t**2 = 0.
-3, 1
Let s(l) be the second derivative of 3*l**5/80 + 8*l**4/9 - 107*l**3/72 - 5*l**2/4 - 1148*l. Factor s(n).
(n - 1)*(n + 15)*(9*n + 2)/12
Let x(i) be the first derivative of -2/75*i**5 - 1/45*i**6 + 0*i**4 + 0*i**3 + 0*i**2 + 0*i - 34. Factor x(o).
-2*o**4*(o + 1)/15
Suppose 98/5*q**4 + 2/5*q**5 + 0*q**3 + 0*q**2 + 0*q + 0 = 0. What is q?
-49, 0
Factor 10584/5*a**4 - 86079/5*a**3 - 343/5*a**5 + 360 + 68678/5*a**2 - 3828*a.
-(a - 15)**2*(7*a - 2)**3/5
Let t(a) be the third derivative of -a**8/1848 - 326*a**7/1155 + 493*a**6/330 - 166*a**5/165 - 985*a**4/132 + 658*a**3/33 + 4*a**2 - 199*a. Solve t(j) = 0.
-329, -1, 1, 2
Let c(v) be the second derivative of 3*v**5/20 - 19*v**4/2 + 197*v**3/2 - 240*v**2 + 2*v - 2542. Find k such that c(k) = 0.
1, 5, 32
Find a such that -3800/13*a - 17328/13 - 164/13*a**2 - 2/13*a**3 = 0.
-38, -6
Solve -1/2*s**3 + 0 + 14*s - 6*s**2 = 0.
-14, 0, 2
Determine p, given that 2*p**4 + 11*p**3 + 45*p**3 + 99*p**3 - 3*p**3 + 186*p**2 + 654*p**2 = 0.
-70, -6, 0
Let b(p) = p**2 - 11*p + 32. Let y be b(5). Factor 0*h**4 - 17*h**2 - 2*h**4 + 24*h + 37*h**2 - 16*h**y - 6*h**3 + 16.
-2*(h - 2)*(h + 1)*(h + 2)**2
Let w(c) be the second derivative of 26569*c**5/5 + 505463*c**4/3 + 24784*c**3/3 + 152*c**2 - 11353*c. Solve w(p) = 0.
-19, -2/163
Let f = 688 - 685. Factor -3 - 56*k - 19 - 10 + k**4 - 2*k**4 - 10*k**f - 33*k**2 - 3*k**2.
-(k + 2)**3*(k + 4)
Let q(b) be the third derivative of -b**5/30 + 425*b**4/12 + 854*b**3/3 + 6447*b**2. Find s, given that q(s) = 0.
-2, 427
Suppose 8*v + 0*v = 16. Factor -124 + 61 + 21*d + 3*d**v + 57 + 36.
3*(d + 2)*(d + 5)
Suppose 4*n**2 - 9 - 1/2*n**5 - 13*n**3 + 27/2*n + 5*n**4 = 0. Calculate n.
-1, 1, 3, 6
Let m(s) be the first derivative of s**6/24 - 11*s**5/12 + 25*s**4/3 - 40*s**3 - s**2 - 22*s + 11. Let i(w) be the second derivative of m(w). Factor i(b).
5*(b - 4)**2*(b - 3)
Let f = 246082/55925 + -12/55925. Factor 0*v - f*v**4 - 2*v**3 - 4/5*v**5 + 0 + 0*v**2.
-2*v**3*(v + 5)*(2*v + 1)/5
Let m be ((-2)/8 - 0)*0. Let t(a) be the first derivative of -1/6*a**3 + m*a - 7/4*a**2 + 2. Solve t(g) = 0.
-7, 0
Suppose 0 = -3*d + 2 - 5. Let h be 4 + 3 + d + -4. Find s such that 3*s**3 - 6*s**3 + 2*s + 2*s**h + s**3 - 2 = 0.
-1, 1
Suppose -5*h + 15 = 4*u, -1 = h - u - 4. Let a(c) be the first derivative of -55/3*c**h + 45/2*c**2 + 10*c + 3. Factor a(r).
-5*(r - 1)*(11*r + 2)
Let d = -457 + 453. Let n be ((-140)/(-4))/5 + d. Determine v, given that 0 + v**n - 22/5*v**2 + 8/5*v = 0.
0, 2/5, 4
Let z(d) be the first derivative of -3/2*d + 5/24*d**4 + 23/12*d**2 - 19/18*d**3 + 11. Factor z(v).
(v - 1)**2*(5*v - 9)/6
Let t(l) = -80*l**3 + 8*l**2 + 290*l - 14. Let u(o) = 79*o**3 - 6*o**2 - 291*o + 9. Let p(f) = -5*t(f) - 6*u(f). Determine k, given that p(k) = 0.
-2, -2/37, 2
Let g(h) be the third derivative of 0*h - 1/120*h**6 + 2/3*h**4 + 0*h**3 + 1/10*h**5 + 0 - 77*h**2. Determine w so that g(w) = 0.
-2, 0, 8
Let p(i) = i**4 + i**3 + i**2 - i - 1. Let k = -80 - -82. Let c(m) = -m**4 + 5*m**3 + m**2 - m - 1. Let g(h) = k*p(h) - 2*c(h). Suppose g(q) = 0. Calculate q.
0, 2
Suppose -20*o + 22*o - 5*f + 1 = 0, 3*o - 5*f = 1. Suppose -12 = -3*b + o*d, 5*b - 10*b + 3*d + 19 = 0. What is s in -1/4*s**3 + 0 + 0*s - 5/4*s**b = 0?
-5, 0
Factor -36*p**2 + 256/5*p - 162/5*p**3 - 64/5.
-2*(p + 2)*(9*p - 4)**2/5
Let x(d) = 21*d**3 + 1212*d**2 - 2445*d + 1200. Let s(t) = -39*t**3 - 2422*t**2 + 4884*t - 2401. Let b(y) = 6*s(y) + 11*x(y). Factor b(n).
-3*(n - 1)**2*(n + 402)
Let d(z) be the second derivative of -2 + 88*z - 1/102*z**4 + 22/