**2 + h*c - 1/3.
(c - 1)*(c + 1)/3
Factor -9*a**2 + 65*a - 25 + 23*a**2 + 15*a**2 + 3*a**3.
(a + 5)**2*(3*a - 1)
Find y, given that -3/2*y + 3/2*y**4 - 3/2*y**2 + 0 + 3/2*y**3 = 0.
-1, 0, 1
Let v(z) be the second derivative of -z**6/540 - z**5/180 - z**3/2 - z. Let i(u) be the second derivative of v(u). Let i(f) = 0. Calculate f.
-1, 0
Let w = -21/2 - -11. Let t be 35/(-28)*(-4)/10. Factor h - t*h**4 - h**3 + 0*h**2 + w.
-(h - 1)*(h + 1)**3/2
Let h(r) be the first derivative of -r**3/3 + r - 1. Let z(x) = -4*x**2 - 2*x + 7. Let w(a) = 14*h(a) - 2*z(a). Factor w(i).
-2*i*(3*i - 2)
Let k(h) be the third derivative of 0*h**6 + 0*h**4 + 0*h + 0 + 3*h**2 - 1/6*h**3 + 1/30*h**5 - 1/210*h**7. Factor k(g).
-(g - 1)**2*(g + 1)**2
Let j(w) be the second derivative of -w**5/110 + w**4/33 + 9*w. Factor j(u).
-2*u**2*(u - 2)/11
Let d(r) be the second derivative of -7*r**5/30 + 23*r**4/18 - 2*r**3/3 + 24*r. Solve d(x) = 0 for x.
0, 2/7, 3
Let j(y) = 1. Suppose 4*w - 3*k = -14, -4*k + 2*k = 2*w + 14. Let s(x) = -x**2 + x - 5. Let d(c) = w*j(c) - s(c). Factor d(v).
v*(v - 1)
Suppose -6*t = -2*t - 20. Let v(h) = -h + 7. Let k be v(t). Suppose 9*n + 2*n**k - 3*n**3 - n**2 - 7*n = 0. What is n?
-2/3, 0, 1
Let m(q) = q**2 + 6*q + 5. Let d(s) = s + 1. Let z(g) = -2*d(g) + m(g). Let c be z(-4). Let 3*p**c + 2*p - 2*p**3 + 3*p**2 + 0*p**2 = 0. What is p?
-2, -1, 0
Suppose 0 = -4*l - 4*d + 32, l + 4 = -5*d + 32. Suppose 1/4 - 1/4*c**4 + 1/2*c + 0*c**2 - 1/2*c**l = 0. Calculate c.
-1, 1
Let x(q) = -2*q. Let i be x(-3). Suppose -2*w + i = -0*w. Factor -p**4 + p**2 + p + w - 3 - 2*p + p**3.
-p*(p - 1)**2*(p + 1)
Let f be ((-2)/4 + (-36)/(-24))/3. What is v in f*v + 1/3*v**2 - 2/3 = 0?
-2, 1
Factor 6 - 10*u + 1 + 5*u**2 + 0 - 2.
5*(u - 1)**2
Let y(d) = d**3 + d**2 + 1. Let f(k) = -4*k**3 + k**2 - 3*k - 3. Let o(z) = -4*f(z) - 12*y(z). Factor o(p).
4*p*(p - 3)*(p - 1)
Let i(c) = 3*c**3 - 3*c**2 + 23*c - 23. Let f(h) = 2*h**3 - 2*h**2 + 12*h - 12. Let q(k) = 7*f(k) - 4*i(k). Factor q(y).
2*(y - 2)*(y - 1)*(y + 2)
Let k(l) be the third derivative of l**11/41580 - l**10/8400 + l**9/15120 + 2*l**5/15 - 3*l**2. Let j(g) be the third derivative of k(g). Factor j(w).
2*w**3*(w - 2)*(4*w - 1)
Suppose -j + 3*f = -f - 4, -4*f + 20 = -3*j. Let l be j/27*-5 - 2. Factor -4/9*y**2 + 0 - l*y.
-2*y*(2*y + 1)/9
Let x be 28/10 - 13/13. Factor -9/5*t**2 + x*t + 3/5*t**3 - 3/5.
3*(t - 1)**3/5
Let m = -22 + 27. Let d(y) be the third derivative of 0*y + 0*y**3 - 1/270*y**m - 2*y**2 - 1/54*y**4 + 0. Suppose d(a) = 0. Calculate a.
-2, 0
Let z = 5/17 - -7/34. Factor -l**2 + 1/2 - z*l.
-(l + 1)*(2*l - 1)/2
Let u = 4056/19 - 214. Let j = 6/133 - u. Factor j*i**2 + 0 + 2/7*i**3 + 2/7*i.
2*i*(i + 1)**2/7
Let l(v) be the second derivative of v**4/12 + 2*v**3/3 + 3*v**2/2 + 6*v. What is d in l(d) = 0?
-3, -1
Let s(p) be the first derivative of 0*p**4 + 1/2*p**6 + 3 + 0*p**3 + 0*p**2 + 0*p**5 + 0*p. Determine j, given that s(j) = 0.
0
Solve -9 - 3/2*d + 3/2*d**2 = 0.
-2, 3
Suppose 4*o - 7 = 5. Let i = -1 + o. Factor p**2 + 3*p**2 - 3*p**i + p.
p*(p + 1)
Suppose 0 = -3*i + 8*i - 20. Factor -4*l**2 + 2*l**5 + 4*l**i + 0*l**2 - l - 4*l + 3*l.
2*l*(l - 1)*(l + 1)**3
What is v in -2/7*v + 0 - 2/7*v**5 - 8/7*v**4 - 8/7*v**2 - 12/7*v**3 = 0?
-1, 0
Let z(p) be the first derivative of -2*p**6/3 + 22*p**5/5 - 23*p**4/2 + 46*p**3/3 - 11*p**2 + 4*p + 14. Determine d, given that z(d) = 0.
1/2, 1, 2
Let i(y) be the second derivative of -1/8*y**4 - y**2 + 0 - 1/56*y**7 - 2*y - 17/80*y**5 + 5/6*y**3 + 7/60*y**6. Solve i(q) = 0 for q.
-1, 2/3, 1, 2
Let h(q) be the second derivative of -2*q + 0*q**5 + 0*q**3 + 0*q**2 + 0 + 1/63*q**7 + 1/45*q**6 + 0*q**4. Solve h(v) = 0 for v.
-1, 0
Let m(z) = -z**3 - 4*z**2 + 14. Let l be m(-3). Factor 9/5*p**3 + 36/5*p**4 + 0 + 0*p - 6/5*p**2 + 21/5*p**l.
3*p**2*(p + 1)**2*(7*p - 2)/5
Let g(z) = -3*z**2 + z. Let s(k) = 16*k**2 - 6*k + 1. Let d(o) = -11*g(o) - 2*s(o). Factor d(q).
(q - 1)*(q + 2)
Let m(s) be the first derivative of -2*s**6 - 6*s**5 - 99*s**4/16 - 5*s**3/2 - 3*s**2/8 - 39. Factor m(x).
-3*x*(x + 1)**2*(4*x + 1)**2/4
Let g(u) = -21*u**5 - 21*u**4 - 9*u**3 + 9*u - 9. Let k(t) = -5*t**5 - 5*t**4 - 2*t**3 + 2*t - 2. Let c(y) = -2*g(y) + 9*k(y). Factor c(h).
-3*h**4*(h + 1)
Let w be (-6)/8*-1*(113 - 109). Factor 2/7*j**4 - 2/7*j**w + 0*j - 4/7*j**2 + 0.
2*j**2*(j - 2)*(j + 1)/7
Let c(p) = -p - 7. Let h be c(-7). Suppose 4*f + h = 4. Suppose 0 - 3*o**2 + o**4 + f + o**2 = 0. What is o?
-1, 1
Find j such that -9/4*j**3 + 3/4*j**4 + 9/4*j**2 - 3/4*j + 0 = 0.
0, 1
Suppose 0 = -2*g + 7 + 1. Let b(k) be the first derivative of -3*k**g - 1 - 12*k**2 - 26/3*k**3 - 2/5*k**5 - 8*k. Suppose b(o) = 0. What is o?
-2, -1
Let y(r) be the first derivative of r**4/36 + 2*r**3/27 - r**2/6 - 9. Factor y(k).
k*(k - 1)*(k + 3)/9
Determine o, given that 0 + 9/7*o**2 + 3/7*o**3 + 0*o = 0.
-3, 0
Let f(b) = b**2 - b - 42. Let j be f(-6). What is l in 0*l**2 + 1/2*l**3 - 1/4*l - 1/4*l**5 + 0 + j*l**4 = 0?
-1, 0, 1
Solve -24*i**2 - i**3 + 3*i**5 + 12*i**3 - 18*i**4 + 25*i**3 = 0 for i.
0, 2
Let v(b) be the third derivative of 0 + b**2 + 0*b + 0*b**3 - 1/30*b**5 + 1/42*b**4. Factor v(l).
-2*l*(7*l - 2)/7
Let m(y) be the third derivative of -y**7/1260 - y**6/720 - 29*y**2. Determine s, given that m(s) = 0.
-1, 0
Let f(z) = -z**5 - 7*z**4 - 3*z**3 + 9*z**2 + 4*z + 2. Let t(v) = v**5 + 13*v**4 + 6*v**3 - 18*v**2 - 7*v - 5. Let o(d) = -5*f(d) - 2*t(d). Factor o(r).
3*r*(r - 1)*(r + 1)**2*(r + 2)
Factor 2/7*y**5 - 4/7*y**2 + 2/7*y**4 + 2/7*y + 2/7 - 4/7*y**3.
2*(y - 1)**2*(y + 1)**3/7
Suppose 0 = k - 6 + 4. Solve 3*b - 3*b + 2*b**3 - k*b**2 + 0*b = 0 for b.
0, 1
Factor 5 - 3*g**3 + 14*g + 3*g**3 + 5*g**3 + g + 15*g**2.
5*(g + 1)**3
Let m = -525/52 + 41/4. Let l(j) = j**2 + 12*j + 13. Let o be l(-11). What is k in 0*k + 0*k**4 + m*k**5 + 0 - 2/13*k**3 + 0*k**o = 0?
-1, 0, 1
Let v(j) = -j**5 + 4*j**4 + 3*j**2 + 3*j. Let k(x) = 3*x**5 - 8*x**4 - 5*x**2 - 5*x. Let z(s) = -3*k(s) - 5*v(s). What is u in z(u) = 0?
0, 1
Let w(m) be the third derivative of 0*m**3 - 2*m**2 + 0*m**4 + 0*m - 1/30*m**5 + 1/105*m**7 + 1/168*m**8 + 0 - 1/60*m**6. Let w(h) = 0. Calculate h.
-1, 0, 1
Let v(b) be the third derivative of b**5/270 - b**4/18 + 5*b**3/27 + 7*b**2. Suppose v(d) = 0. What is d?
1, 5
Suppose -4*n + 1 + 7 = 0. Factor -1/3 - c**3 + 5/3*c**n - 1/3*c.
-(c - 1)**2*(3*c + 1)/3
Let j(n) be the second derivative of 4*n**7/105 - 7*n**6/75 + n**5/25 + n**4/30 - 4*n. Factor j(a).
2*a**2*(a - 1)**2*(4*a + 1)/5
Let x(z) be the second derivative of z**6/15 - z**4/6 + 6*z. Find r such that x(r) = 0.
-1, 0, 1
Let i(k) be the second derivative of -k**4/60 - 2*k**3/15 - 3*k**2/10 - 4*k. Factor i(m).
-(m + 1)*(m + 3)/5
Solve -16/9*d**3 + 0*d - 32/9*d**2 + 0 - 2/9*d**4 = 0 for d.
-4, 0
Find r such that -2/9*r**5 + 0*r - 4/9*r**4 + 4/9*r**2 + 0 + 2/9*r**3 = 0.
-2, -1, 0, 1
Let f be (-7)/(-2)*280/98. Let l(c) = -c**3 + 9*c**2 + 11*c - 7. Let g be l(f). Suppose -1/2*r**4 + 1/2*r**2 + 0 - r - 1/2*r**5 + 3/2*r**g = 0. Calculate r.
-2, -1, 0, 1
Find b such that -16/3*b**4 + 20/3*b**2 + 2*b - 4/3 + 0*b**3 - 2*b**5 = 0.
-2, -1, 1/3, 1
Let o be (3*-3)/(-3)*(-4)/(-108). Let t(p) be the first derivative of 3 - o*p**2 + 10/27*p**3 - 2/9*p - 1/6*p**4. Factor t(y).
-2*(y - 1)**2*(3*y + 1)/9
Let k = -4/27 + 89/54. Factor k*j**2 - 3/2 + 9/2*j - 9/2*j**3.
-3*(j - 1)*(j + 1)*(3*j - 1)/2
Let j(h) be the first derivative of h**8/2100 + h**7/525 + h**6/450 - 8*h**3/3 - 2. Let f(u) be the third derivative of j(u). Solve f(r) = 0 for r.
-1, 0
Let n(q) be the first derivative of -q**8/1344 - 17*q**7/3360 - q**6/90 - q**5/120 - 5*q**3/3 + 3. Let v(x) be the third derivative of n(x). Factor v(h).
-h*(h + 1)*(h + 2)*(5*h + 2)/4
Let b be (8/(-10))/(9/(-5)). Suppose 7*s - 5*s = -4*s. Determine y so that -b*y**2 + 2/9*y**4 + 0*y + s*y**3 + 2/9 = 0.
-1, 1
Let s(w) = -6*w**4 - w**3 - 5*w**2 + 5*w - 5. Let r(f) = 3*f**4 + 3*f**2 - 3*f + 3. Let n(x) = -5*r(x) - 3*s(x). Let n(q) = 0. What is q?
-1, 0
Factor -3*k**2 - 2*k**2 - 1 + 8*k + k**2 - 3.
-4*(k - 1)**2
Let n = 321/5 - 64. Let v(p) be the first derivative of -1/15*p**3 - 2 + n*p + 0*p**2. Find d such that v(d) = 0.
-1, 1
Let y(w) be the first derivative of -3/2*w**2 + 0*w - 4*w**3 - 4. Solve y(o) = 0.
-1/4, 0
