 second derivative of -k**4/48 + k**3/12 + 3*k**2/8 + 50*k. Find u, given that a(u) = 0.
-1, 3
Let i(h) = h**2 - 2*h. Let z(g) = 2*g**3 + 21*g**2 - 26*g. Let b(c) = -3*i(c) + z(c). Determine s, given that b(s) = 0.
-10, 0, 1
Let g(k) be the second derivative of -k**7/1260 - 7*k**6/1080 + k**5/90 - 3*k**3 + 20*k. Let d(w) be the second derivative of g(w). Factor d(a).
-a*(a + 4)*(2*a - 1)/3
Let g(m) = -19*m**3 - 25*m**2 - 26*m - 13. Let q(n) = -9*n**3 - 12*n**2 - 12*n - 6. Let t(y) = -6*g(y) + 13*q(y). Determine o so that t(o) = 0.
-2, 0
Factor -4*f + 19/3*f**2 - 36 - 1/3*f**3.
-(f - 18)*(f - 3)*(f + 2)/3
Suppose 11 = 5*z + y, -96 = 2*z + 5*y - 82. Determine v so that 2/5*v**5 - 32/5 + 32/5*v + 16/5*v**2 - 16/5*v**z - 2/5*v**4 = 0.
-2, 1, 2
Let z = 24 + -369. Let b be ((-2)/8 - 1)*138/z. Find c such that b + 3/4*c + 1/4*c**2 = 0.
-2, -1
Suppose -w = n - 2, w = -4*n + 5 - 3. Let p(g) = -15*g**2 - 15*g. Let k(o) = 7*o**2 + 7*o. Suppose 2*i + 3*i - 25 = 0. Let j(l) = i*k(l) + w*p(l). Factor j(z).
5*z*(z + 1)
Let z(i) = i - 8. Let h be z(8). Let v be (-6)/(-8)*(4 - h). Factor 3*j - 3*j**3 - 3*j**v + 4*j**2 - j**2 + 0*j.
-3*j*(j - 1)*(2*j + 1)
Let u(y) be the first derivative of 1/2*y**4 + 4/3*y**3 + y**2 + 0*y - 18. Solve u(a) = 0 for a.
-1, 0
Let j(p) be the second derivative of 1/4*p**5 - 5/6*p**3 - 37*p + 5*p**2 - 5/6*p**4 + 0. Factor j(a).
5*(a - 2)*(a - 1)*(a + 1)
Let -16/13*n - 114/13*n**3 + 0 - 10/13*n**5 + 64/13*n**4 + 76/13*n**2 = 0. Calculate n.
0, 2/5, 1, 4
Let r(n) = -n**3 + 13*n**2 - 72*n + 162. Let w be r(5). Find b, given that -2/3*b - 2/9*b**w - 4/9 = 0.
-2, -1
Suppose 2*l + 4*f = 8, -5*l + 27 = 3*f - 0. Suppose 2*t - l + 4 = 2*u, 5*u - 3 = 3*t. Factor -5/7*g**5 - 8/7*g**4 + 0*g - 1/7*g**u + 0 + 2/7*g**2.
-g**2*(g + 1)**2*(5*g - 2)/7
Let n(y) be the second derivative of -y**5/5 - y**4/3 + 26*y. Determine z so that n(z) = 0.
-1, 0
Let a be ((-44)/77)/(20/(-30)). Factor a*x**2 - 3/7*x**4 + 3/7*x - 3/7 + 3/7*x**5 - 6/7*x**3.
3*(x - 1)**3*(x + 1)**2/7
Let f(q) = -3*q**3 + 2*q**2 - 5. Let w be f(4). Let k = w - -499/3. Factor 0 - 4/3*n**4 + 2/3*n + 0*n**3 - 2/3*n**5 + k*n**2.
-2*n*(n - 1)*(n + 1)**3/3
Let s be 246/40*6*(-2)/(-108). Let u = 1/15 + s. Factor 0 - 3/4*f + 3/2*f**2 - 3/2*f**4 + u*f**5 + 0*f**3.
3*f*(f - 1)**3*(f + 1)/4
Suppose 8*f - 36 = -12. Let a(z) be the second derivative of 3*z + 0 - 4*z**2 - 2/3*z**4 - 17/3*z**f. Suppose a(p) = 0. What is p?
-4, -1/4
Let g(d) = 2*d**3 + 11*d**2 - 21*d. Let j be g(-7). Factor -10/9*f**5 + 0 - 22/9*f**4 + j*f - 14/9*f**3 - 2/9*f**2.
-2*f**2*(f + 1)**2*(5*f + 1)/9
Suppose 4*q - 6 - 6 = 0. Suppose 5*v = -2*k + 33, q*k = -k + 2*v + 6. Factor -k*z**2 + 6*z + 5*z**2 + 2*z**2 + 3.
3*(z + 1)**2
Let m(q) = q**3 + 2*q**2 - q. Let o be m(1). Let 6*w + 5*w**3 - 8*w**o - 10 + 19*w - 12*w**2 = 0. What is w?
1, 2
Factor 3/2*v**3 + 18*v**2 + 0 + 0*v.
3*v**2*(v + 12)/2
Let g(n) be the second derivative of 0 - 5/6*n**3 + 5/4*n**4 - 3/4*n**5 + 1/6*n**6 + 0*n**2 + 20*n. Factor g(p).
5*p*(p - 1)**3
Let g = -5/11 + 21/22. Let r(i) be the second derivative of 5*i - g*i**2 - 3/4*i**3 - 7/24*i**4 + 0. Factor r(x).
-(x + 1)*(7*x + 2)/2
Let v be -1*4*(-6 + (-13)/(-2)). Let w(s) = -s**2 - 12*s - 14. Let q(n) = n**2 - 1. Let x(u) = v*q(u) + w(u). Suppose x(t) = 0. What is t?
-2
Let o(j) = -j**2 + 41*j - 284. Let z be o(32). What is y in 0 + 4/3*y**3 - 4/3*y + 2*y**z - 2*y**2 = 0?
-1, -2/3, 0, 1
Let v = 713/12 - 235/4. Let b be (-2)/12 - 2/(-4). Factor -b*i**3 - v*i - i**2 + 0.
-i*(i + 1)*(i + 2)/3
Let k = 12845/9 - 1427. Let 8/9 - k*a**2 - 2/3*a = 0. Calculate a.
-4, 1
Let n(l) be the first derivative of 4*l**3/3 - 108*l**2 + 2916*l - 153. Factor n(o).
4*(o - 27)**2
Let p = 9877/150 + 574/75. Determine b so that -p - 21*b - 3/2*b**2 = 0.
-7
Suppose 2*h = 4 - 0. Factor 11*f**4 + 4*f + 11*f**2 + 5*f**4 + 24*f**3 + f**h + 4*f**2 + 4*f**5.
4*f*(f + 1)**4
Let f(p) = -8*p**3 - 25*p**2 - 15*p + 12. Let r(t) = t**3 - t. Let y(u) = -f(u) - r(u). Determine m, given that y(m) = 0.
-2, 3/7
Suppose -2*k = 9*k - 132. Let o be 1*(-2 - (-33)/k). Factor 3/4*w - o*w**3 - 3/4 + 3/4*w**2.
-3*(w - 1)**2*(w + 1)/4
Let w(c) be the third derivative of c**8/33600 - c**7/6300 + 7*c**4/12 - 25*c**2. Let n(f) be the second derivative of w(f). Let n(h) = 0. What is h?
0, 2
Let l(j) be the third derivative of 3/20*j**5 - 8*j**2 + 7/120*j**6 + 0 + 0*j + 1/12*j**4 + 0*j**3. Suppose l(u) = 0. What is u?
-1, -2/7, 0
Let y = 1021 - 1018. Let l(m) be the first derivative of 0*m - 4/7*m**2 + 4/21*m**y - 1. Factor l(b).
4*b*(b - 2)/7
Let q(g) be the third derivative of g**5/180 - g**4/36 - 4*g**3/9 - 163*g**2. Factor q(x).
(x - 4)*(x + 2)/3
Let q be (1/(-4))/(12/(-144)). Suppose 4*a = 13*o - 15*o + 8, -q*o + 10 = 5*a. Factor -3*d + 3/5 + 12/5*d**a.
3*(d - 1)*(4*d - 1)/5
Let r(u) be the third derivative of u**5/30 + u**4/2 + 3*u**3 - 10*u**2 + 2. Factor r(x).
2*(x + 3)**2
Let b(t) be the first derivative of 5/2*t**2 + 1/3*t**3 + 2*t - 1/2*t**4 - 2. Factor b(h).
-(h - 2)*(h + 1)*(2*h + 1)
Find g, given that 3*g**2 - 2038*g**4 + 2018*g**4 + 4*g**5 - 147*g**2 - 128*g**3 = 0.
-2, 0, 9
Let o = -50359/4 - -12741. Let w = o + -151. Find s, given that 0 - 1/4*s**3 - w*s**2 + 1/2*s**4 + 0*s = 0.
-1/2, 0, 1
Let g(m) be the third derivative of m**5/30 + 7*m**4/12 - 6*m**3 - 312*m**2. Factor g(j).
2*(j - 2)*(j + 9)
Let y(a) be the third derivative of -1/120*a**5 + 0*a**3 + 9*a**2 + 0 - 1/48*a**4 + 0*a. Factor y(p).
-p*(p + 1)/2
Let g(p) be the first derivative of -2*p**3/33 + 2*p**2/11 + 6*p/11 - 47. Factor g(h).
-2*(h - 3)*(h + 1)/11
Let o(n) be the first derivative of n**3/8 - 9*n**2/8 + 27*n/8 - 44. Suppose o(p) = 0. What is p?
3
Solve 105/2*k**2 + 117*k**3 + 21/2*k + 459/4*k**4 + 81/2*k**5 + 3/4 = 0 for k.
-1, -1/3, -1/6
Let -1/9*i - 4/9 + 1/9*i**3 + 4/9*i**2 = 0. What is i?
-4, -1, 1
Let r(w) = w**3 + 28*w**2 - 3*w - 79. Let v be r(-28). Suppose 1/2*d**v + d**2 - d**4 + 0 + 3/2*d - 2*d**3 = 0. Calculate d.
-1, 0, 1, 3
Let c(o) = -10*o**4 + 12*o**3 + 33*o**2 - 17*o. Let p(j) = -9*j**4 + 11*j**3 + 32*j**2 - 16*j. Let k(w) = -4*c(w) + 5*p(w). Suppose k(q) = 0. Calculate q.
-2, 0, 2/5, 3
Let x(p) be the third derivative of -p**7/42 - 13*p**6/8 - 37*p**5/12 + 65*p**4/8 + 95*p**3/3 + 33*p**2. Factor x(y).
-5*(y - 1)*(y + 1)**2*(y + 38)
Let p(q) = -2*q + 8. Let h be p(3). Let -3*b**3 + 7*b**2 + 10 - 9*b - 7 + 2*b**h = 0. What is b?
1
Let l = -94999/46056 - -483/808. Let d = -12/19 - l. Let -2/3*t + 1/6*t**4 - d*t**3 + 4/3*t**2 + 0 = 0. What is t?
0, 1, 2
Let p(q) be the third derivative of -q**8/120 - 82*q**7/525 - 97*q**6/100 - 26*q**5/15 + 5*q**4/3 - 2*q**2 + 3*q. Find x, given that p(x) = 0.
-5, -2, 0, 2/7
Suppose -2*s**4 + 6*s**4 + 29*s**5 - 4*s**2 - 12*s**3 - 25*s**5 + 8*s = 0. Calculate s.
-2, -1, 0, 1
Let u(r) be the first derivative of -3*r**4/28 + 89*r**3/7 - 390*r**2/7 + 516*r/7 - 561. Factor u(t).
-3*(t - 86)*(t - 2)*(t - 1)/7
Let n(k) be the second derivative of -16*k**7/7 - 1652*k**6/5 - 126057*k**5/10 + 128545*k**4/8 - 8086*k**3 + 2028*k**2 + 775*k. Let n(f) = 0. Calculate f.
-52, 1/4
Let a(o) be the second derivative of -o**5/4 + 95*o**4/6 - 800*o**3/3 - 2000*o**2 + o + 8. Let a(u) = 0. Calculate u.
-2, 20
Let m(x) be the third derivative of x**6/280 - 209*x**5/140 + 1378*x**4/7 - 5408*x**3/7 - 36*x**2 + 2. Determine p, given that m(p) = 0.
1, 104
Let w be (-2)/(-120)*387/18. Let y = w + 1/24. Factor a + 4/5*a**2 + y + 1/5*a**3.
(a + 1)**2*(a + 2)/5
Let h(b) be the first derivative of 0*b**3 + 0*b**2 - 4/5*b**5 + 1/2*b**4 + 0*b + 1/3*b**6 + 12. Factor h(u).
2*u**3*(u - 1)**2
Suppose 0 = 3*r - s - 5, r = -s + 2 + 1. Factor 8 + 6 - 19 - 15*g**r + 20 - 5*g**3 + 5*g.
-5*(g - 1)*(g + 1)*(g + 3)
Let l(r) = 8*r**4 + 7*r**3 - 13*r**2 - 5. Let m(y) = 33*y**4 + 30*y**3 - 51*y**2 - 21. Let v(q) = -21*l(q) + 5*m(q). Determine h, given that v(h) = 0.
-2, 0, 3
Factor 1/2*i**5 + 29/2*i**3 + 0 + 9/2*i**4 + 9*i + 39/2*i**2.
i*(i + 1)*(i + 2)*(i + 3)**2/2
Let j(z) be the second derivative of z**6/24 - z**5/4 + 25*z**4/48 - 5*z**3/12 - 113*z. Factor j(k).
5*k*(k - 2)*(k - 1)**2/4
Suppose -9*j - 135 = -162. Let r(p) be the first derivative of 0*p - 3/10*p**5 + 0*p**2 - 8 - 1/6*p**j + 3/8*p**4 + 1/12*p**6. Factor r(w).
w**2*(w - 1)**3/2
Let v(d) = 3*d**5 + 22*d**4 + 12