et b(a) be the first derivative of 4 - 3/25*a**5 + s*a**2 - 3/20*a**4 + 1/5*a**3 + 0*a. Find n, given that b(n) = 0.
-1, 0, 1
Let m(d) = -9*d**2 + 6*d - 3. Let s(w) = 8*w**2 - 6*w + 3. Let o(j) = 5*m(j) + 6*s(j). Determine f, given that o(f) = 0.
1
Factor -6/5 + 3/5*l**2 + 3/5*l**4 - 9/5*l**3 + 9/5*l.
3*(l - 2)*(l - 1)**2*(l + 1)/5
Let a = -10 - -12. Factor 2*n**3 + 4*n**3 - 2*n**3 + 2*n**5 - a*n - 4*n**5.
-2*n*(n - 1)**2*(n + 1)**2
Let w be (-12 + (-20)/5)*1/(-3). Solve -10/3*c**3 + 2/3*c**5 + w*c + 2/3*c**4 - 2/3*c**2 - 8/3 = 0.
-2, 1
Let l(m) be the second derivative of -m**4/28 + 3*m**3/14 - 3*m**2/7 + 20*m. Let l(w) = 0. Calculate w.
1, 2
Let l(n) be the first derivative of n**7/140 - n**6/120 - n**5/120 - n**2/2 + 2. Let p(s) be the second derivative of l(s). Factor p(m).
m**2*(m - 1)*(3*m + 1)/2
Suppose 2*p - 3 = 5. Suppose 0 = -r + 3*x - p, -2*x = 4*r - x - 10. Factor 1/2*w + 0 + 1/2*w**r.
w*(w + 1)/2
Suppose -6*r + 20 = -4. Solve -2/7*y + 2/7*y**5 + 0*y**3 + 4/7*y**r + 0 - 4/7*y**2 = 0.
-1, 0, 1
Suppose -8*j = -6*j - 40. Suppose -33 = -2*n + 5*d, 4*n - j - 11 = 3*d. Suppose -1/4*z**3 + 3/4*z**n - 1/2*z**2 + 0 + 0*z = 0. Calculate z.
-2/3, 0, 1
Suppose 0 = -o - 37 - 2. Let n be o/(-63) + (-8)/28. Suppose -2/3*b + 1/3*b**2 + n = 0. Calculate b.
1
Let h(t) = t**3 - t**2 - t. Let k(y) = y. Let a be (4/6)/(18/27). Let m(q) = a*h(q) + k(q). Factor m(n).
n**2*(n - 1)
Let u(y) = y - 1. Let k be u(4). Let h(c) be the third derivative of -1/12*c**4 + 0 + 0*c + k*c**2 + 2/3*c**3 - 1/30*c**5. Factor h(n).
-2*(n - 1)*(n + 2)
Let o(n) be the second derivative of -3*n + 1/6*n**4 + n**3 + 0*n**2 + 0. Factor o(k).
2*k*(k + 3)
Factor 2/9*t**4 + 2/9*t**2 + 0*t + 0 - 4/9*t**3.
2*t**2*(t - 1)**2/9
Let l(i) = -2*i**3 + 8*i**2 - 10*i + 7. Let h(d) = -2*d**3 + 8*d**2 - 10*d + 8. Let u(w) = -3*h(w) + 4*l(w). Factor u(g).
-2*(g - 2)*(g - 1)**2
Let i be 1 + (-30)/(-28) - 21/(-42). Suppose -2/7 - 54/7*r**2 - i*r - 54/7*r**3 = 0. What is r?
-1/3
Let d(g) = 2*g**3 - 2*g**2 - 5*g + 5. Let j(x) = 25*x**3 - 25*x**2 - 60*x + 60. Let r(u) = 35*d(u) - 3*j(u). What is s in r(s) = 0?
-1, 1
Suppose 0 = v + 4 - 6. Let x(k) be the third derivative of 0*k + 1/180*k**6 + 0 + 1/12*k**4 - 1/30*k**5 - 1/9*k**3 - k**v. Let x(l) = 0. What is l?
1
Let 0 + 4/9*l**4 - 4/9*l**2 - 14/9*l**3 + 0*l + 14/9*l**5 = 0. What is l?
-1, -2/7, 0, 1
Let s(v) be the third derivative of v**6/120 + v**5/45 - v**4/18 - 14*v**2. Solve s(u) = 0 for u.
-2, 0, 2/3
Let c = 58 + -54. Let i(z) be the second derivative of -3*z - 1/45*z**5 + 0 + 1/54*z**c + 0*z**2 + 0*z**3 + 1/135*z**6. Solve i(h) = 0.
0, 1
Let l(c) be the third derivative of -c**6/10 + c**5/20 + c**4/2 - c**3/2 - c**2. Solve l(g) = 0 for g.
-1, 1/4, 1
Let j(b) be the third derivative of b**8/112 - 2*b**7/35 + 3*b**6/20 - b**5/5 + b**4/8 - 3*b**2. Factor j(m).
3*m*(m - 1)**4
Factor 0 + 8/7*o + 2*o**2 - 2/7*o**4 + 4/7*o**3.
-2*o*(o - 4)*(o + 1)**2/7
Let b be 1 + ((-20)/4 - -2 - -2). Suppose -2/3*r**3 + 1/3 - r**2 + b*r = 0. What is r?
-1, 1/2
Factor -4/5*z + 3/5*z**2 + 1/5.
(z - 1)*(3*z - 1)/5
Let a(l) be the second derivative of l**6/20 - 3*l**5/40 - l**4/2 + l**3 - 19*l. Solve a(x) = 0.
-2, 0, 1, 2
Let y be (-82)/336 + (-24)/(-84). Let x(i) be the second derivative of 0*i**2 - y*i**4 + 2*i - 1/20*i**5 - 1/21*i**7 + 0*i**3 + 0 + 7/60*i**6. Factor x(q).
-q**2*(q - 1)**2*(4*q + 1)/2
Factor -8/11*m**4 + 0*m + 0 - 4/11*m**2 + 10/11*m**3 + 2/11*m**5.
2*m**2*(m - 2)*(m - 1)**2/11
Let 0 + 2/9*i**2 - 2/9*i = 0. What is i?
0, 1
Suppose -28*u + 3 = 3. Suppose u + 6/7*a**3 + 4/7*a**2 + 0*a + 2/7*a**4 = 0. What is a?
-2, -1, 0
Let 5*r**4 - 26*r**3 + 27*r**3 - 6*r**4 = 0. What is r?
0, 1
Suppose 0 = -2*u + 5*b + 25, 5 = -b - 0. Suppose -h - 5*i + 14 = u, 4*h - i - 5 = 9. Factor -t**3 + 2*t + t**2 + 3*t**2 - t**3 - h.
-2*(t - 2)*(t - 1)*(t + 1)
Let y(o) be the third derivative of o**6/540 + o**5/180 - o**4/18 + o**3/6 - 3*o**2. Let m(p) be the first derivative of y(p). Solve m(k) = 0.
-2, 1
Let o(i) be the first derivative of i**4/54 + 7*i + 2. Let y(f) be the first derivative of o(f). Determine g so that y(g) = 0.
0
Let w be (-21)/27*1 - (-4 + 3). Determine i, given that w*i**2 - 4/9*i + 2/9 = 0.
1
Determine r so that -3/7*r**2 - 4/7*r + 0 + 1/7*r**3 = 0.
-1, 0, 4
Let t(l) be the third derivative of -l**7/315 + 4*l**6/315 + l**5/210 - 4*l**4/63 + 4*l**3/63 + l**2. What is f in t(f) = 0?
-1, 2/7, 1, 2
Determine q, given that 1/2*q**4 + 0*q**2 + 0*q + 0 + q**3 = 0.
-2, 0
Let b(v) = 5*v**3 - 7*v**2 - 5*v + 7. Let x(t) = 4*t**3 - 6*t**2 - 4*t + 6. Let q(d) = -5*b(d) + 6*x(d). What is w in q(w) = 0?
-1, 1
Determine a so that -4/3*a - 2/3*a**2 + 2 = 0.
-3, 1
Suppose 0 = -5*r + 15. Let w(y) be the second derivative of 0 - 1/12*y**4 - 1/2*y**r - 2*y - y**2. Factor w(j).
-(j + 1)*(j + 2)
Suppose -2*q = -2*o - 2*o - 16, -2*o - 12 = -3*q. Find r, given that 3 - 2 - 1 - r**q = 0.
0
Let x be 368/1185 - (-20)/(-150). Let d = 888/553 - x. What is j in -4/7 - 8/7*j**2 + 2/7*j**3 + d*j = 0?
1, 2
Let v = 0 + 16. Suppose 0*u + v = -4*u - 4*t, 4*t + 16 = -u. Solve u*o + 0 - 6/5*o**2 - 3/5*o**3 = 0.
-2, 0
Let q = 46/75 + -1/75. Find b, given that -3/5 + q*b**2 + 0*b = 0.
-1, 1
Factor -10/9*x - 2/9*x**2 - 4/3.
-2*(x + 2)*(x + 3)/9
Let y be 34/36 + 14/21. Let v = y + -5/18. Suppose 4/3*g - 4/3*g**3 + g**2 - v + 1/3*g**4 = 0. Calculate g.
-1, 1, 2
Let c = -88/9 + 635/18. Let q = -25 + c. Solve -q*g**3 + 1/4*g + 1/4*g**5 + 0*g**4 + 0 + 0*g**2 = 0.
-1, 0, 1
Let k be ((-6)/(-9))/(26/(-120)). Let q = 172/39 + k. Solve -1/3 - 11/3*l**3 + q*l**4 + 3*l**2 - 1/3*l = 0.
-1/4, 1
Let a be 3/6*(13 + -1). Suppose -a = -0*v - 3*v. Factor 4*x**v - 6*x**2 + 2*x + 3*x**2 + 1.
(x + 1)**2
Let x(d) = -2 - 3 - 1 - d. Let b be x(-7). Factor 0 + b + 0 - 6*s + 1 + 6*s**2 - 2*s**3.
-2*(s - 1)**3
Let n(o) = -o**2 + 4*o + 10. Let l be n(12). Let g = -169/2 - l. Factor 0*w + g*w**3 + 0 - 3/2*w**2.
3*w**2*(w - 1)/2
Let t be 16/6*6/4. Suppose -3*c + c = 0. Factor 1 + 0 - 2*p**3 + c*p**4 - p**t + 2*p.
-(p - 1)*(p + 1)**3
Let k(d) = d**2 + 2*d - 1. Let m(j) = 4*j**2 + 7*j - 4. Let p(x) = -21*k(x) + 6*m(x). Factor p(b).
3*(b - 1)*(b + 1)
Factor 6*d - 4*d - 2 + d**2 + 3.
(d + 1)**2
Let l(d) = d**3 + 4*d**2 - 7*d - 6. Let u be l(-5). Suppose u*y = y. Factor -4/5*h**3 + 2/5*h**5 + 2/5*h + 0*h**4 + y + 0*h**2.
2*h*(h - 1)**2*(h + 1)**2/5
Let u be (46 - 0) + -1 + 0. Let w be (-2)/(-8) + u/12. Let -2*z**3 + 0*z**4 - 2*z**w + z + 2*z**2 + z = 0. Calculate z.
-1, 0, 1
Suppose 0*k**3 - 192*k - 24*k**2 - 3*k**3 + 2*k**3 - 512 = 0. What is k?
-8
Let o(a) be the second derivative of 1/5*a**6 - 1/2*a**4 - 1/14*a**7 + 1/2*a**3 + 0*a**2 - a + 0*a**5 + 0. Factor o(s).
-3*s*(s - 1)**3*(s + 1)
What is r in r + 1/4*r**2 + 3/4 = 0?
-3, -1
Suppose 5*g - 7 - 5 = b, -2*g + b = -6. What is s in -s**3 + 3*s**3 + 0*s**3 + g*s - 4*s**2 = 0?
0, 1
Factor 6/13*y**3 + 0 - 2/13*y**4 + 10/13*y + 18/13*y**2.
-2*y*(y - 5)*(y + 1)**2/13
Let z(v) be the second derivative of -v**5/110 - v**4/66 + v**3/33 + v**2/11 + 32*v. Find p, given that z(p) = 0.
-1, 1
Suppose 4*s = v + 21, -s + 2*v + 18 = s. Let 3*o**2 + 3*o - 5*o**3 - o**s + o**3 + o**3 - 2*o**4 = 0. Calculate o.
-1, 0, 1
Let m(g) = g**3 + g**2 + g. Let c be (1 - 3)/(0 - 2). Let p(b) = 14*b**3 + 10*b**2 + 12*b. Suppose -2 - 58 = 5*u. Let r(d) = c*p(d) + u*m(d). Factor r(l).
2*l**2*(l - 1)
Let t(s) be the first derivative of 2/21*s**4 + 0*s**3 + 0*s**2 + 2*s + 1/105*s**6 - 1 - 2/35*s**5. Let x(u) be the first derivative of t(u). Factor x(o).
2*o**2*(o - 2)**2/7
Let f = 18/31 - -442/93. What is a in 2/3 + f*a**2 - 7/3*a**3 - 11/3*a = 0?
2/7, 1
Let h(n) be the second derivative of -n**8/840 - n**7/420 + n**6/180 + n**5/60 - n**3/6 - 3*n. Let d(f) be the second derivative of h(f). Factor d(b).
-2*b*(b - 1)*(b + 1)**2
Find w such that 1/2*w**4 - 1/2*w + 1/2*w**3 + 0 - 1/2*w**2 = 0.
-1, 0, 1
Let -1/3*j**3 + j**2 - j + 1/3 = 0. Calculate j.
1
Factor 0 - 1/4*u - 1/4*u**5 + u**4 - 3/2*u**3 + u**2.
-u*(u - 1)**4/4
Let r(a) be the third derivative of -a**7/210 - a**6/60 + a**5/20 + a**4/3 + 2*a**3/3 + 45*a**2. Factor r(y).
-(y - 2)*(y + 1)**2*(y + 2)
Let b(d) be the second derivative of -3*d**5/100 - 3*d**4/20 + 6*d**2/5 + 11*d. Find k, given that b(k) = 0.
-2, 1
Let b(k) be the third derivative of 