 g be 4/(-3)*(-12)/8. Suppose -g*a - a = 0. What is w in 0*w - 6/7*w**4 + 0 + a*w**2 - 2/7*w**3 = 0?
-1/3, 0
Let y(d) be the third derivative of -d**6/24 + d**5/30 + 5*d**4/6 - 4*d**3/3 - 19*d**2. Factor y(b).
-(b - 2)*(b + 2)*(5*b - 2)
Let n(o) be the third derivative of 1/210*o**5 + 0*o**3 - 1/84*o**4 + 0 + 0*o + 2*o**2. Determine m, given that n(m) = 0.
0, 1
Let j(z) = -z**2 - 8*z - 9. Let r be j(-6). Suppose 5*v = 5*h - 20, -r*h + 12 = -2*h - 5*v. Factor -1/3*x**h + 0*x - 1/3*x**3 + 0.
-x**2*(x + 1)/3
Let k(c) be the first derivative of 2/13*c**2 + 2/13*c**3 + 0*c**4 + 9 + 0*c - 2/65*c**5. Factor k(j).
-2*j*(j - 2)*(j + 1)**2/13
Suppose -3*w = -2*k + 6*k + 19, 6 = -k - w. Let a = k + 1. Factor 2/7 - 4/7*r**2 + a*r + 0*r**3 + 2/7*r**4.
2*(r - 1)**2*(r + 1)**2/7
Let c be 472/10 + (-9)/45. Determine j so that 7*j + 3*j**3 - 9*j**2 + c - 49 + j**2 = 0.
2/3, 1
Let n(l) be the first derivative of -4*l**7/189 + 13*l**6/135 - l**5/6 + 7*l**4/54 - l**3/27 + l - 3. Let i(x) be the first derivative of n(x). Factor i(q).
-2*q*(q - 1)**3*(4*q - 1)/9
Let z(v) be the third derivative of v**6/210 + 2*v**5/105 - v**4/42 - 4*v**3/21 - 13*v**2. Factor z(k).
4*(k - 1)*(k + 1)*(k + 2)/7
Let g = 12 + 0. Let n be (-4)/(-5)*(-7 + g). Factor -x + 2/3*x**2 + 1/3*x**5 + 2/3*x**3 - x**n + 1/3.
(x - 1)**4*(x + 1)/3
Let z(d) = 2*d**5 - 11*d**4 + 16*d**3 + 7*d. Let v(o) = -o**5 + 4*o**4 - 5*o**3 - 2*o. Let b(l) = -7*v(l) - 2*z(l). Solve b(c) = 0 for c.
0, 1
Let q(r) be the second derivative of -13*r**4/12 - r**3/3 + r. Find l, given that q(l) = 0.
-2/13, 0
Let l be 360/44 + -6 + -2. Factor l*y**2 - 4/11 + 2/11*y.
2*(y - 1)*(y + 2)/11
Let n = -1 - -1. Suppose 0 = 3*k - n*k - 6. Factor 3/4*p**3 + 0 + 1/4*p**4 + 3/4*p**k + 1/4*p.
p*(p + 1)**3/4
Suppose -2*b + 5 = 3*l + 1, -b = 4*l - 7. Factor 4/7 - 6/7*f - l*f**3 - 24/7*f**2.
-2*(f + 1)**2*(7*f - 2)/7
Let t(g) be the first derivative of 3 - 1/4*g**2 - 1/12*g**3 + 0*g. Factor t(k).
-k*(k + 2)/4
Let r = -19/24 + 9/8. Let m(a) be the second derivative of 1/15*a**6 + 0 + 0*a**2 + 3*a - 1/10*a**5 - 1/6*a**4 + r*a**3. Factor m(z).
2*z*(z - 1)**2*(z + 1)
Factor -1/4*z**3 + 1/4*z**4 + 0 - 1/4*z**2 + 1/4*z**5 + 0*z.
z**2*(z - 1)*(z + 1)**2/4
Factor 2/9*o**2 - 16/9*o + 32/9.
2*(o - 4)**2/9
Find a, given that -4*a**4 + 3*a + 4 + 8*a**3 + 0*a**3 - 10*a - a = 0.
-1, 1
Let o(c) be the first derivative of -c**5/75 + c**4/20 + 2*c**3/15 - c**2 + 10. Let k(v) be the second derivative of o(v). Factor k(z).
-2*(z - 2)*(2*z + 1)/5
Let p be (-8)/(-20)*(2 + 8). Determine q, given that -131*q**3 + p*q**4 + 131*q**3 - 4*q**2 = 0.
-1, 0, 1
Let b(k) be the third derivative of -k**11/166320 + k**10/37800 - k**8/5040 + k**7/2520 + k**5/60 - k**2. Let n(q) be the third derivative of b(q). Factor n(g).
-2*g*(g - 1)**3*(g + 1)
Let t be (-2)/(-4)*4*2. Factor x**3 - x**4 - 5*x**4 + 4*x**4 + 3*x**t.
x**3*(x + 1)
Let c = 167 + -2504/15. Let s(n) be the third derivative of 0*n - 1/30*n**4 - 1/150*n**5 - c*n**3 - 2*n**2 + 0. Factor s(z).
-2*(z + 1)**2/5
Let n(c) be the third derivative of c**9/241920 - c**7/20160 + c**5/60 - 2*c**2. Let s(j) be the third derivative of n(j). Factor s(z).
z*(z - 1)*(z + 1)/4
Let o(h) be the third derivative of -h**6/420 - h**5/210 + h**4/84 + h**3/21 - 7*h**2. What is b in o(b) = 0?
-1, 1
Let j = 151/69 - 12/23. Let w = j + -29/21. Factor 2/7*v**2 + w + 4/7*v.
2*(v + 1)**2/7
Let c be (-1 - 20/(-24))/(3/(-4)). Factor 4/9*q + c*q**2 - 4/9*q**3 - 2/9.
-2*(q - 1)*(q + 1)*(2*q - 1)/9
Let f = 8 + -5. Solve -5*t**4 - t**f + 6*t**4 - t**3 = 0.
0, 2
Let h(a) = 16*a**3 + 22*a**2 - 6*a - 12. Let x(z) = 5*z**3 + 7*z**2 - 2*z - 4. Let r(n) = 3*h(n) - 10*x(n). What is b in r(b) = 0?
-2, -1, 1
Suppose 2*d - v = -7, -32 = d + d + 4*v. Let o(y) = y + 4*y - 2*y - 2*y. Let k(a) = 3*a**2 + 3. Let i(l) = d*o(l) - k(l). Factor i(z).
-3*(z + 1)**2
Let o = -44 + 24. Let z be (2/(-5))/(16/o). Determine k so that -1/2*k**5 + 5/2*k**4 + 5*k**2 + z - 5/2*k - 5*k**3 = 0.
1
Suppose 0*w = 3*w - 9. Let y(r) be the second derivative of 0 - 1/54*r**4 + 1/9*r**2 + 0*r**3 + w*r. Factor y(f).
-2*(f - 1)*(f + 1)/9
Let 0*y + 1/2*y**2 - 1/2 = 0. What is y?
-1, 1
Suppose -6*y = -2*y. Let n be ((-2)/(-54))/(4/24). Solve y - n*v**2 + 0*v = 0.
0
Let u(b) be the third derivative of -b**7/315 - b**6/36 - b**5/30 + 5*b**4/36 + 4*b**3/9 - 37*b**2. Let u(x) = 0. Calculate x.
-4, -1, 1
Let r = -15 + 17. Let s = -290/3 + 98. Let 0 + 2/3*x**r - s*x = 0. What is x?
0, 2
Factor 233*v + 4*v**2 - 275*v + 147 - v**2.
3*(v - 7)**2
Let f(y) = 3*y + 2. Let k be f(10). Factor 2*v**2 + 6*v**3 + k - 48*v - 2*v**3 + 2*v**4 + 12*v**3 - 4*v**3.
2*(v - 1)**2*(v + 4)**2
What is z in 17*z - 11*z - 2 + 15*z**2 + 2 = 0?
-2/5, 0
Let z be -5 - (-5 + 2) - 10/(-4). Let n be 3 - ((-75)/(-6))/5. Factor 0*b**2 + n*b - z*b**3 + 0.
-b*(b - 1)*(b + 1)/2
Let f = 136 - 134. Factor -1/5*s**3 + 0*s**f + 0 + 1/5*s.
-s*(s - 1)*(s + 1)/5
Let w be 88/77*6/24. Factor w*i**2 + 18/7 - 12/7*i.
2*(i - 3)**2/7
Suppose 6/17 - 4/17*y - 2/17*y**2 = 0. What is y?
-3, 1
Let i be -1*9*(2 - 1). Let c be (i + 8)*2/(-6). Factor 1/3*x**2 - c + 0*x.
(x - 1)*(x + 1)/3
Let j(q) = 3*q**3 - 10*q**2 + 26*q - 14. Let y(i) = 2*i**3 - 10*i**2 + 26*i - 14. Let h(p) = 4*j(p) - 5*y(p). Solve h(m) = 0.
-7, 1
Factor -65*f**2 - 11*f**3 - 3*f**4 + 68*f**2 + 4*f + 0*f**3 - 5*f**5 + 12*f**5.
f*(f - 1)**2*(f + 1)*(7*f + 4)
Let w(s) be the third derivative of 0*s**7 + 0*s**3 + 0*s**4 + 3*s**2 - 1/1008*s**8 + 0*s**5 + 0 + 0*s + 1/360*s**6. Factor w(q).
-q**3*(q - 1)*(q + 1)/3
Let y(m) = -m**2 - 5*m - 2. Let f be y(-3). Find k such that -k**3 - 2*k**2 + 0*k**4 - k**f - 7*k + 8*k + 3*k**2 = 0.
-1, 0, 1
Let u(b) = -b**3 + b**2 - b + 4. Let y be u(0). Suppose 0 = -m - y*m + 10. Suppose -2/9*j**5 + 0*j**4 + 0*j**3 + 0*j**m + 0 + 0*j = 0. What is j?
0
Let y(d) be the second derivative of -d**8/23520 + d**6/2520 - d**4/12 + 3*d. Let l(z) be the third derivative of y(z). Let l(x) = 0. Calculate x.
-1, 0, 1
Let x(d) be the second derivative of d**5/5 + 2*d**4/3 + 2*d**3/3 + 6*d. Factor x(u).
4*u*(u + 1)**2
Solve 12*f**3 + 0 + 3*f**4 + 1/4*f**5 + 0*f + 16*f**2 = 0.
-4, 0
Let z = 273/2 + -136. Factor 7/2*c + z*c**4 + 1 + 9/2*c**2 + 5/2*c**3.
(c + 1)**3*(c + 2)/2
Let l(n) be the second derivative of n**4/9 + n**3/18 + 29*n. Let l(q) = 0. What is q?
-1/4, 0
Determine d, given that 0 + 0*d**2 - 2/19*d + 2/19*d**3 = 0.
-1, 0, 1
Let n(b) be the second derivative of 1/63*b**7 + 0*b**2 + 0*b**4 + 0 + 0*b**3 + 1/30*b**5 + b + 2/45*b**6. Determine m, given that n(m) = 0.
-1, 0
Let f(p) be the first derivative of -1/6*p**3 - p + 5/8*p**4 + 3/10*p**5 - 5/4*p**2 - 1. What is h in f(h) = 0?
-1, -2/3, 1
Solve -10*x**2 - 7*x**4 + 302*x**3 - 287*x**3 + 2*x**4 = 0.
0, 1, 2
Let d(g) be the first derivative of g**7/1050 + g**6/300 + 3*g**2/2 + 4. Let c(s) be the second derivative of d(s). Let c(f) = 0. What is f?
-2, 0
Let b(o) be the first derivative of 1/30*o**4 + 0*o - 2/15*o**3 - 1/24*o**6 - 4 + 1/2*o**2 + 1/12*o**5. Let g(a) be the second derivative of b(a). Factor g(f).
-(f - 1)*(5*f - 2)*(5*f + 2)/5
Let c(y) be the second derivative of 9/20*y**5 - 1/2*y**4 - 1/10*y**6 + 0*y**2 + 0 - 8*y + 0*y**3. Factor c(a).
-3*a**2*(a - 2)*(a - 1)
Suppose -16 = 3*m - 22. Determine x, given that 0 - 15/7*x**m - 9/7*x**4 + 3*x**3 + 3/7*x = 0.
0, 1/3, 1
Let m(x) be the third derivative of x**9/40320 - x**8/6720 + x**7/3360 - x**5/60 + 2*x**2. Let j(k) be the third derivative of m(k). Factor j(h).
3*h*(h - 1)**2/2
Factor 11*z + 50 + 5*z - 36*z + 3*z**2 - z**2.
2*(z - 5)**2
Let w(q) = -4*q**3 + 2*q**2 + 2*q - 4. Let a(c) = c**3 + c**2 + c + 1. Let i(d) = a(d) + w(d). Factor i(p).
-3*(p - 1)**2*(p + 1)
Let f(w) be the second derivative of 2*w**6/5 + 6*w**5/5 - 3*w**4/4 - 5*w**3/2 + 3*w**2 - 3*w. Solve f(g) = 0 for g.
-2, -1, 1/2
Let w be (-2)/(-40) + 2 - 2. Let m(t) be the second derivative of 1/30*t**6 + 0*t**2 + 0 + 1/6*t**3 - 1/12*t**4 - w*t**5 + t. Factor m(z).
z*(z - 1)**2*(z + 1)
Let n(k) = -3*k**4 + 29*k**3 - 16*k**2 + 5. Let d(l) = 4*l**4 - 44*l**3 + 24*l**2 - 8. Let r(s) = -5*d(s) - 8*n(s). Suppose r(o) = 0. Calculate o.
0, 1, 2
Factor 3*k - 10*k - 15*k**2 + 10*k + 12*k**3.
3*k*(k - 1)*(4*k - 1)
Let t be 1*(-3)/(-6)*6. What is a in -3*a + 6 - t*a + 3*a + 2*a**2 - 5*a**2 = 0?
-2, 1