2)/3
Let i(s) = -s**3 + 5*s**2 + 2*s - 7. Let o be i(5). Let -8*a**o + 4 + 2*a**4 - 8*a + 1 - 3 + 12*a**2 = 0. What is a?
1
Let u(q) be the first derivative of -q**3/3 + 7*q**2/2 + 2*q + 3. Let c be u(7). Suppose 2*g**3 - c*g**5 + 2*g**4 - 6 + 6 - 2*g**2 = 0. What is g?
-1, 0, 1
Let w(z) be the third derivative of 0*z**5 + 1/540*z**6 - 1/36*z**4 - 2/27*z**3 + 0*z + 3*z**2 + 0. Factor w(o).
2*(o - 2)*(o + 1)**2/9
Let y(p) be the first derivative of -2*p**4/9 - 14*p**3/27 - 2*p**2/9 + 2*p/9 - 6. Suppose y(f) = 0. What is f?
-1, 1/4
Suppose 6 = -2*d + 4*d. Suppose 0*q**2 + d*q - 2*q**2 + 3*q**2 - 2*q = 0. Calculate q.
-1, 0
Let z(f) = 3*f - 1 + 2*f**2 - 2*f + 4*f**2 - 5*f**2. Let b be (2/(-4))/((-1)/(-2)). Let q(y) = -4*y**2 - 5*y + 5. Let g(i) = b*q(i) - 5*z(i). Factor g(r).
-r**2
Let h = 3585/52 + -69. Let k = 217/156 + h. Factor 2*m - 2/3*m**5 + k*m**2 - 4/3*m**3 - 2*m**4 + 2/3.
-2*(m - 1)*(m + 1)**4/3
Let p(w) be the third derivative of 0 + 1/144*w**4 + 0*w**3 + 3*w**2 + 0*w**5 - 1/720*w**6 + 0*w. Factor p(h).
-h*(h - 1)*(h + 1)/6
Let k = 461/2 + -2303/10. Factor k*l + 0 + 1/5*l**3 - 2/5*l**2.
l*(l - 1)**2/5
Let s(g) be the second derivative of g**9/30240 + g**8/13440 + g**4/12 - 4*g. Let r(a) be the third derivative of s(a). Let r(w) = 0. What is w?
-1, 0
Let g(a) be the first derivative of -a**6/7 - 22*a**5/35 - 9*a**4/14 + 2*a**3/3 + 12*a**2/7 + 8*a/7 + 3. Find o, given that g(o) = 0.
-2, -1, -2/3, 1
Let z(h) be the second derivative of 1/12*h**4 + 0*h**2 + 0*h**3 + 0 - 3/40*h**5 + 1/84*h**7 + 7*h + 0*h**6. Factor z(d).
d**2*(d - 1)**2*(d + 2)/2
Let h be 2 + 0/1 + 0. Suppose -8*d + 6*d**h - 2*d**3 + 0*d + 2*d**2 = 0. Calculate d.
0, 2
Suppose -2*h + 5*y = 17, -y = -h + y - 6. Let i(q) be the second derivative of -2/21*q**3 - 2*q + 0 + 1/7*q**2 + 1/42*q**h. Factor i(u).
2*(u - 1)**2/7
Let b(a) be the second derivative of a**5/240 - a**4/24 + a**3/6 + a**2 - 4*a. Let d(s) be the first derivative of b(s). Let d(i) = 0. Calculate i.
2
Let r be 9/(-15)*1 + (-813)/(-105). Determine y, given that 0 + 50/7*y**3 - r*y**4 + 8/7*y**2 - 8/7*y = 0.
-2/5, 0, 2/5, 1
Let s(b) = -b - 7. Let l be s(-9). Let v(p) be the first derivative of 0*p + 0*p**l + 1/4*p**4 + 2/9*p**3 + 1/15*p**5 - 1. Factor v(o).
o**2*(o + 1)*(o + 2)/3
Let l(m) = -3*m - 9. Let h be l(-6). Let s = h + -6. Let 1/2*g**2 + 3/2*g**s - 1/4 - 3/4*g**5 - 3/4*g - 1/4*g**4 = 0. Calculate g.
-1, -1/3, 1
Let y(q) be the third derivative of -q**7/11340 - q**6/3240 - 5*q**4/24 - 4*q**2. Let c(k) be the second derivative of y(k). What is v in c(v) = 0?
-1, 0
Let l(z) be the second derivative of -z**4/30 + 8*z**3/15 - 16*z**2/5 - 9*z. Find b such that l(b) = 0.
4
Factor -5/4*y**2 - 5/4*y**4 + 0*y + 5/2*y**3 + 0.
-5*y**2*(y - 1)**2/4
Let b = 17 - 22. Let c = 7 + b. Factor 1/2*j + 1/2*j**c - 1.
(j - 1)*(j + 2)/2
Let x(y) be the second derivative of -y**7/3780 + y**6/540 - y**5/180 + y**4/4 - y. Let h(c) be the third derivative of x(c). Solve h(l) = 0 for l.
1
Let c = -18 + 18. Let n(r) be the third derivative of 0 + 0*r - 1/150*r**6 + 1/150*r**5 + 0*r**4 + 1/525*r**7 - 2*r**2 + c*r**3. Factor n(g).
2*g**2*(g - 1)**2/5
Let o(g) = 20*g**5 - 2*g**4 - 8*g**3 - 10*g**2 - 6*g + 6. Let l(w) = w**5 - w**4 + w**3 - w**2 - w + 1. Let j(u) = -6*l(u) + o(u). Solve j(p) = 0.
-1, -2/7, 0, 1
Suppose 11 = q - 3*s, q + 4*s = 5*q - 28. Factor -10 + q*a + 4 - 6 + 7*a - 3*a**2.
-3*(a - 2)**2
Suppose 0 = 2*w + 3*i - 21, 2*i - 7 = -4*w + 15. Suppose w = m - 0. What is u in 2/3*u**2 + 0 + 2/3*u**m - 4/3*u = 0?
-2, 0, 1
Suppose 15 = 3*u, -19 = -2*f - 3*u + 2. Factor -f*x + 3 + 3/4*x**2.
3*(x - 2)**2/4
Let q(m) = -m**3 - 6*m**2 + 6*m - 1. Let i be q(-7). Let t be 2/6 - (-4)/i. Suppose w**2 + t - w - w - 5*w + 5*w = 0. What is w?
1
Let d(a) be the third derivative of a**7/210 - a**6/40 + a**5/30 - 3*a**2 + 24. What is u in d(u) = 0?
0, 1, 2
Let s(b) be the first derivative of -5*b**4/4 + 10*b**3/3 + 5*b**2/2 - 10*b - 17. Find m, given that s(m) = 0.
-1, 1, 2
Let m(y) be the first derivative of 49/50*y**5 - 2 - 2*y + 7/10*y**4 - 8/5*y**3 + 4/5*y**2. Let g(n) be the first derivative of m(n). Solve g(z) = 0 for z.
-1, 2/7
Suppose -72*k = -67*k - 10. Factor 0*t**k + 1/3*t**3 - 1/3*t + 0.
t*(t - 1)*(t + 1)/3
Let m(r) = 4*r**4 + 12*r**3 - 4*r**2 - 8*r - 4. Let k(b) = b**3 - b**2. Let z(i) = -4*k(i) + m(i). Factor z(j).
4*(j - 1)*(j + 1)**3
Let x(b) be the third derivative of b**7/525 - b**6/600 - b**5/100 + b**4/120 + b**3/30 - 5*b**2. Determine t, given that x(t) = 0.
-1, -1/2, 1
Let k(d) be the second derivative of d**5/4 + 5*d**4/6 - 30*d. What is i in k(i) = 0?
-2, 0
Let t be (-1)/3 + 65/15. Let w(v) be the first derivative of 1/9*v**2 - 2 + 0*v - 1/6*v**t + 4/27*v**3. Factor w(p).
-2*p*(p - 1)*(3*p + 1)/9
Let v(a) = -6*a**3 + 4*a**2 + 4. Let k(p) be the second derivative of p**5/4 - p**4/4 - 3*p**2/2 - 2*p. Let u(c) = -4*k(c) - 3*v(c). Factor u(l).
-2*l**3
Let s = 0 + 3. Let z(k) be the first derivative of s - 4 + k**3 - 2*k**3 + 0. Solve z(l) = 0.
0
Let c be 170/(-612)*(-4)/5. Factor 0*m**2 + 0 + 2/9*m**5 + 0*m - 4/9*m**4 + c*m**3.
2*m**3*(m - 1)**2/9
Let k(a) = -2*a**5 - 4*a**4 + 4*a**3 + 8*a**2 - 2*a + 4. Let u(s) = s**5 - s**3 - s**2 - 1. Let w(m) = -k(m) - 4*u(m). Suppose w(d) = 0. What is d?
-1, 0, 1
Let q = 3 - -9. Let q*g**3 - 2*g**2 + 3 + 33*g + 20*g**2 + 3*g**4 - 21*g = 0. Calculate g.
-1
Suppose -10*b + 7*b = -24. Let q be (-15)/(-20) - 6/b. Factor 3/5*y**3 + q*y - 3/5*y**2 + 0.
3*y**2*(y - 1)/5
Let b(f) be the third derivative of 0*f + 0*f**5 + 0*f**4 + 2*f**2 + 0*f**3 - 1/210*f**7 + 0 + 1/120*f**6. Factor b(s).
-s**3*(s - 1)
Let y(g) be the third derivative of -1/168*g**8 + 0 - 2/105*g**7 + 0*g**3 + 0*g**4 + 3*g**2 + 0*g**5 - 1/60*g**6 + 0*g. Factor y(v).
-2*v**3*(v + 1)**2
Let i(t) be the second derivative of -t**4/21 + 6*t. Factor i(x).
-4*x**2/7
Let v(h) = h**4 + 3*h**3 - 3*h**4 + h**4 + h - 3*h**2 - 2. Let a(m) = 7*m**4 - 23*m**3 + 25*m**2 - 9*m + 17. Let b(j) = 6*a(j) + 51*v(j). Solve b(t) = 0 for t.
-1/3, 0, 1
Solve 21/5*g**2 - 18/5 + 3/5*g - 3/5*g**4 - 3/5*g**3 = 0.
-3, -1, 1, 2
Determine h, given that 35/2*h**5 - 1/2*h + 15/4*h**2 + 0 - 69/4*h**4 - 7/2*h**3 = 0.
-1/2, 0, 1/5, 2/7, 1
Let i(f) be the third derivative of f**5/80 + f**4/32 - f**3/4 - 7*f**2. Determine t so that i(t) = 0.
-2, 1
Let f(y) be the third derivative of -y**10/45360 - y**4/12 - 4*y**2. Let k(p) be the second derivative of f(p). Factor k(x).
-2*x**5/3
Let i = 76 - 76. Let w(q) be the first derivative of -3/10*q**4 + i*q - 3 + 1/5*q**3 + 3/25*q**5 + 0*q**2. What is m in w(m) = 0?
0, 1
Suppose 5*u - 23 = -4*z, -1 = 3*u - 5*z - 0*z. Suppose u*f = 3*m, -4*m = -3*f - 3 - 0. Suppose -3*t**2 + 5*t**4 - f*t**4 + 2 - t**2 = 0. What is t?
-1, 1
Let o be (-6)/15 + (-132)/(-30). Suppose 4*s - 2*w = o, -4*s + w = -5 + 3. Factor 0*h + 4/5*h**2 + 14/5*h**3 + s.
2*h**2*(7*h + 2)/5
Let f be 3 + -2 - (-3 + 1). Let g(u) be the third derivative of 1/21*u**f + 0 - 1/210*u**5 + 0*u**4 - u**2 + 0*u. Solve g(p) = 0 for p.
-1, 1
Let f(o) = o**2 - o. Let l(x) = 5*x**2 - x - 1. Let p(v) = -3*f(v) + l(v). Let g be p(1). Suppose 3*h**3 + 15*h**g + 0*h**3 - 6*h**2 - 3*h**3 = 0. What is h?
0, 2/5
Let j(i) be the first derivative of 2*i**6/3 + 4*i**5 + 8*i**4 + 16*i**3/3 + 4. Factor j(h).
4*h**2*(h + 1)*(h + 2)**2
Let k(c) = -3*c**4 - 48*c**3 - 65*c**2 - 11*c - 17. Let p(x) = -x**4 - 12*x**3 - 16*x**2 - 3*x - 4. Let n(h) = -6*k(h) + 26*p(h). Factor n(d).
-2*(d + 1)**2*(2*d + 1)**2
Let g = 23 - 15. Find n, given that -4*n + 3*n**3 + g*n**3 - 13*n**3 + 6*n**2 = 0.
0, 1, 2
Suppose 292 = 4*l + 284. Suppose 2/7*v**l + 8/7*v + 6/7 = 0. Calculate v.
-3, -1
Let d(p) be the first derivative of -2 + 8/3*p**3 - 3/2*p**4 - p**2 + 0*p. Find x, given that d(x) = 0.
0, 1/3, 1
Let l(d) be the first derivative of 0*d + 1/90*d**5 - d**2 - 1 + 0*d**3 + 1/36*d**4. Let t(m) be the second derivative of l(m). Find h, given that t(h) = 0.
-1, 0
Let y(c) = 7*c**2 + 11*c + 37. Let v(i) = 6*i**2 + 12*i + 36. Let n(k) = -5*v(k) + 4*y(k). Factor n(d).
-2*(d + 4)**2
Let w(y) be the first derivative of -5*y**3 + 25*y**2/2 - 10*y - 21. Suppose w(a) = 0. Calculate a.
2/3, 1
Let f(z) be the second derivative of -z**7/105 - z**6/30 - z**5/30 - 3*z**2/2 + z. Let h(x) be the first derivative of f(x).