the second derivative of -19/72*k**4 + 0 - 27/4*k**2 + 11/4*k**3 + 28*k + 1/120*k**5. Factor g(c).
(c - 9)**2*(c - 1)/6
Let v(y) be the second derivative of -y**4/15 - 2*y**3/5 - 67*y + 2. Find t such that v(t) = 0.
-3, 0
Let d(v) be the second derivative of 2*v**7/21 - 4*v**6/15 - 18*v**5/5 - 32*v**4/3 - 46*v**3/3 - 12*v**2 - 135*v. Factor d(t).
4*(t - 6)*(t + 1)**4
Let q(b) be the third derivative of -b**7/13860 + b**6/3960 + b**4/6 + 11*b**2. Let s(h) be the second derivative of q(h). What is t in s(t) = 0?
0, 1
Let t(f) be the third derivative of -1/300*f**6 + 1/25*f**5 + 1/1680*f**8 + 0*f**3 - 13*f**2 - 1/15*f**4 + 0 + 0*f - 1/350*f**7. Let t(r) = 0. Calculate r.
-2, 0, 1, 2
Suppose 0 = 4*k - 2*q - 56, -48 = -k + 5*q - 16. Suppose 5*s - 20 = 2*w, 5*w + 3*s - k = -0*s. Solve 1/5*p**3 + w*p**2 - 1/5*p + 0 = 0 for p.
-1, 0, 1
Let h(l) = -l**3 + 16*l**2 - 17*l + 18. Let k be h(15). Let s be (k/(-4))/6*-4*-1. Solve -12/7 - 12/7*x - 3/7*x**s = 0.
-2
Let i = 839/483 + -41/69. Let 10/7*h**2 - i*h**3 + 0*h + 0 - 2/7*h**4 = 0. Calculate h.
-5, 0, 1
Let a = 8320/11 + -16541/22. Factor -a*l**2 - 243/2 + 1/6*l**3 + 81/2*l.
(l - 9)**3/6
Factor 8 + 46*r + r**3 - 29*r + 25*r**2 - 15*r**2.
(r + 1)**2*(r + 8)
Suppose 0 = -5*q + 5*q - 4*q. Suppose 0*a - 6*a = q. Factor -1/5*t**2 + 1/5*t + a.
-t*(t - 1)/5
Let b(j) = -62*j - 51. Let w be b(-23). Let -1375*x - 5*x**2 - 5*x**3 + 5*x**5 + 5*x**4 + w*x = 0. What is x?
-1, 0, 1
Solve -9 - 198/7*x**2 - 72/7*x**3 - 3/7*x**4 - 192/7*x = 0 for x.
-21, -1
Let l be (0 - 1)*-514*(-1)/6. Let j = -85 - l. Factor 0 - 2/3*v**4 - j*v + 2/3*v**2 + 2/3*v**3.
-2*v*(v - 1)**2*(v + 1)/3
Let q(b) be the third derivative of -17*b**2 + 4/15*b**6 + 32/105*b**7 + 0*b - 4/3*b**4 + 0 - 2/3*b**3 - b**5. Determine d so that q(d) = 0.
-1, -1/4, 1
Suppose 21*a + 198 = 219. Factor a - 1/3*b**3 - b**2 + 1/3*b.
-(b - 1)*(b + 1)*(b + 3)/3
Let p = -132 + 129. Let l be 0 - p - (16 + -13). Suppose 4/7*h**3 - 6/7*h**5 + 2/7*h**4 + 0 + l*h**2 + 0*h = 0. What is h?
-2/3, 0, 1
Let c(u) be the first derivative of -1/3*u**3 - 4 - 1/2*u**4 + 0*u**2 + u. Let x(y) be the first derivative of c(y). Factor x(q).
-2*q*(3*q + 1)
Let l be -5 + 4 + 64/40. Factor -6/5*o**2 + 3/5*o + l*o**3 + 0.
3*o*(o - 1)**2/5
Let h(k) = 11*k**4 - k**3 + 8*k**2 - 10. Let u(o) = 16*o**4 - 3*o**3 + 12*o**2 - 14. Let f(j) = 7*h(j) - 5*u(j). Suppose f(m) = 0. Calculate m.
0, 2/3, 2
Let k(q) be the third derivative of 0 - 8*q**2 + 1/120*q**6 + 1/40*q**5 - 1/4*q**4 + 0*q - 5/3*q**3. Let w(z) be the first derivative of k(z). Factor w(m).
3*(m - 1)*(m + 2)
Let z = -497/2 - -249. Let r**2 - 1/2*r - z*r**3 + 0 = 0. Calculate r.
0, 1
Let f be 30*((-3)/(-3))/6. Let r(k) be the second derivative of 0*k**2 - 2/15*k**6 + 0*k**3 + 0*k**4 + 0 - 2/5*k**f + 8*k. Factor r(y).
-4*y**3*(y + 2)
Let a(c) = -c + 13. Let v be a(11). Suppose 7*z + 328 = 3*u + v*z, 332 = 3*u - z. Factor 3*i**3 + 108*i + 12*i**2 - 12*i**4 + 0*i**3 - u*i.
-3*i*(i - 1)*(i + 1)*(4*i - 1)
Let y(t) be the third derivative of 0 + 1/150*t**6 + 0*t**3 + 0*t - 1/15*t**4 - 1/75*t**5 - 6*t**2. Factor y(n).
4*n*(n - 2)*(n + 1)/5
Let m(f) = 14*f**3 + 9*f**2 + 10*f + 15. Let v(t) = 5*t**3 + 3*t**2 + 3*t + 5. Let o = 45 - 39. Let g(s) = o*m(s) - 17*v(s). Factor g(k).
-(k - 5)*(k + 1)**2
Let q = -16306 + 114148/7. Factor q*p - 2/7 - 4/7*p**2.
-2*(p - 1)*(2*p - 1)/7
Suppose -4*i + 0 = 12. Let g be ((3 - i)/(-3))/(6/(-4)). Factor 0 + q**3 + g*q + 8/3*q**2.
q*(q + 2)*(3*q + 2)/3
Factor -4/7*u**2 + 10/7 - u + 1/7*u**3.
(u - 5)*(u - 1)*(u + 2)/7
Let o(l) be the third derivative of 0*l**6 - 4/735*l**7 + 0 + 2/105*l**5 + 0*l**3 - 1/42*l**4 + 50*l**2 + 1/588*l**8 + 0*l. Factor o(j).
4*j*(j - 1)**3*(j + 1)/7
Let s(m) be the first derivative of -3/13*m**4 - 38 - 200/13*m - 2/65*m**5 + 60/13*m**2 + 22/39*m**3. Factor s(i).
-2*(i - 2)**2*(i + 5)**2/13
Suppose 14*i - 11*i = 9. Let c(k) = 2*k**2 - 6*k + 1. Let l be c(4). Factor 9*a - l*a - i + 3*a**2.
3*(a - 1)*(a + 1)
Let b = 46 + -137/3. Let h(x) be the second derivative of -1/10*x**5 + 0*x**2 + 0 + 0*x**3 + b*x**4 - 7*x. Let h(o) = 0. Calculate o.
0, 2
Let a(j) = -3*j**2 - j + 2. Let y(r) = r**3 + r + 2. Let g(v) = 3*a(v) + 3*y(v). Factor g(q).
3*(q - 2)**2*(q + 1)
Let q be 88/(-880)*5/(-4). Let c(x) be the first derivative of 0*x**3 - q*x**2 + 1/8*x**4 + 7 + 0*x**5 + 0*x - 1/24*x**6. Solve c(j) = 0 for j.
-1, 0, 1
What is y in -8*y + 0 + 1/3*y**4 - 2/3*y**2 + 5/3*y**3 = 0?
-4, -3, 0, 2
Let s(o) be the second derivative of -o**5/5 + 2*o**4 + 38*o**3/3 - 48*o**2 + 121*o + 5. Factor s(c).
-4*(c - 8)*(c - 1)*(c + 3)
Solve 2*a**3 + 2*a**3 + 1514*a**2 - 8*a**3 - 1486*a**2 = 0 for a.
0, 7
Let r be -1 + -2 + 6 - (17 - 14). What is y in 0*y**2 - 3/2*y**3 + r + 0*y = 0?
0
Let s(k) be the third derivative of -k**7/1785 + 13*k**6/510 - 5*k**5/102 + 400*k**2. What is b in s(b) = 0?
0, 1, 25
Let u(q) be the third derivative of q**7/1050 + q**6/15 + 2*q**5 + 100*q**4/3 + 1000*q**3/3 + 14*q**2 - 4*q. Factor u(l).
(l + 10)**4/5
Suppose -7*a = 30*j - 29*j - 7, 2*a - 2 = 3*j. Suppose 1/7*y**2 + 0 - 1/7*y**3 + j*y = 0. What is y?
0, 1
Let u(p) = -5*p**4 + 18*p**3 - 28*p**2 + 22*p - 5. Let i(o) = 10*o**4 - 35*o**3 + 55*o**2 - 45*o + 10. Let v(y) = 2*i(y) + 5*u(y). Let v(b) = 0. Calculate b.
1
Suppose z - 5 + 3 = 0. Factor 21*n - 5*n + 0*n**2 + 4*n**z + 0*n + 16.
4*(n + 2)**2
Factor -32/3 - 20/3*n**3 - 22*n**2 - 80/3*n - 2/3*n**4.
-2*(n + 1)**2*(n + 4)**2/3
Let z(r) be the second derivative of 0 + 5/32*r**4 + 1/60*r**6 + 1/16*r**2 + 13/160*r**5 + 7/48*r**3 + 3*r. What is i in z(i) = 0?
-1, -1/4
Suppose -25 = 5*a - 5*p, 3*a - 25 = -0*a - 5*p. Let k(o) be the first derivative of a*o + 8 + 2*o**2 - 4/3*o**3. Solve k(i) = 0 for i.
0, 1
Let w(y) be the first derivative of 3*y**5/20 - 15*y**4/16 + 9*y**3/4 - 21*y**2/8 + 3*y/2 + 1. Factor w(p).
3*(p - 2)*(p - 1)**3/4
Suppose 0 = 69*t - 67*t - 10. Let q(x) = -x**2 + 7*x - 10. Let v be q(t). Find a, given that -1/5*a**2 + v + 1/5*a = 0.
0, 1
Let z(q) = 3*q + 3. Let p be z(-2). Let b be 1 - (p - -1)/2. Factor -5*w - w**2 - b + 2*w**2 + 2*w**3 + 5 - w**3.
(w - 1)**2*(w + 3)
Suppose -3*h = -2*h - 26. Let i = 28 - h. Find k such that 0 + 7/5*k**3 + 3/5*k**5 - i*k**4 + 4/5*k**2 - 4/5*k = 0.
-2/3, 0, 1, 2
Factor -121*f**2 + 26*f + 5 + 123*f**2 + 55.
2*(f + 3)*(f + 10)
Solve -3*f**3 - 35*f**2 + f**2 + 11*f**2 - 57 - 79*f + 0*f**3 + 2*f**3 = 0 for f.
-19, -3, -1
Factor 35040*t**2 + 15*t**4 + 99*t - 90*t**3 + 381*t - 35200*t**2 + 5*t**5.
5*t*(t - 3)*(t - 2)*(t + 4)**2
Suppose -v - 72 = -2*p, -7*v + 3*v - 103 = -3*p. Let g = p - 37. Solve -2/3*c - 1/3*c**2 + g = 0.
-2, 0
Let u(o) = -2*o**2 + 16*o - 9. Let j be u(6). Let z be (-20)/j*9/(-6). What is a in -32/5*a**3 - 44/5*a**4 - 12/5*a**5 + 0 + 0*a + 16/5*a**z = 0?
-2, 0, 1/3
Let o(v) = -17*v**3 - 7*v**2 + 39*v - 28. Let d(a) = -4*a**3 - 2*a**2 + 10*a - 7. Let j(u) = -26*d(u) + 6*o(u). Determine p so that j(p) = 0.
-7, 1
Let h(k) be the first derivative of k**4/38 + 10*k**3/57 + 4*k**2/19 + 21. Factor h(a).
2*a*(a + 1)*(a + 4)/19
Let q = -488090/13 + 37546. Factor 2/13*y**3 - q*y**2 + 0 - 10/13*y.
2*y*(y - 5)*(y + 1)/13
Let k be (-34)/(-6) - -3*11/99. Let o(m) be the third derivative of -49/30*m**k + 0*m + 0 + 4/3*m**3 - 49/60*m**7 + 21/5*m**5 - 10/3*m**4 - 2*m**2. Factor o(g).
-(g + 2)*(7*g - 2)**3/2
Let c be (15/(-21))/(95/(-76)). Factor 10/7 - c*d**2 - 18/7*d.
-2*(d + 5)*(2*d - 1)/7
Solve -9/7*u + 0*u**2 + 1/7*u**3 + 0 = 0 for u.
-3, 0, 3
Suppose 4*l + 1 = -n, -130*n + 126*n = 5*l + 4. Factor -3/4*v**2 + 3/4 + l*v.
-3*(v - 1)*(v + 1)/4
Let 34*j - 45 - 3*j**2 - 117 + 2*j + 54 = 0. Calculate j.
6
Let b(c) be the second derivative of -c**4/6 + 4*c**2 + 3*c + 13. Let b(x) = 0. What is x?
-2, 2
What is m in 18 - 3*m + 1/8*m**2 = 0?
12
Let b(w) be the third derivative of -w**5/420 + 145*w**4/42 - 42050*w**3/21 - 901*w**2. Factor b(a).
-(a - 290)**2/7
Suppose 0*m + 6*m - 24 = 0. Suppose -5*l + 20 = -0*l - 4*i, -m*l = i + 5. Find u such that l*u - 12/5*u**2 + 3/5*u**5 + 0*u**3 + 0 + 9/5*u**4 = 0.
-2, 0, 1
Let v(f) = 2*f**2 + 14*f - 10. Let x(k) = 8*k**2 + 56*k - 37. Let r(n) = -18*v(n) + 4*x(n). Suppose r(l) = 0. What is l?
-8, 1
Let u be (-8)/(((-2)/4)/((-43)/(-344))). Factor 1/7*q**u - 4/7*q + 3/7.
(q - 3)*(q - 1)/7
Let i(n) be the first de