 second derivative of -d**5/190 + d**4/19 + d**3/57 - 6*d**2/19 + 48*d - 2. Determine j so that q(j) = 0.
-1, 1, 6
Let r be (0 - 0)/((-50)/25). Suppose -5*i + 2*m - 4 = r, -2*m + 7*m - 10 = -2*i. Determine w so that i + 0*w + 1/3*w**5 - 1/3*w**3 - 1/3*w**2 + 1/3*w**4 = 0.
-1, 0, 1
Let i(d) be the first derivative of -d + 1/35*d**6 - 1/14*d**4 + 1/70*d**5 - 1/21*d**3 - 7 + 0*d**2. Let s(u) be the first derivative of i(u). Solve s(f) = 0.
-1, -1/3, 0, 1
Let n = 2/1597 + 4783/6388. Factor -6*r - 12 - n*r**2.
-3*(r + 4)**2/4
Let b(g) be the third derivative of -g**5/60 - 109*g**4/12 - 11881*g**3/6 - 90*g**2. Find p such that b(p) = 0.
-109
Let o(v) = -2*v**2 - 20*v + 54. Let w(p) = -p**2 + 1. Let r(d) = o(d) - 4*w(d). Factor r(z).
2*(z - 5)**2
Let w = 117 + -117. Factor 46*z**5 + w*z - 2*z**4 + 0*z - 4*z**3 - 40*z**5.
2*z**3*(z - 1)*(3*z + 2)
Let x(r) be the first derivative of 4 - 1/24*r**4 + 1/2*r**3 - 9/4*r**2 - 4*r. Let o(j) be the first derivative of x(j). Factor o(f).
-(f - 3)**2/2
Let l(r) be the first derivative of 0*r**2 + 0*r + 1 + 1/3*r**3 + 1/4*r**4. Suppose l(y) = 0. What is y?
-1, 0
Factor -27/2*y + 3 + 21/2*y**2.
3*(y - 1)*(7*y - 2)/2
Let f = 7 + -5. Factor -y**2 + y + y - y**f.
-2*y*(y - 1)
Let p be 88/(-792)*(-16 + 1). Let x(g) be the second derivative of p*g**4 + 32/15*g**3 + 2/105*g**7 + 19/25*g**5 + 5*g + 14/75*g**6 + 0 + 8/5*g**2. Factor x(m).
4*(m + 1)**3*(m + 2)**2/5
Let w(v) be the third derivative of 16*v**2 + 1/40*v**6 - 1/30*v**5 - 1/210*v**7 + 0*v**4 + 0*v**3 + 0 + 0*v. Factor w(k).
-k**2*(k - 2)*(k - 1)
Let o(w) = w**2 - 1. Let j(m) = 6*m**2 + 4*m - 2. Suppose 19 + 86 = 3*q. Let f(t) = q*o(t) - 5*j(t). Determine x so that f(x) = 0.
-1, 5
Let b(i) = -4*i**2 + 15 - 5*i**2 + 3*i**3 - 6*i**3 + 4*i**3 - 11*i. Let q be b(10). Factor -4 - 3*y - 2 + q*y**2 + 2*y**2 - y**2 + 3*y**3.
3*(y - 1)*(y + 1)*(y + 2)
Let v(b) = 4*b**2 - 10*b. Let k(c) = c**2 - c. Let n be 6/2 - (0 - -4). Let f(w) = n*v(w) + 6*k(w). Determine d, given that f(d) = 0.
-2, 0
Let i(q) be the second derivative of -q**4/4 + 7*q**3 + 45*q**2/2 - q + 2. Let i(b) = 0. What is b?
-1, 15
Let j(s) = 3*s**4 + 26*s**3 + 28*s**2 - 19*s - 41. Let h(b) = b**4 + 9*b**3 + 10*b**2 - 6*b - 14. Let o(m) = -17*h(m) + 6*j(m). Suppose o(x) = 0. Calculate x.
-2, -1, 2
Let p be 37 + -55 + (-960)/(-52). Factor -44/13 + 62/13*q + p*q**2.
2*(q + 11)*(3*q - 2)/13
Let f(k) be the third derivative of k**9/20160 + k**8/3360 + k**7/1680 - 11*k**5/30 + k**2. Let x(h) be the third derivative of f(h). Factor x(z).
3*z*(z + 1)**2
Let y(q) be the first derivative of 3*q**4/4 + 28*q**3 - 177*q**2/2 + 90*q + 142. Let y(r) = 0. Calculate r.
-30, 1
Let b(a) be the third derivative of 0*a - 6*a**2 + 0*a**3 - 1/180*a**5 + 1/360*a**6 + 0 + 0*a**4. Factor b(q).
q**2*(q - 1)/3
Let u be (-5 - (-222)/30) + (-2)/5. Determine p so that -2*p**3 + 7*p**3 + p**2 - 7*p**3 + 4*p - 3*p**u = 0.
-2, 0, 1
Let f(c) = 2*c**2 - 7*c - 2. Let o be f(4). Find r such that 6*r**4 - 3*r**2 + 3*r**3 - 2*r**5 - o*r**5 + r**5 - 3*r**2 = 0.
-1, 0, 1, 2
Let y = -3 - -7. Suppose y*q = -0*q + 12. Determine i so that -i**3 + 4*i**3 - i**q - 2*i = 0.
-1, 0, 1
Let p(q) be the first derivative of q**6/20 - 21*q**5/40 + 3*q**4/4 - 33*q + 6. Let k(t) be the first derivative of p(t). Factor k(u).
3*u**2*(u - 6)*(u - 1)/2
Let m(f) be the third derivative of 1/6*f**4 + 0 + 1/3*f**3 + 0*f + 7*f**2. Let h(b) = b**2 + 9*b + 5. Let n(i) = 2*h(i) - 5*m(i). Factor n(v).
2*v*(v - 1)
Let t(h) be the second derivative of -h**5/10 - 7*h**4/3 - 20*h**3 - 72*h**2 + 68*h. What is v in t(v) = 0?
-6, -2
Let v(b) be the first derivative of 3/20*b**4 - b**3 + 0*b**2 - 7 + 0*b. Determine h so that v(h) = 0.
0, 5
Let p(t) be the first derivative of -t**6/8 - 9*t**5/20 + t**3 + 38. Let p(i) = 0. What is i?
-2, 0, 1
Let i(u) = 9*u**2 + 51. Let m(h) = -h**2 - h - 8. Let j(d) = i(d) + 6*m(d). Factor j(p).
3*(p - 1)**2
Let s be 3/12 - (737/(-44) + 14). Let g(n) be the first derivative of -3/5*n**5 + s*n**3 - 3/4*n**4 + 3/2*n**2 - 8 - 6*n. Suppose g(z) = 0. What is z?
-2, -1, 1
Let j(x) = -8*x**3 + 204*x**2 + 3*x + 3. Let r(i) = -2*i**3 + 2*i**2 + i + 1. Let u(k) = j(k) - 3*r(k). Factor u(t).
-2*t**2*(t - 99)
Let y(z) be the second derivative of -1/3*z**3 - 11/36*z**4 - 1/504*z**7 + 0 - 1/8*z**5 - 1/40*z**6 + 0*z**2 - 25*z. Solve y(g) = 0.
-3, -2, 0
Let w(z) be the second derivative of -z**5/4 + 35*z**4/12 - 10*z**3 - 3*z + 18. Let w(x) = 0. Calculate x.
0, 3, 4
Let n(s) be the second derivative of -s**6/135 - 13*s**5/45 + s**4/2 + 14*s + 21. Find d such that n(d) = 0.
-27, 0, 1
Let u(k) = 4*k**3 + 36*k**2 + 21*k + 10. Let i be u(-9). Let r = 183 + i. Solve -4/9*y**2 + 2/9 + 2/9*y**r + 0*y + 0*y**3 = 0.
-1, 1
Factor 4/5 - 2/5*w**2 + 2/5*w.
-2*(w - 2)*(w + 1)/5
Let b(z) = 4*z + 13*z - 2*z**2 - z**3 - 6*z + 11*z**2 - 10. Let d be b(10). Find t such that d + 3/5*t**2 - 3/5*t**3 + 0*t = 0.
0, 1
Suppose -2*u = -3*h + 2*u + 153, -4*u + 12 = 0. Let i = -55 + h. Factor 0*v + 1/5*v**2 + i.
v**2/5
Let z(d) be the first derivative of d**4/12 + 17*d**3/9 + 21*d**2/2 - 27*d + 144. Factor z(j).
(j - 1)*(j + 9)**2/3
Let g be ((-5)/2)/((-6)/12). Suppose -g*p = -q - 22, -2*p + 1 = -0*p - 3*q. Suppose 4*i**p - 31 - 4*i**4 + i + 31 - 9*i - 12*i**3 + 20*i**2 = 0. What is i?
-2, 0, 1
Let t(y) be the third derivative of -y**8/1512 + y**7/189 - 6*y**2. What is q in t(q) = 0?
0, 5
Suppose -290 = 9*l - 67*l. Let o(t) be the first derivative of 5/4*t**2 + 4 - 5/4*t**4 + 5/12*t**6 + t**l + 5*t - 10/3*t**3. Find f such that o(f) = 0.
-2, -1, 1
Suppose -3*i + 3 = -v - 2*v, 2*v + 2*i - 10 = 0. Suppose g**3 - 1 + 3*g - 5*g + g**v + g + 0*g**3 = 0. Calculate g.
-1, 1
Factor -1/4*q**2 - 1/4 + 1/2*q.
-(q - 1)**2/4
Let i be 9*(-2)/12*-8. Let x = i - 8. Solve -d**3 + 8*d**2 + 10*d - 2*d**3 + 0*d + 5*d**3 + x = 0.
-2, -1
Let q(f) be the second derivative of f**7/42 - 11*f**6/150 - f**5/50 + 2*f**4/15 - 2*f + 542. Suppose q(p) = 0. What is p?
-4/5, 0, 1, 2
Let w = 20 + -15. Factor 2027*u**2 - 15*u**3 - 2022*u**2 + w*u**4 + 3 + 15*u - 13.
5*(u - 2)*(u - 1)**2*(u + 1)
Let u(m) be the first derivative of 0*m + 0*m**4 - 13 + 1/10*m**5 - 1/6*m**3 + 0*m**2. Find i, given that u(i) = 0.
-1, 0, 1
Let u = -751/60 + 63/5. Let z(h) be the first derivative of 2/15*h**5 + 0*h - u*h**4 - 4 - 1/18*h**6 + 0*h**2 + 0*h**3. Factor z(f).
-f**3*(f - 1)**2/3
Let t(l) = -3*l**4 + 12*l**3 - 111*l**2 - 108*l + 1194. Let c(m) = 2*m**4 - 11*m**3 + 112*m**2 + 110*m - 1195. Let a(n) = -6*c(n) - 5*t(n). Factor a(k).
3*(k - 4)**2*(k + 5)**2
Let l = 24/23 + -128/299. What is z in 38/13*z**3 + 46/13*z**4 - 60/13*z**5 + 0 - 16/13*z**2 - l*z = 0?
-1/2, -2/5, 0, 2/3, 1
Let m(v) be the second derivative of -363*v**5/20 - 11*v**4/2 - v**3/2 + 267*v. Factor m(n).
-3*n*(11*n + 1)**2
Let k be (13 - (-288)/(-21)) + (-1 - -2). Solve 2/7*x**2 - k + 1/7*x**3 - 1/7*x = 0 for x.
-2, -1, 1
Let n(q) be the second derivative of -3*q**4/4 - 59*q**3/2 + 30*q**2 - 8*q - 14. Factor n(m).
-3*(m + 20)*(3*m - 1)
Let l(n) be the third derivative of -7*n**6/180 - 17*n**5/90 - 13*n**4/36 - n**3/3 + 905*n**2. Determine a so that l(a) = 0.
-1, -3/7
Suppose 5*i = -3*i + 72. Determine r, given that 23 - 5*r + 11*r - 5*r**2 - 3 + i*r = 0.
-1, 4
Let c(u) be the second derivative of 7*u**6/360 - 23*u**5/180 + 5*u**4/18 - 2*u**3/9 + 5*u**2/2 - 9*u. Let j(f) be the first derivative of c(f). Factor j(h).
(h - 2)*(h - 1)*(7*h - 2)/3
Let d(g) be the third derivative of 160/9*g**3 + 1/36*g**5 - 10/9*g**4 + 0*g + 39*g**2 + 0. Factor d(t).
5*(t - 8)**2/3
Let z(h) be the first derivative of -9*h**4/32 + 43*h**3/8 - 483*h**2/16 + 147*h/8 + 27. Factor z(p).
-3*(p - 7)**2*(3*p - 1)/8
Let f be 5152/6720 - (3/(-18) + 4/15). Let -l**2 + 5/3*l - f + 1/3*l**4 - 1/3*l**3 = 0. What is l?
-2, 1
Let d = -73/170 - -35/34. Find k, given that -1/5*k**2 + d*k - 2/5 = 0.
1, 2
Let p(l) be the first derivative of -2*l**3/3 + 254*l**2 + 822. Factor p(d).
-2*d*(d - 254)
Let c = -360568/7 + 51510. Solve -c*o**2 + 4 - 10/7*o = 0.
-7, 2
Let p(t) = 16*t**4 + 11*t**3 + 67*t**2 + 95*t + 62. Let c(m) = -7*m**4 - 6*m**3 - 33*m**2 - 47*m - 30. Let a(y) = -7*c(y) - 3*p(y). Factor a(d).
(d + 2)**3*(d + 3)
Let d(q) be the first derivative of -q**7/105 - q**6/60 + q**5/30 + q**4/12 + 3*q**2 - 11. Let o(