he first derivative of -5*t**6/6 + t**5 + 5*t**4/2 - 10*t**3/3 - 5*t**2/2 + 5*t - 12. Find h, given that d(h) = 0.
-1, 1
Let n(z) be the second derivative of 0 + 6*z + 1/3*z**2 + 1/18*z**3 - 1/36*z**4. Factor n(t).
-(t - 2)*(t + 1)/3
Let j = 4 - 0. Suppose -5*l + j*l = 0. Determine k so that -14/3*k**3 + l*k**2 + 4*k**4 + 2/3*k + 0 = 0.
-1/3, 0, 1/2, 1
Let r(f) = -4*f**2 - 12*f - 20. Let q(v) = v**2 + 1. Let i(s) = 2*q(s) + r(s). Factor i(w).
-2*(w + 3)**2
Factor -5*m - 5 - 5/4*m**2.
-5*(m + 2)**2/4
Let o(l) be the first derivative of l**9/19656 + l**8/3640 + l**7/1820 + l**6/2340 + l**3 - 5. Let q(b) be the third derivative of o(b). Factor q(n).
2*n**2*(n + 1)**3/13
Factor 4/11*i + 2/11*i**2 + 2/11.
2*(i + 1)**2/11
Let c be 106/120 + (-8)/32. Let s = -3/10 + c. Factor 1/3*a - 2/3*a**3 + s*a**4 - 2/3*a**2 + 1/3 + 1/3*a**5.
(a - 1)**2*(a + 1)**3/3
Let l(b) be the third derivative of 13/60*b**6 - 2/5*b**5 + 0 + 1/3*b**4 + 0*b + b**2 + 1/168*b**8 - 2/35*b**7 + 0*b**3. Factor l(j).
2*j*(j - 2)**2*(j - 1)**2
Let m = -55 + 58. Let j(y) be the second derivative of 0 + 1/27*y**m + 1/45*y**5 + 1/18*y**4 + 0*y**2 - y. Factor j(q).
2*q*(q + 1)*(2*q + 1)/9
Let w be 3/(-4) + 76/16. Let 4*g**w - 4*g**4 - g**4 - g**3 + 0*g**3 = 0. What is g?
-1, 0
Suppose -48 = -37*f + 21*f. Factor 10/7*x**2 + 16/7*x + 2/7*x**f + 8/7.
2*(x + 1)*(x + 2)**2/7
Suppose 8 = 13*w - 9*w. Factor -2/5*f - 4/5*f**w - 2/5*f**5 + 2/5 + 2/5*f**4 + 4/5*f**3.
-2*(f - 1)**3*(f + 1)**2/5
Let s(f) be the third derivative of -f**5/300 + 2*f**3/15 - 18*f**2. Suppose s(n) = 0. Calculate n.
-2, 2
Let z(x) be the second derivative of -4*x**6/15 - 9*x**5/10 - x**4 - x**3/3 + 18*x. What is i in z(i) = 0?
-1, -1/4, 0
Factor -4/3*o**2 + 2/3*o**3 + 2/3*o + 0.
2*o*(o - 1)**2/3
Factor 0 - 2/11*v**3 + 2/11*v**2 + 0*v.
-2*v**2*(v - 1)/11
Let a(g) = -2*g**4 - 2*g**3 + 4*g**2 + 3*g + 1. Let l(v) = v**4 + v**2 + v + 1. Let w(b) = -5*a(b) + 5*l(b). Factor w(h).
5*h*(h - 1)*(h + 1)*(3*h + 2)
Let r(a) be the second derivative of a**7/42 - a**6/15 + a**5/20 + 14*a. What is t in r(t) = 0?
0, 1
Let y(c) be the third derivative of 0*c**5 + 0*c**4 + 1/336*c**8 + 0*c + 0*c**6 + 0 + 1/210*c**7 + 0*c**3 + 2*c**2. Factor y(q).
q**4*(q + 1)
Let i(m) be the first derivative of 2 + 0*m**2 - 1/3*m + 1/9*m**3. Factor i(q).
(q - 1)*(q + 1)/3
Let t(w) = 13*w**3 + 18*w**2 + 5*w - 11. Let h(r) = 6*r**3 + 9*r**2 + 3*r - 6. Let l(s) = 11*h(s) - 6*t(s). Factor l(f).
-3*f*(f + 1)*(4*f - 1)
Suppose -6/7*d**2 - 2/7 - 8/7*d = 0. Calculate d.
-1, -1/3
Let a(o) be the first derivative of 1 + 0*o**2 + 1/24*o**4 - 1/24*o**3 + o - 1/80*o**5. Let d(m) be the first derivative of a(m). Determine b so that d(b) = 0.
0, 1
Let t(h) be the second derivative of -h**6/45 + h**4/9 - h**2/3 + 3*h - 22. Factor t(i).
-2*(i - 1)**2*(i + 1)**2/3
Let v = -3/925 + 931/1850. Let d be (-2)/(-2)*(-2 + 4). Factor v*p + 1/4 - 3/4*p**d.
-(p - 1)*(3*p + 1)/4
Let c(k) = -k**3 + 3*k**2 - 2. Suppose -5*l = -4*v - 6, 0 = 2*l + 4*v + 1 - 9. Let s be c(l). Factor 0*m**s + 1/3*m + 0 - 1/3*m**3.
-m*(m - 1)*(m + 1)/3
Let y(p) = -p**2 - p + 1. Let r(x) = 2*x**2 - 4. Let j(c) = -r(c) - 4*y(c). Find n such that j(n) = 0.
-2, 0
Let s(v) be the second derivative of v**5/2 - v**4/3 + 13*v. Factor s(d).
2*d**2*(5*d - 2)
Suppose 24/5 - 36/5*b**2 + 12/5*b**4 + 28/5*b**3 - 28/5*b = 0. What is b?
-3, -1, 2/3, 1
Let o(s) = -s**2 + s + 1. Let u = 16 + -10. Let w(r) = 3*r**4 + 5*r**3 - 5*r**2 + 5*r + 6. Let d(a) = u*o(a) - w(a). Factor d(l).
-l*(l + 1)**2*(3*l - 1)
Suppose 12 = 5*h - h. Let z = -3 + h. Factor z*p - 2/3*p**3 + 1/3*p**4 + 1/3*p**2 + 0.
p**2*(p - 1)**2/3
Let y(n) be the third derivative of n**7/70 + n**6/20 + n**5/20 + 8*n**2. Factor y(q).
3*q**2*(q + 1)**2
Let p(n) = 38*n**3 + 46*n**2 + 18*n - 2. Let h(m) = 39*m**3 + 45*m**2 + 19*m - 3. Let f(x) = 2*h(x) - 3*p(x). Let f(s) = 0. What is s?
-2/3, 0
Suppose -5/3*j**5 + 0 - 5/3*j**3 + 10/3*j - 5*j**2 + 5*j**4 = 0. Calculate j.
-1, 0, 1, 2
Suppose -l = 4*w - 4, -3*l + 4*w = 2*w + 2. Let k = -103 + 207/2. Let 0 + l*h + 0*h**2 + k*h**5 + h**4 + 1/2*h**3 = 0. What is h?
-1, 0
Suppose 11 = -4*z + 2*s + 5, -5*z + 3*s = 9. Factor -2/5*q**5 - 2/5*q**2 + 0*q + z + 2/5*q**3 + 2/5*q**4.
-2*q**2*(q - 1)**2*(q + 1)/5
Let i(s) be the first derivative of s**4 + 8*s**3/3 - 2*s**2 - 8*s - 14. Factor i(u).
4*(u - 1)*(u + 1)*(u + 2)
Suppose 0 = -4*l - 156 + 156. Let h(u) be the third derivative of -1/330*u**5 + 1/132*u**4 + l*u**3 + 0 - 3*u**2 + 0*u. Factor h(q).
-2*q*(q - 1)/11
Factor -80*t**3 + 10 - 81*t**3 + 15*t + 156*t**3.
-5*(t - 2)*(t + 1)**2
Factor 0 + 1/9*f**2 + 2/9*f.
f*(f + 2)/9
Factor 229*l**2 - 2*l - 229*l**2 + 2*l**3.
2*l*(l - 1)*(l + 1)
Let w(b) = -b**3 + 11*b**2 + 12*b + 9. Let j be w(12). What is l in 2 - 3*l**2 + j*l - 14 + 2*l + l = 0?
2
Let a be (4/90)/((-48)/(-240)). Find r such that -a*r**2 + 0 + 0*r - 4/9*r**3 - 2/9*r**4 = 0.
-1, 0
Determine f, given that -2/5*f**2 - 2/5 - 4/5*f = 0.
-1
Let y(w) be the second derivative of 1/6*w**3 + 0 + 0*w**4 - 1/4*w**2 + 1/60*w**6 - 1/20*w**5 - 2*w. Let y(q) = 0. Calculate q.
-1, 1
Factor 6*x**3 + 3*x**4 - 4*x**3 - x**4.
2*x**3*(x + 1)
Suppose -3*j - j + 24 = 4*i, -2*i = 5*j - 24. Let q(u) be the third derivative of 1/150*u**5 + 0*u**3 - 1/60*u**j - 2*u**2 + 0 + 0*u. Factor q(x).
2*x*(x - 1)/5
Let c = 5 + 2. Determine d, given that -11*d**2 - 9 + c*d**2 - 15*d + 0*d + 3*d = 0.
-3/2
Let z be (40/(-6))/(28/(-402)). Let h = 96 - z. Determine u so that -h*u + 0 - 2/7*u**2 + 2/7*u**3 + 2/7*u**4 = 0.
-1, 0, 1
Let d be 3/2*(-2)/(-6). Let c = 61/106 - 4/53. Factor n + c + d*n**2.
(n + 1)**2/2
Let z = 684 - 679. Let 1/5*a**2 - 2/5*a - 1/5*a**4 + 0 - 1/5*a**z + 3/5*a**3 = 0. What is a?
-2, -1, 0, 1
What is q in -q**2 + 3/5*q**4 + 0 - 2/5*q + 4/5*q**3 = 0?
-2, -1/3, 0, 1
Let n = 132 - 130. Let j(l) = 2*l**2 - 2*l. Let i be j(2). Factor -16/7 - n*y**3 - 2/7*y**i - 40/7*y - 36/7*y**2.
-2*(y + 1)*(y + 2)**3/7
Let q be 6/(-24) + (-82)/(-8). Suppose 12*g - 10 = q*g. Factor 1/5*r**2 + 0*r - 1/5*r**3 + 0 - 1/5*r**4 + 1/5*r**g.
r**2*(r - 1)**2*(r + 1)/5
Let a(v) be the first derivative of -v**5/20 + v**4/4 + 5*v**2/2 + 5. Let n(m) be the second derivative of a(m). Factor n(j).
-3*j*(j - 2)
Factor 15*h**2 + h**3 - 3*h**2 - 16 + 4*h**4 + 8*h**3 + 7*h**3 - 16*h.
4*(h - 1)*(h + 1)*(h + 2)**2
Let p(t) be the third derivative of -1/165*t**7 - 1/132*t**4 - 6*t**2 - 1/66*t**5 + 0 + 0*t + 0*t**3 - 3/220*t**6 - 1/924*t**8. Solve p(c) = 0 for c.
-1, -1/2, 0
Let g(j) be the second derivative of -4/21*j**3 + 2*j - 1/210*j**5 + 0 + 1/21*j**4 - j**2. Let y(c) be the first derivative of g(c). Factor y(k).
-2*(k - 2)**2/7
Factor 2*i + 2*i**2 - i**2 - 1 + 0*i - 12*i**3 + 10*i**3.
-(i - 1)*(i + 1)*(2*i - 1)
Suppose 5*s + 3*s**2 + 2*s**2 + 5*s + 3 + 2 = 0. Calculate s.
-1
Factor -140*q - 3*q**2 - 184 + 0*q**4 + 84 - q**4 - 66*q**2 - 14*q**3.
-(q + 2)**2*(q + 5)**2
Let u(x) = -x**3 - 1. Let h(w) = -1 - 5*w**3 - w**2 + 0*w - 3 + w + 1. Let b(y) = -h(y) + 4*u(y). Let b(j) = 0. What is j?
-1, 1
Let n(g) be the third derivative of -g**8/30240 - g**7/1890 - g**6/270 + g**5/60 - 3*g**2. Let j(f) be the third derivative of n(f). Factor j(w).
-2*(w + 2)**2/3
Suppose 2*k + 15 - 5 = 0. Let g be (-6)/(-42) + k/(-14). Determine p, given that -1/2 + 1/2*p**2 + g*p - 1/2*p**3 = 0.
-1, 1
Factor -538*y**5 - 16*y**2 + 20*y**4 + 542*y**5 + 15*y**3 - 32*y + 9*y**3.
4*y*(y - 1)*(y + 2)**3
Let v(k) = -2*k - 14. Let g be v(-9). Let s be g + (-3)/(-6) + -2. Factor 1 + 2*j**3 + j**2 - s*j + 1/2*j**5 - 2*j**4.
(j - 2)*(j - 1)**3*(j + 1)/2
Suppose 3*f = -4*f + 28. Let q(o) be the first derivative of 0*o + 1/8*o**f - 3 + 1/6*o**3 + 0*o**2. Factor q(h).
h**2*(h + 1)/2
Let h(q) = q**2 + 7*q + 12. Let t be h(-3). Determine i, given that 2/5*i**4 + 0*i**2 - 1/5*i**3 + 0*i + t = 0.
0, 1/2
Let l(v) = -4*v**4 + 2*v**2 + 2*v. Let h(t) = -t**5 + 4*t**4 - t**2 - 2*t. Let f(j) = 4*h(j) + 6*l(j). Suppose f(g) = 0. Calculate g.
-1, 0, 1
Let i(p) be the second derivative of p**9/18144 + p**8/10080 - p**3/2 + 3*p. Let r(u) be the second derivative of i(u). Factor r(l).
l**4*(l + 1)/6
Let z be 118/177 - (-2 + (-8)/6). Factor 0*g - 2/7*g**2 + 128/7*g**5 + 0 - 96/7*g**z + 24/7*g**3.
2*g**2*(4*g - 1)**3/7
Let t(n) be the second derivative of 0*n**2 + 1/240*n**5 + 0 