derivative of -1/240*z**6 + 1/120*z**5 + 0*z + 0 + 0*z**3 + 1/48*z**4 - d*z**7 - z**2. Factor g(c).
-c*(c - 1)*(c + 1)**2/2
Let m = -577/3 - -195. Let h be (-208)/(-429) - 2/(-11). Let 8/3*o + h*o**2 + m = 0. What is o?
-2
Let g(b) = b**2 + 21*b - 67. Let y(x) = -3*x**2 - 43*x + 133. Let o(c) = -5*g(c) - 3*y(c). Solve o(k) = 0.
-8, 2
Let u be (-8)/(-2) - 816/260. Let k = u - 6/13. Factor -k*q**4 + 0*q - 2/5*q**5 + 0 + 2/5*q**3 + 2/5*q**2.
-2*q**2*(q - 1)*(q + 1)**2/5
Factor 1/6*v**2 + 7/6*v + 0.
v*(v + 7)/6
Let u(b) = b**2 + 2*b - 2. Let v be u(2). Suppose 5*p - 5*y + 1 = -4, -3*p = -4*y + v. Let -32*n**3 + 14*n**4 - 7*n + n + p*n + 22*n**2 = 0. What is n?
0, 2/7, 1
Suppose 2*l - 4*b - 11 - 7 = 0, 4*l + 3*b - 36 = 0. Suppose -14*i = -l*i. Factor i + 3/2*n**2 + 3*n.
3*n*(n + 2)/2
Let j(y) = -3*y**4 - 14*y**3 - 61*y**2 - 60*y - 17. Let q(f) = -3*f**4 - 15*f**3 - 60*f**2 - 60*f - 18. Let r(m) = -6*j(m) + 7*q(m). Factor r(k).
-3*(k + 1)*(k + 2)**3
Let z(p) be the first derivative of -1/3*p + 1/4*p**2 + 8 - 1/18*p**3. Determine d, given that z(d) = 0.
1, 2
Let q be (-702)/(-198) + (-1)/((-44)/(-24)). Factor -3/2*n**3 + q*n**2 + 0 - 3/2*n.
-3*n*(n - 1)**2/2
Suppose 3*k - 4 = 7*k, 40 = -5*x - 5*k. Let m = 22/3 + x. Determine o so that 0*o + 1/3*o**2 - m = 0.
-1, 1
Let i(r) = -r**2 - 16*r - 9. Let h(b) be the second derivative of -b**3/3 - 2*b. Let k(d) = 22*h(d) - 2*i(d). What is f in k(f) = 0?
3
Let g(h) be the second derivative of -1/3*h**4 + 0*h**2 + 0 + 3*h + 2/3*h**3 + 1/20*h**5. Let g(n) = 0. What is n?
0, 2
Let j(x) = 4*x - 5 - 2*x - 4*x**2 + 1 + x**3. Let z be j(4). Find r, given that r**3 + r**5 + 4 + 2*r**z - 4 = 0.
-1, 0
Let a(b) be the second derivative of b**5/90 + b**4/54 - b**3/27 - b**2/9 + 65*b. Factor a(l).
2*(l - 1)*(l + 1)**2/9
Let p(j) be the first derivative of 16/21*j**3 - 1/7*j**4 + 0*j - 6/7*j**2 - 1. Find b, given that p(b) = 0.
0, 1, 3
Let a(x) be the first derivative of 3*x**4/2 + 8*x**3/3 + 4*x**2/3 - 3. Find h, given that a(h) = 0.
-2/3, 0
What is s in 81*s + 41*s**2 + 81 + 3*s**3 - 8*s**2 - 6*s**2 = 0?
-3
Let d be (-3)/5 - (-4)/(-10). Let a(i) = -3*i**4 - i**3 + 3*i**2 - 1. Let n(l) = l**2 - 1. Let o(v) = d*a(v) + n(v). Factor o(s).
s**2*(s + 1)*(3*s - 2)
Let g(d) = d**2 - d + 1. Let n(x) = -x**4 + 2*x**3 - x + 1. Let m(c) = 4*g(c) - 4*n(c). Find b, given that m(b) = 0.
0, 1
Let w(f) be the second derivative of -4*f**7/91 + 19*f**6/195 + 8*f**5/65 - f**4/6 + 2*f**3/39 + 33*f - 1. Suppose w(v) = 0. Calculate v.
-1, 0, 1/4, 1/3, 2
Let y be 130/(-90)*(-80)/22. Let t = y + -48/11. Suppose 8/9*h + t*h**3 - 2/9*h**4 - 2/9 - 4/3*h**2 = 0. What is h?
1
Factor 46*u + 14*u + 16*u**2 + 3 - 19.
4*(u + 4)*(4*u - 1)
Let a(x) be the third derivative of -1/18*x**4 - 1/60*x**6 - 1/45*x**7 + 7/90*x**5 + 5/504*x**8 + 0*x**3 + 0*x + 0 + x**2. Suppose a(p) = 0. What is p?
-1, 0, 2/5, 1
Suppose 3*h = -x + 8, h + 2*x = 6*x + 20. Find u, given that 3*u**3 + 0 + 1/2*u + 1/2*u**5 - 2*u**h - 2*u**2 = 0.
0, 1
Let w = 205/651 - -4/217. Solve w - 5/3*a + 4/3*a**2 = 0 for a.
1/4, 1
Let t = 10 + -7. Factor -10 - 2*u**t + 2*u + 10.
-2*u*(u - 1)*(u + 1)
Suppose 26*t**4 - t**5 - 20*t**3 + 32 + 144*t**2 + 4*t**5 + 108*t**3 + 112*t = 0. Calculate t.
-2, -2/3
Let y = 6 + -3. Factor 3*o**2 - 6*o**2 + 3*o**y + 3*o - 5*o**2 + 2*o**2.
3*o*(o - 1)**2
Let g(q) = q**2 - 25*q + 1. Let y(r) = -r. Let w(s) = -25*s. Let a(d) = -w(d) + 20*y(d). Suppose 9*h - 16 = h. Let o(x) = h*g(x) + 11*a(x). Factor o(z).
(z + 2)*(2*z + 1)
Determine z, given that 51*z - 27*z + 48*z + 93*z**2 - 36*z**3 - 105*z**4 - 36*z**5 + 12 = 0.
-2, -1, -2/3, -1/4, 1
Let v(o) = -9*o**4 + o**3 + 19*o**2 - 5*o - 6. Let l(b) = -b**4 - b**3 + b**2 + 1. Let k(z) = -4*l(z) + v(z). Let k(i) = 0. Calculate i.
-1, 1, 2
Let h(t) be the first derivative of -8*t**5/5 + 3*t**4 + 8*t**3/3 - 6*t**2 + 25. Factor h(q).
-4*q*(q - 1)*(q + 1)*(2*q - 3)
Let w(q) be the first derivative of 7 - 2/9*q**3 - 1/3*q**2 + 0*q. Find c, given that w(c) = 0.
-1, 0
Let f = 0 + 2. Let m = -232 - -232. Determine r, given that 0 - 14/3*r**4 - 8/3*r**f - 32/3*r**3 + m*r = 0.
-2, -2/7, 0
Let q = 24 - 21. Let a(d) be the third derivative of 0 + 0*d**q + 0*d - 1/48*d**4 + 1/80*d**6 + 0*d**5 + 2*d**2 + 1/210*d**7. Solve a(u) = 0 for u.
-1, 0, 1/2
Let k(m) = 3*m**3 + m**2 - 1. Let h be k(1). Factor -1/2 + 1/2*b + 1/2*b**2 - 1/2*b**h.
-(b - 1)**2*(b + 1)/2
Let x = -7 + 8. Suppose x = z + 2. Let h(m) = 2*m**2 + 3*m. Let c(q) = q. Let w(r) = z*h(r) + 2*c(r). Let w(j) = 0. What is j?
-1/2, 0
Let q(v) be the third derivative of 1/270*v**5 - 3*v**2 + 0 + 0*v + 0*v**4 - 1/315*v**7 + 0*v**3 - 1/270*v**6. Find r such that q(r) = 0.
-1, 0, 1/3
Let c be 6/9 + (-10)/15. Let j(y) be the third derivative of c*y**4 + 0*y**3 + 0 + 1/735*y**7 + 1/210*y**5 + 0*y + y**2 - 1/210*y**6. Factor j(b).
2*b**2*(b - 1)**2/7
Let x(w) be the second derivative of -1/6*w**4 + 0 - 1/2*w**2 + 1/10*w**6 - 2*w + 1/10*w**5 + 1/42*w**7 - 1/2*w**3. Factor x(m).
(m - 1)*(m + 1)**4
Let y(c) be the third derivative of c**7/30 + 13*c**6/360 + c**5/90 + 2*c**2. Factor y(s).
s**2*(3*s + 1)*(7*s + 2)/3
Let p(w) be the first derivative of -w**7/420 - w**6/60 + w**4/3 + 2*w**3/3 - 1. Let v(b) be the third derivative of p(b). Determine y, given that v(y) = 0.
-2, 1
Let p(b) be the first derivative of 4*b**3/27 - 7*b**2/9 - 8*b/9 + 8. What is g in p(g) = 0?
-1/2, 4
Let i(p) = -p**3 + 5*p**2 + p - 2. Let q be 219/45 + (-6)/(-45). Let u be i(q). Factor 4/9*b**2 + 0*b + 2/9*b**u + 0.
2*b**2*(b + 2)/9
Suppose -2*s + 5*x + 14 = 10, 0 = -2*x. Factor -1/5*j**s - 1/5*j + 1/5*j**4 + 0 + 1/5*j**3.
j*(j - 1)*(j + 1)**2/5
Suppose 5*k - 10 = 30. Solve -2*h**3 - 8*h + k*h = 0.
0
Let k be 138/21 + 9/21. Find g such that -15*g + 0*g**2 - 12*g**2 - k + 1 - 3*g**3 = 0.
-2, -1
Find s, given that -101*s + 2*s**4 + 101*s - 4*s**3 = 0.
0, 2
Suppose 7*r = 5*j + 9*r - 4, 15 = -5*r. Solve 144/5*c - 192/5 + 3/5*c**3 - 36/5*c**j = 0 for c.
4
Let y(z) be the first derivative of -z**7/105 + 5*z + 4. Let r(v) be the first derivative of y(v). Factor r(c).
-2*c**5/5
Let m be (-1)/(-2) + 10/12. Suppose -2*k = -13 + 3, 4*x = 3*k - 7. Factor -10/3*z - 2/3*z**3 - m - 8/3*z**x.
-2*(z + 1)**2*(z + 2)/3
Let d(u) be the third derivative of 0*u**4 + 0*u**3 - 1/720*u**6 + 1/360*u**5 + 0*u + 0 + 4*u**2. Factor d(n).
-n**2*(n - 1)/6
Let j = 0 - 1. Let o = 1 - j. Solve 0 + 1/2*v**o + 1/2*v = 0.
-1, 0
Let i(d) = d**2. Let z(m) = -4*m**2 + 4*m + 2. Suppose -3*j + 15 = -0*j. Suppose -5*q = 2*r - 2 + j, -3 = 2*q - r. Let n(f) = q*z(f) - 6*i(f). Factor n(k).
-2*(k + 1)**2
Let a(b) be the first derivative of -3*b**4/8 + b**3/2 + 6. Find s such that a(s) = 0.
0, 1
Let q(f) = 12*f**4 + 12*f**3 + 6*f**2 + 3*f - 3. Let h(t) = t**5 + t**3 - t + 1. Let z(i) = 3*h(i) + q(i). What is a in z(a) = 0?
-2, -1, 0
Let h(u) = u**2 + 5*u + 2. Let i be h(-5). Let s = -14 - -18. Let 0*m + 4*m**s + 2*m**3 + 0*m + i*m**5 = 0. Calculate m.
-1, 0
Let j(y) be the second derivative of y**4/84 + y**3/7 + 5*y**2/14 - 21*y + 1. What is m in j(m) = 0?
-5, -1
Let p(d) be the third derivative of d**5/140 + 17*d**2. Suppose p(k) = 0. What is k?
0
Factor -8/5*k + 4/5 + 8/5*k**3 + 0*k**2 - 4/5*k**4.
-4*(k - 1)**3*(k + 1)/5
Let v(n) be the second derivative of n**5/80 + n**4/12 - n**3/8 - 9*n**2/4 - 8*n. Factor v(w).
(w - 2)*(w + 3)**2/4
Let p(k) = 3*k + 3. Let o be p(0). Let v be -4 + 28/8 + o. Let -2 + v*c**4 + c**3 - 8*c - 15/2*c**2 = 0. Calculate c.
-1, -2/5, 2
Suppose 10 = 3*q - q. Let h be 0/((-1 - -4)/3). Find a such that 0*a**2 + h + 0*a**4 - a**3 + 1/2*a + 1/2*a**q = 0.
-1, 0, 1
Let o = -121 + 123. What is a in 8/9*a - 2/9 - 8/9*a**o - 4/9*a**3 + 10/9*a**4 - 4/9*a**5 = 0?
-1, 1/2, 1
Suppose -3*m - 1 = -2*n - 8, 14 = 2*m + n. Factor -1/4*v + 0 - 1/4*v**m - v**2 - v**4 - 3/2*v**3.
-v*(v + 1)**4/4
Let y = 6 + -4. Let g(v) = v**3 + 8*v**2 - 11*v - 14. Let x be g(-9). Find a, given that -2/3*a - 1/3*a**y + 0 + 2/3*a**3 + 1/3*a**x = 0.
-2, -1, 0, 1
Let b(t) be the second derivative of 0*t**2 - 1/24*t**4 + 1/60*t**6 + 0*t**5 + 0*t**3 + 0 + 3*t. Factor b(f).
f**2*(f - 1)*(f + 1)/2
Let j(v) be the second derivative of -v**4/3 - 2*v**3/3 + 12*v**2 - 15*v. Factor j(o).
-4*(o - 2)*(o + 3)
Let w(t) = -t**3 - 8*t**2 + 3*t + 8. Let x be w(-8). Let r(z) = -2*z**2 + 7*z - 