he second derivative of u(t). Solve z(m) = 0.
-1/4, 2/5
Let x(g) = -g - 8. Let p be x(-10). Suppose 4*n**4 - 4*n - p*n**4 + 14*n**3 + 30*n**2 + 22*n + 0*n = 0. What is n?
-3, -1, 0
Solve -2 - 76/3*r**2 - 16*r**3 + 8/3*r**5 + 2/3*r**4 - 40/3*r = 0 for r.
-1, -1/4, 3
Suppose 2*g + 4 = -0. Let m be (-8 + 14)*(-1)/g. Find i, given that m*i**2 - 4*i**3 - 6*i**2 - 3*i**3 + 4*i**3 = 0.
-1, 0
Let m(h) be the third derivative of h**7/63 + 7*h**6/180 + h**5/45 + 21*h**2. Factor m(w).
2*w**2*(w + 1)*(5*w + 2)/3
Let i(c) = -c - 2. Let f be i(-4). Suppose -z - 10 = -2*h, 2*z + 16 = -f*z. Determine b so that -2 - b**2 - b**4 + 2*b**4 + 2*b**h + 2 - 2*b = 0.
-2, -1, 0, 1
Let r(a) be the first derivative of -a**5/20 + 39*a**4/4 - 1441*a**3/3 - 3120*a**2 - 6400*a + 939. Let r(t) = 0. What is t?
-2, 80
Let p(g) be the first derivative of g**3/24 + 35*g**2/4 + 1225*g/2 + 107. What is b in p(b) = 0?
-70
Let h(v) be the second derivative of -v**4/32 - 9*v**3/4 + 161*v. Let h(g) = 0. Calculate g.
-36, 0
Let j(w) = -5*w**4 - 7*w**2 - 8*w + 4. Let i(h) = 6*h**4 + h**3 + 8*h**2 + 9*h - 4. Let a(g) = -4*i(g) - 5*j(g). Factor a(p).
(p - 2)**2*(p - 1)*(p + 1)
Let f(w) be the third derivative of -w**4/6 + w**3/6 - 5*w**2. Let s be f(-4). Factor -4*a**3 - s*a**4 + 4*a**2 + a**2 - 2*a + 18*a**4.
a*(a - 2)*(a - 1)**2
Factor 3 - 46*h**3 - 20*h - 5 - 20*h**2 + 2 + 41*h**3.
-5*h*(h + 2)**2
Factor 16*p**4 - 46*p**4 + 11*p**4 - 4*p**3 + 6*p**2 - 2*p**2 + 15*p**4 + 4*p.
-4*p*(p - 1)*(p + 1)**2
Let q(w) = -2*w + 4*w**2 - 8*w - 1 + 5*w + 4*w. Let d be q(-1). Solve -4*r + d*r + 1 - r**2 = 0.
-1, 1
Let r(z) = z - 1. Let t(p) = -p**5 + 6*p**4 - 11*p**3 + 2*p**2 + 8*p - 4. Let y(m) = 4*r(m) + t(m). Find s, given that y(s) = 0.
-1, 1, 2
Factor -10*o**3 - 10*o**3 + 2*o**2 - 16 + 16*o + 2*o**2 + 16*o**3.
-4*(o - 2)*(o - 1)*(o + 2)
Let a(g) = g**3 + 12*g**2 - 14*g - 3. Let w be a(-13). Let 5/2*j**5 + 0 + 10*j**2 - w*j**4 + 5*j**3 - 15/2*j = 0. What is j?
-1, 0, 1, 3
Let a(p) = -p**2 + 25*p - 19*p - 13*p - 7. Let h be a(-4). Suppose -1/2 + o**2 + o**3 - 1/2*o - 1/2*o**4 - 1/2*o**h = 0. Calculate o.
-1, 1
Let g(w) be the third derivative of -1/2016*w**8 - 1/18*w**3 - 1/48*w**4 + 1/180*w**6 + 0*w + 0*w**7 + 1/180*w**5 - 14*w**2 + 0. Suppose g(a) = 0. Calculate a.
-1, 1, 2
Let c(k) be the third derivative of -k**6/360 + k**5/15 - 2*k**4/3 - k**3/6 - 17*k**2. Let d(w) be the first derivative of c(w). Find z such that d(z) = 0.
4
Determine j, given that 125/9*j**3 + 4/3*j**4 + 85/9*j - 14/3 + 100/3*j**2 = 0.
-7, -3, -2/3, 1/4
Factor 4135*r + 7*r**2 - 4247*r + 28*r**3 - 4*r**4 + 9*r**2.
-4*r*(r - 7)*(r - 2)*(r + 2)
Determine n, given that 3/8*n**4 + 33/8*n**3 + 0 + 0*n + 15/4*n**2 = 0.
-10, -1, 0
Factor -5*y**3 + 1/2*y**4 + 11/2 + 5*y - 6*y**2.
(y - 11)*(y - 1)*(y + 1)**2/2
Let k(f) be the third derivative of 1/60*f**6 + 0*f + 3/80*f**5 + 9*f**2 + 0 - 1/168*f**7 - 1/6*f**3 - 1/12*f**4. Find h, given that k(h) = 0.
-1, -2/5, 1, 2
Suppose 2639*o = 2536*o + 515. Find h, given that -3/5*h**o + 24/5*h**4 - 48/5*h**3 + 0*h**2 + 0 + 0*h = 0.
0, 4
Find s, given that s - 3/5 - 1/5*s**3 - 1/5*s**2 = 0.
-3, 1
Suppose 10*x + 638 = 668. Let m(r) be the first derivative of 1/3*r**4 + 0*r**x + 0*r**2 + 2/15*r**5 + 8 + 0*r. Factor m(q).
2*q**3*(q + 2)/3
Let c = 16174 - 64693/4. Factor -3/2*o**2 + c*o**4 + 9*o + 27/4 - 3*o**3.
3*(o - 3)**2*(o + 1)**2/4
Find s such that -459*s**3 - 462*s**3 + 2*s**5 - 28*s**2 + 8*s**4 + 923*s**3 - 40*s - 16 = 0.
-2, -1, 2
Let -8341*d**2 + 4167*d**2 - 2*d**3 + 4170*d**2 = 0. Calculate d.
-2, 0
Suppose 5 - 23 = -2*o. Let f(j) = j**3 + 2*j**2 + 3*j - 10. Let s(p) = 3*p**3 + 3*p**2 + 6*p - 21. Let c(n) = o*f(n) - 4*s(n). Solve c(m) = 0 for m.
-1, 1, 2
Let w(x) = x**2 - 19*x - 31. Let z(f) be the third derivative of f**5/30 - 3*f**4/4 - 5*f**3 - 7*f**2. Let r(a) = 6*w(a) - 5*z(a). Suppose r(u) = 0. What is u?
-3
Let t(r) be the second derivative of 2/3*r**3 + 3*r + 4*r**2 + 0 + 1/24*r**4. Suppose t(p) = 0. Calculate p.
-4
Let i(w) be the first derivative of -w**2 - 6*w - 2. Let o be i(-5). Factor 2*r**4 + r**o + 4*r**2 - 6*r**3 - 13*r**2 + 12*r + 12.
3*(r - 2)**2*(r + 1)**2
Let s(p) = p**4 + p**3 + p - 1. Let d(o) = 2*o**5 + 5*o**4 + 3*o**3 + 5*o - 5. Let l(t) = 3*t - 19. Let r be l(8). Let b(j) = r*s(j) - d(j). Factor b(w).
-2*w**3*(w - 1)*(w + 1)
Let p be 3 - 609/84 - 5/(-1). What is c in 0 - c**2 + p*c**3 + 1/4*c = 0?
0, 1/3, 1
Let n(b) be the first derivative of -22*b**2 - 4*b - 73*b**4 - 172/3*b**3 - 224/5*b**5 - 32/3*b**6 + 4. Factor n(x).
-4*(x + 1)**3*(4*x + 1)**2
Let o(x) be the second derivative of x**5/40 + 23*x**4/8 + 529*x**3/4 + 12167*x**2/4 - 149*x. Let o(t) = 0. What is t?
-23
Let v be 20/(-21) + 2/3 + 96/336. Let 1/4*m**2 + 0*m + 1/4*m**3 + v = 0. What is m?
-1, 0
Let w(n) = -n**2 - 4*n + 5. Let s be w(-4). Solve 0*r**2 + s - 9*r + 0 - r + 5*r**2 = 0.
1
Let p(x) be the third derivative of x**6/30 - 32*x**5/15 + 61*x**4/6 - 20*x**3 - 172*x**2. Determine i, given that p(i) = 0.
1, 30
Factor -1/2*x**2 + 4 - x.
-(x - 2)*(x + 4)/2
Let k = -22195 + 110979/5. Let -8/5*p - 4/5*p**2 + k*p**3 + 0 = 0. What is p?
-1, 0, 2
Let d(n) be the third derivative of n**5/210 - 2*n**4/21 + 16*n**3/21 + 7*n**2 + 41*n. Suppose d(m) = 0. Calculate m.
4
Let n = -1151 - -1151. Factor 1/3*y**4 + 4/3*y + 8/3*y**2 + n + 5/3*y**3.
y*(y + 1)*(y + 2)**2/3
Suppose -16*d + 18*d = 0. Let r be (-4 + d + 8)/30. Suppose r*h**3 + 0*h + 0 + 0*h**2 = 0. What is h?
0
Let c = 247 + -244. Let a(l) be the first derivative of 0*l - 2/3*l**c - 5/6*l**4 - 2/9*l**2 - 22/45*l**5 - 4 - 1/9*l**6. Factor a(y).
-2*y*(y + 1)**3*(3*y + 2)/9
Let g(l) be the second derivative of -l**4/6 - 106*l**3/3 - 105*l**2 - 205*l + 1. Let g(c) = 0. What is c?
-105, -1
Let l = -1/1496 + 375/1496. Factor 0*t - 1/4*t**2 - 1/4*t**3 + 1/4*t**5 + 0 + l*t**4.
t**2*(t - 1)*(t + 1)**2/4
Let f(v) be the third derivative of -v**4/6 - 7*v**3/3 + v**2. Let j be f(-6). Determine y so that 7*y + 2*y**3 - j*y**2 + y + 2*y**2 + 0*y**3 = 0.
0, 2
Let i be (-2)/7 - (-3695)/7420. Let r = i + 2/53. Factor 1/4*b**3 - r*b**2 + 1/4 - 1/4*b.
(b - 1)**2*(b + 1)/4
Let p(c) = -42*c**2 + 105*c + 15. Let t(k) = 5*k**2 - 13*k - 2. Let a(o) = 4*p(o) + 33*t(o). Let a(x) = 0. What is x?
-2, -1
Suppose 6*c + 5*z - 20 = c, 0 = 3*c - 2*z - 2. Suppose 3*o - 7 = -1, -2*k + c*o + 4 = 0. Determine r so that 22*r**2 + 4*r**3 + 0*r**2 - k*r**4 - 14*r**2 = 0.
-1, 0, 2
Let p(n) = 4*n**4 - 33*n**3 - 11*n**2 + 208*n + 192. Let x(i) = 2*i**4 - 17*i**3 - 5*i**2 + 104*i + 96. Let g(a) = -3*p(a) + 5*x(a). Solve g(b) = 0.
-2, -1, 4, 6
Determine o, given that -3*o**2 - 72/5 + 186/5*o = 0.
2/5, 12
Let h be 8/12*(-123)/4. Let q = h + 22. Let 0 - 3/2*z**2 - 3/2*z + q*z**3 + 3/2*z**4 = 0. What is z?
-1, 0, 1
Let y(v) be the first derivative of -v**5/45 - v**4/9 - 2*v**3/27 + 2*v**2/9 + v/3 + 201. Let y(i) = 0. Calculate i.
-3, -1, 1
Let q(u) be the first derivative of -5*u**4/4 - 10*u**3/3 + 45*u**2/2 + 90*u + 665. Factor q(t).
-5*(t - 3)*(t + 2)*(t + 3)
Let m = 41 + -39. Factor 81*u - 35*u**3 - 43*u**3 - 5*u**5 + 49*u**m + 27*u**4 - 81 + 5*u**2 + 2*u**5.
-3*(u - 3)**3*(u - 1)*(u + 1)
Let i(x) = -3*x**3 + 70*x**2 - 26*x + 71. Let l be i(23). Let 0 + 2/11*b**l + 2/11*b = 0. Calculate b.
-1, 0
Suppose 5*u + 8 = 7*u. Let j(c) = -c**3 + 3*c**2 + 3*c + 4. Let h be j(u). Let 3*w + h*w**2 + 3*w - 10 - w + 5*w**2 = 0. What is w?
-2, 1
Suppose 74*z**2 - 4 + 85*z**2 + 52 - 135*z**2 - 15*z**3 + 132*z = 0. What is z?
-2, -2/5, 4
Let w = -59/749 + 1103/4494. Factor -w*u**2 + 0 - 1/6*u.
-u*(u + 1)/6
Let z = 1963/11 - 7841/44. Suppose -1 + 5/4*x**2 - z*x**4 - 3/4*x**3 + 3/4*x = 0. What is x?
-4, -1, 1
Let y(t) = 2*t**2 + 36*t - 78. Let h be y(-20). Let m(f) be the first derivative of 3/7*f**4 - 3/7*f - 6/7*f**3 + 1 - 3/35*f**5 + 6/7*f**h. Factor m(g).
-3*(g - 1)**4/7
Suppose -40 + 31 = -3*p. Let 71*h**3 + 7*h**2 - p*h**2 - 67*h**3 + h - 4*h**4 - 5*h = 0. Calculate h.
-1, 0, 1
Let i be ((-5)/3)/((-4)/12). Let x(d) be the first derivative of 7 + 0*d + 1/7*d**4 - 2/35*d**i - 2/7*d**2 + 2/21*d**3. Factor x(b).
-2*b*(b - 2)*(b - 1)*(b + 1)/7
Let c(w) be the first derivative of w**5/45 + 2*w**4/9 - 26*w**3/27 - 28*w**2/3 + 49*w + 688. Determine g so that c(g) = 0.
-7, 3
Let g(k) be the first derivative of k**3 