+ 3*u**4.
2*(u - 7)**2*(u + 1)*(u + 4)
Let w(x) = x**3 - x**2 + 1. Let u(m) = 100*m**4 - 314*m**3 + 90*m**2 + 256*m + 70. Let p(c) = u(c) - 6*w(c). Determine g, given that p(g) = 0.
-2/5, 2
Suppose -100000*j - 2*j**5 + 20000*j**2 + 92629 + 100*j**4 - 1303*j**3 - 697*j**3 + 107371 = 0. What is j?
10
Let m(o) be the third derivative of -o**6/120 - 7*o**5/20 + 11*o**4/12 - 23*o**2 - o. Factor m(x).
-x*(x - 1)*(x + 22)
Let b(t) = -5*t**2 - 35*t + 18. Let d(k) = 2*k**2 + 12*k - 6. Suppose -6*g + 5*g - 21 = -4*z, 0 = -5*z - 2*g + 10. Let p(x) = z*b(x) + 11*d(x). Factor p(y).
2*(y - 3)*(y - 1)
Let w(u) be the second derivative of u**6/105 - 36*u**5/35 + 611*u**4/21 + 888*u**3/7 + 1369*u**2/7 - 2*u - 30. Factor w(q).
2*(q - 37)**2*(q + 1)**2/7
Suppose 2*k - 5*p - 14 = 0, -4 = -4*k - 3*p - 2. Solve 4 + 25*m + 2*m**k - 32*m + 13*m = 0.
-2, -1
Suppose 44/13*u - 2/13*u**2 + 0 = 0. Calculate u.
0, 22
Let c(o) = -o**2 - o + 1. Let f(y) = -y**2 - 7*y - 7. Suppose -3*r + 2*u = -18, 2*r + 4 = 2*u + 16. Let k(n) = r*c(n) + 2*f(n). Find v, given that k(v) = 0.
-2, -1/2
Let o(g) = -5*g**2 + 3*g**2 + 0 + g + 3*g**2 - 1. Let r be 1/(-3)*(4 - 1). Let x(w) = -51*w**2 + 26*w - 2. Let a(u) = r*x(u) - 2*o(u). Factor a(s).
(7*s - 2)**2
Factor 12/5*u**2 - 1/5*u**3 + 2 - 21/5*u.
-(u - 10)*(u - 1)**2/5
Suppose -21*c - 136 = -68*c - 21*c. Solve -32/3 + 16/3*d - 2/3*d**c = 0.
4
Factor 71/3*c**2 + 1225/3 - 1/3*c**3 - 1295/3*c.
-(c - 35)**2*(c - 1)/3
Suppose -38*a + 214 = 100. Suppose 0*k**2 + 0*k + 0 - 2/7*k**4 - 2/7*k**a = 0. Calculate k.
-1, 0
Let s = -15/2077 - 6/67. Let a = s - -161/62. Factor 2*d + a*d**3 + 4*d**2 + 1/2*d**4 + 0.
d*(d + 1)*(d + 2)**2/2
Let k be ((-1037)/(-136) + -7 + 0)*24/30. Suppose k*b**2 + 3/2*b + 0 = 0. Calculate b.
-3, 0
Suppose -g + 1 = 0, a + 4*g - 40 = -a. Let d = -12 + a. Factor -4*f**2 + 4*f - 10*f**3 + d*f + 4 - 4*f + 4*f.
-2*(f - 1)*(f + 1)*(5*f + 2)
Suppose -9*n - 6*n = -18 - 42. Solve -6/5*i**3 + 9/5 + 6/5*i - 12/5*i**2 + 3/5*i**n = 0.
-1, 1, 3
Suppose 3*s = 16 - 7. Factor -s*a**3 + 4*a - 7 - a**3 - 1 - 4*a**4 + 12*a**2.
-4*(a - 1)**2*(a + 1)*(a + 2)
Determine d so that -3/5 - 4*d + 23/5*d**2 = 0.
-3/23, 1
Let d be ((-8)/(-12))/((-6)/(-1593)). Factor -d - 3*s**5 + 24*s**2 - 36*s**3 + 177 + 18*s**4.
-3*s**2*(s - 2)**3
Determine i so that 116*i**3 - 61*i**3 - 252 + 204*i - 51*i**3 - 52*i**2 = 0.
3, 7
Let i(a) be the first derivative of -a**5/80 - a**4/8 + 39*a + 22. Let t(v) be the first derivative of i(v). Factor t(g).
-g**2*(g + 6)/4
Let z(k) be the first derivative of k**3/5 - 3*k/5 - 164. Find n, given that z(n) = 0.
-1, 1
Determine b so that -9 - 16*b - 8*b + 45*b + 3*b**3 - 17*b**2 + 2*b**2 = 0.
1, 3
Let f(b) be the second derivative of 9*b**7/350 - 11*b**6/200 + b**5/50 + 7*b**2/2 - 4*b. Let j(a) be the first derivative of f(a). Factor j(h).
3*h**2*(h - 1)*(9*h - 2)/5
Suppose 2*d = -8*d + 50. Suppose 3*s = -3*c + 5*c - 16, c + 18 = -d*s. Factor 0 + 0*g + 0*g**c - 1/4*g**4 + 1/2*g**3.
-g**3*(g - 2)/4
Let q(r) be the first derivative of 0*r**2 + 1/4*r**4 + 0*r + 0*r**3 + 30 - 1/20*r**5. Factor q(o).
-o**3*(o - 4)/4
Factor -15/4*l - 1/4*l**2 - 13/2.
-(l + 2)*(l + 13)/4
Let q be (-5)/24 - ((-8)/(-32))/(3/(-4)). Solve -1/4 - 1/2*z**2 - 5/8*z - q*z**3 = 0.
-2, -1
Let u(l) be the first derivative of l**4/4 - 62*l**3/3 + 510*l**2 - 1800*l + 114. Find s, given that u(s) = 0.
2, 30
Let y(i) be the first derivative of 8/3*i - 6 - 4/3*i**2 + 2/9*i**3. Determine m, given that y(m) = 0.
2
Let z(t) = -11*t**2 + 13*t - 2. Let g(q) = q**2 - q. Let w be 89/(-5) + 6/(-30). Let h(p) = w*g(p) - 2*z(p). Let h(m) = 0. What is m?
1
Suppose 2*g + 5*r = 26 + 63, 2*g - 93 = -r. Let d = -139/3 + g. What is n in 2/3*n + 2/3 - d*n**2 - 2/3*n**3 = 0?
-1, 1
Let z(m) be the second derivative of m**8/2520 - m**6/180 + m**5/90 - 3*m**3 + 11*m. Let l(v) be the second derivative of z(v). Factor l(k).
2*k*(k - 1)**2*(k + 2)/3
Let q(m) be the third derivative of 1/24*m**4 - 35*m**2 + 0*m**3 + 1/630*m**7 + 0*m - 1/72*m**6 + 0 + 1/504*m**8 - 1/180*m**5. What is u in q(u) = 0?
-3/2, -1, 0, 1
Let k(s) = -1. Let n be -3 + 4 + -2 + -1. Let z(g) = -10*g**3 - 6*g + 4*g**3 + 5 + g + 5*g**3 + 4*g**2. Let y(b) = n*z(b) - 6*k(b). Factor y(h).
2*(h - 2)*(h - 1)**2
Factor -z**2 + 328*z + 154*z - 158*z + 4968 + 3780 + 4*z**2.
3*(z + 54)**2
Let z(h) be the second derivative of 49*h**6/36 + 119*h**5/60 + 19*h**4/18 + 2*h**3/9 + 59*h. Solve z(u) = 0.
-2/5, -2/7, 0
Suppose 14*n**2 - 136*n + 6*n**2 - 160 + 12*n**3 + 64 = 0. Calculate n.
-4, -2/3, 3
Let w be ((-19 - -2)/(-119) - 0)*(0 + 2). Solve -8/7 - 2*z - 4/7*z**2 + w*z**3 = 0.
-1, 4
Suppose 1520 = 4*j + 9*j + 1494. Factor -2*a + 2/3*a**j + 0.
2*a*(a - 3)/3
Let l(b) = 7*b - 20. Let f be l(4). Let i(o) = -2*o**2 - 5*o + 7. Let k(q) = -3*q**2 - 8*q + 11. Let p(h) = f*i(h) - 5*k(h). Factor p(g).
-(g - 1)*(g + 1)
Let k(g) be the first derivative of -g**4/108 + 2*g**3/27 - 2*g**2/9 - 13*g + 22. Let j(x) be the first derivative of k(x). Factor j(o).
-(o - 2)**2/9
Let s(h) be the second derivative of 3*h**5/40 - h**4/4 - 63*h**3/4 + 19*h + 5. Factor s(o).
3*o*(o - 9)*(o + 7)/2
What is c in 2*c**4 - 36*c**2 - 14 + 5*c - 45*c + 4795*c**3 - 4803*c**3 = 0?
-1, 7
Suppose -3*p = p + 3*q - 9, -4*q + 12 = -p. Suppose -9*z + 13*z = u - 27, 27 = 5*u - 2*z. Factor 1/2*f**4 + p - 5/2*f**u - 3/2*f + 7/2*f**2.
f*(f - 3)*(f - 1)**2/2
Let z(p) = 2 - 18 - 4*p - 44*p - 22*p**2. Let o(w) = w**2. Let h(r) = 2*o(r) + z(r). Factor h(t).
-4*(t + 2)*(5*t + 2)
Let p = 94 + -52. Let x be (-3 - 1)*(-4 - (-161)/p). Factor -x*r - 2/9*r**2 - 4/9.
-2*(r + 1)*(r + 2)/9
Let b = 28166 - 28162. Determine i, given that -21/2*i + 21/2*i**3 + 0 + 3/2*i**b - 3/2*i**2 = 0.
-7, -1, 0, 1
Suppose 16 = z + 13. Let 20*y**5 - 6*y**5 - 4*y**4 - 12*y**5 + 4*y**2 - 2*y**z = 0. What is y?
-1, 0, 1, 2
Suppose 11*z - 26*z + 1605 = 0. Factor 38*c**4 - 20*c - 10*c**4 + z*c**2 + 8 - 143*c**2 + 20*c**3.
4*(c - 1)*(c + 1)**2*(7*c - 2)
Let z be 2692/(-260) - 3/18. Let u = z + 551/30. Find k, given that u*k**3 + 72/13*k**4 - 2/13 + 2*k**2 - 6/13*k = 0.
-1, -1/3, 1/4
Let p = 157/3 - 1051/21. What is o in 4/7*o**2 + p - 16/7*o = 0?
2
Let b(f) be the first derivative of -2*f**5 - 40*f + 50/3*f**3 + 5/6*f**6 + 10*f**2 - 3 - 25/4*f**4. Solve b(n) = 0.
-2, -1, 1, 2
Find f such that 0*f - 18/7*f**2 - 3/7*f**3 + 0 - 3/7*f**5 + 12/7*f**4 = 0.
-1, 0, 2, 3
Let p(r) be the first derivative of -15*r**6/2 + 30*r**5 - 55*r**4/2 - 40*r**3/3 + 35*r**2/2 + 10*r - 268. What is i in p(i) = 0?
-1/3, 1, 2
Let z(t) be the first derivative of -t**3/12 - 13*t**2/4 - 169*t/4 + 24. Solve z(d) = 0 for d.
-13
Let u(i) = i**3 + 8*i**2 + 8*i + 10. Let b be u(-7). Let o = -3 + 5. Factor -5*d**2 + 6*d**o + 6*d**b + 2*d**2 + 3*d**4.
3*d**2*(d + 1)**2
Determine l, given that 3*l**3 + 19*l**2 - 9*l - 8*l**2 - 6*l**2 - 11*l**2 = 0.
-1, 0, 3
Let c(x) be the second derivative of x**4/4 - 39*x**3/2 - 60*x**2 + 226*x. Factor c(b).
3*(b - 40)*(b + 1)
Let b(w) = 3*w**2 + 38*w - 10. Let h be b(-13). Suppose 6*o - 9 = h*o. Factor 2/15*g**o + 2/15*g + 0 - 4/15*g**2.
2*g*(g - 1)**2/15
Let l = -11528 + 11533. Suppose 108/5*y**2 + 126/5*y**4 - 162/5 - 3*y**l - 318/5*y**3 + 81*y = 0. What is y?
-1, 2/5, 3
Let o(p) be the third derivative of p**8/448 - 13*p**7/504 - 5*p**6/72 + p**4/12 + 31*p**2. Let j(s) be the second derivative of o(s). Factor j(c).
5*c*(c - 5)*(3*c + 2)
Let z(a) be the third derivative of 0 + 0*a**4 - 1/40*a**6 + 0*a**3 - 9*a**2 + 0*a**5 + 0*a. Factor z(k).
-3*k**3
Suppose 11 = 6*q - 1. Let p be (-9)/q - 0 - -5. Find m such that p + 3*m + 9/2*m**2 = 0.
-1/3
Let f(o) be the third derivative of 2*o**4 + 24*o**3 + 0*o + 1/15*o**5 + 0 - 14*o**2. Solve f(k) = 0 for k.
-6
Let l = 43 + -21. Suppose -4*s + l = 3*f - f, 0 = f - 5. Let 0*v - 2/11*v**4 - 2/11*v**s + 2/11*v**5 + 0 + 2/11*v**2 = 0. Calculate v.
-1, 0, 1
Let m be 6698/4692 + 24/(-92). Factor -28/3*d + 17/2*d**2 - m*d**3 + 2.
-(d - 6)*(d - 1)*(7*d - 2)/6
Let z(n) = 1. Let g(p) = 3*p + 12. Let k(y) = -g(y) + 9*z(y). Let u be k(-2). Solve 4*s**3 - 3*s**3 + u*s**5 + 0*s**3 - 4*s**5 = 0.
-1, 0, 1
Let s(y) = -3*y - 82. Let v be s(-28). Suppose 16*f**v - 2330*f + 2*f**2 + 9*f**5 + 36*f**3 + 2333*f + 30*f**4 = 0. Calculate f.
-1, -1/3, 0
Let t(o) = 4*o**4 + 55*o**3 + 93*o**2 + 53*o + 1