 - 1/3*x**2.
-x*(x - 1)/3
Let p be ((-2)/54)/(20/(-6)). Let c(a) be the second derivative of -p*a**5 + 4/9*a**2 + 5/54*a**4 + 0 - 8/27*a**3 - 3*a. Factor c(d).
-2*(d - 2)**2*(d - 1)/9
Let s(b) be the third derivative of 0 + 0*b - 2*b**2 + 1/24*b**4 + 0*b**3 - 1/60*b**5. Factor s(h).
-h*(h - 1)
Let r(g) be the first derivative of -g**6/4 + 3*g**5/10 + 3*g**4/8 - g**3/2 - 1. Suppose r(a) = 0. What is a?
-1, 0, 1
Let b(l) be the third derivative of 5*l**8/1344 - l**7/140 + l**6/480 - 11*l**2. Factor b(m).
m**3*(m - 1)*(5*m - 1)/4
Let o(j) be the third derivative of -j**8/6720 + j**7/1260 - j**6/720 + j**4/24 - 2*j**2. Let z(t) be the second derivative of o(t). Let z(y) = 0. Calculate y.
0, 1
Let a(n) = -n**3 + 2*n**2 - n + 10. Let i be a(0). Let d be i/(-4)*(-24)/20. What is r in 0*r + 0*r**d - 1/3*r**2 + 0 + 1/3*r**4 = 0?
-1, 0, 1
Factor -2/5*l**3 + 0 + 2/5*l + 2/5*l**4 - 2/5*l**2.
2*l*(l - 1)**2*(l + 1)/5
Let z(o) be the first derivative of -o**5/5 - 3*o**4/2 - 13*o**3/3 - 6*o**2 - 4*o + 7. Let z(u) = 0. What is u?
-2, -1
Suppose -4*v + 3 = -5. Let z(g) be the first derivative of 1/9*g**6 + 0*g - 1/6*g**4 + 0*g**v + 0*g**5 - 3 + 0*g**3. Solve z(f) = 0.
-1, 0, 1
Let -360/7*x + 27/7 + 1200/7*x**2 = 0. Calculate x.
3/20
Let n(c) = -5*c**2 - 6*c - 4. Let l(a) = 6*a**2 + 7*a + 5. Suppose -3 = 2*f - 2*p - 1, 3*p - 27 = -3*f. Let b(t) = f*l(t) + 5*n(t). Solve b(m) = 0.
-2, 0
Let a(k) be the first derivative of -k**7/2940 + k**6/1260 - 5*k**3/3 + 2. Let j(l) be the third derivative of a(l). Factor j(y).
-2*y**2*(y - 1)/7
Let j(t) be the first derivative of 4*t**3/3 - 6*t**2 + 8*t + 6. Factor j(q).
4*(q - 2)*(q - 1)
Let x(o) be the second derivative of o**7/3360 - o**6/2880 + o**4/3 - 3*o. Let p(v) be the third derivative of x(v). Factor p(q).
q*(3*q - 1)/4
Let b(u) be the third derivative of -u**5/8 + 25*u**4/48 + 5*u**3/6 + 24*u**2. Suppose b(i) = 0. Calculate i.
-1/3, 2
Let k(t) be the first derivative of -t**4/36 + 2*t**3/9 - 2*t**2/3 + 2*t - 2. Let d(g) be the first derivative of k(g). Determine r, given that d(r) = 0.
2
Let n(s) = -s**2 + 7*s - 3. Let k(z) = -z**3 + 7*z**2 - 4*z - 6. Let w be k(6). Let a be n(w). Let f**2 - a*f**2 + 0*f**4 + 2*f**4 = 0. Calculate f.
-1, 0, 1
Let d(p) = p**3 - 9*p**2 - 9*p - 5. Let i be d(10). Suppose 2*s - i = s. Factor -3*b - 2*b - 6*b**3 - 2*b + 6*b**2 + s*b + 2*b**4.
2*b*(b - 1)**3
Let a(r) be the first derivative of 3*r**5 - 35*r**4/4 + 5*r**3 + 15*r**2/2 - 10*r + 18. Factor a(g).
5*(g - 1)**3*(3*g + 2)
Suppose 2*k = -4 - 36. Let r be (-26)/(-8) - (-5)/k. Factor d - d**2 - 4*d + 0*d + 0*d + 3*d**r + 1.
(d - 1)*(d + 1)*(3*d - 1)
Let n(f) = -f**2 - f - 1. Suppose 3*m + 2*p = p + 4, 2 = m + p. Let t(y) = -4*y**5 + 4*y**4 + 8*y**3 - 7*y**2 - 3*y + 5. Let r(k) = m*n(k) + t(k). Factor r(l).
-4*(l - 1)**3*(l + 1)**2
Suppose 0 = 3*v + 6, u - 12 = -3*v + 8*v. Let t = 2 + -2/3. Factor 2/3*n**u - t - 2/3*n.
2*(n - 2)*(n + 1)/3
Determine m, given that m**4 - 1 - 9*m**4 + 6*m**2 - 10*m**3 + 3 + 10*m = 0.
-1, -1/4, 1
Let m be 2 + -1 - (-1 + 0). Suppose 0 = 5*j - m*j - 9. What is i in j*i**5 - 3*i**4 - 5*i**4 + 5*i**4 + 0*i**5 = 0?
0, 1
Let g be (0 + -118)/((-856)/18). Let c = g - -2/107. Solve -9/4*b**2 + c*b**3 + 0 + 1/2*b = 0 for b.
0, 2/5, 1/2
Factor 6/5*n - 6/5*n**3 + 3/5*n**4 - 3/5 + 0*n**2.
3*(n - 1)**3*(n + 1)/5
Suppose -3*d + j = 1 - 5, 4 = -2*d + 4*j. Solve -3*i**2 + 10*i**2 - 5 - 2*i**4 - 3*i**d + 3 = 0 for i.
-1, 1
Let m be 6 + (-15)/25*(6 - 1). Suppose 0 = 3*f - f + 4*y - 16, 0 = 5*f - 5*y + 5. Solve 5*x**3 + 2*x**3 - 5*x**m - 2*x + 2 - 2*x**f = 0.
-1, 1
Suppose 0 = -w - 4*w + 100. Let h be w/(-12)*(-10)/25. Determine k, given that 0 + 0*k + h*k**2 = 0.
0
Let u(i) be the second derivative of i**7/105 - i**6/75 - i**5/50 + i**4/30 + 37*i. Factor u(q).
2*q**2*(q - 1)**2*(q + 1)/5
Let i(m) be the second derivative of -1/6*m**4 + 0 + 6*m + 1/25*m**6 - 2/105*m**7 + 1/10*m**5 + 2/5*m**2 - 1/5*m**3. Find o such that i(o) = 0.
-1, 1/2, 1, 2
Let n(c) = c + 8. Let t be n(-8). Let h(z) be the second derivative of t + 0*z**3 + 1/35*z**5 + z - 1/42*z**4 + 0*z**2. Factor h(s).
2*s**2*(2*s - 1)/7
Solve 28*a - 1 - 81*a**4 - 2 + 198*a**3 + 16*a - 157*a**2 - 1 = 0.
2/9, 1
Let z(s) be the third derivative of 2*s**7/105 - 11*s**6/120 + s**5/12 + s**4/12 + 3*s**2. Factor z(r).
r*(r - 2)*(r - 1)*(4*r + 1)
Let k(d) = -d**2 + d - 1. Let x(z) = 6*z + 3. Let g(p) = k(p) - x(p). Factor g(q).
-(q + 1)*(q + 4)
Let u(j) = -j**4 + 3*j**3 - 7*j**2 + 5*j + 5. Let i(q) = q**4 - 3*q**3 + 8*q**2 - 6*q - 6. Let l(o) = 5*i(o) + 6*u(o). Factor l(g).
-g**2*(g - 2)*(g - 1)
Let r = -27 + 82/3. Let d(z) be the first derivative of -2 + 3/2*z**2 + 2*z + r*z**3. Factor d(i).
(i + 1)*(i + 2)
Let f(v) be the third derivative of -833*v**6/30 - 574*v**5/15 - 62*v**4/3 - 16*v**3/3 - 66*v**2. Factor f(s).
-4*(7*s + 2)**2*(17*s + 2)
Let l(f) be the second derivative of f**6/33 - 9*f**5/110 + f**4/22 + f**3/33 + 21*f. Suppose l(g) = 0. What is g?
-1/5, 0, 1
Find c, given that 1/4*c**2 - 3/4*c - 1 = 0.
-1, 4
Let f = -34/7 + 158/21. Factor 10/3*v + 2/3*v**3 - f*v**2 - 4/3.
2*(v - 2)*(v - 1)**2/3
Find w such that 10 - 12 + 4*w**2 - 5*w**2 - 3*w = 0.
-2, -1
Let w(u) be the second derivative of u**7/280 - u**6/120 + 2*u**3/3 - 6*u. Let z(s) be the second derivative of w(s). Factor z(g).
3*g**2*(g - 1)
Let m(r) = -9*r**3 + 5*r**2 - 7*r. Let y(x) = -x**2 + x. Let q(a) = 5*m(a) + 35*y(a). Factor q(f).
-5*f**2*(9*f + 2)
Let o(a) be the first derivative of -1 + 1/3*a**2 - 1/6*a**4 + 4/3*a - 4/9*a**3. Factor o(j).
-2*(j - 1)*(j + 1)*(j + 2)/3
Let r(a) = a**5 + a**4 - a**2 + a + 1. Let i(l) = 9*l**5 + 12*l**4 + 3*l**3 - 6*l**2 + 6*l + 6. Let q(d) = i(d) - 6*r(d). Factor q(z).
3*z**3*(z + 1)**2
Suppose 35 = 2*l + 9. Suppose -l - 3*x - x**2 + 11 + 0*x**2 = 0. What is x?
-2, -1
Let u(d) = d**2 + 3*d - 15. Let w be u(-7). Let j be 28/w - 0 - 2. Factor 0 - 6/13*p**4 - 6/13*p**3 + 0*p - j*p**5 - 2/13*p**2.
-2*p**2*(p + 1)**3/13
Let v(c) be the second derivative of -c**4/12 - c**3/6 - 47*c. What is f in v(f) = 0?
-1, 0
Factor 0 - 1/2*k**4 - 3/2*k**3 + 1/2*k**2 + k + 1/2*k**5.
k*(k - 2)*(k - 1)*(k + 1)**2/2
Factor 44/5*a**2 + 2/5*a**5 + 6/5 + 14/5*a**4 + 26/5*a + 36/5*a**3.
2*(a + 1)**4*(a + 3)/5
Let b(u) = 4*u**5 - 4*u**4 - 10*u**3 - 2*u**2 - 6*u. Let f(a) = -a**3 - a**2 - a. Let n(l) = b(l) - 6*f(l). Factor n(y).
4*y**2*(y - 1)**2*(y + 1)
What is d in -2/13*d**3 - 4/13*d + 0 - 6/13*d**2 = 0?
-2, -1, 0
Let u(j) be the third derivative of j**7/6300 - j**6/1800 - j**5/150 + j**4/24 - j**2. Let t(s) be the second derivative of u(s). Factor t(o).
2*(o - 2)*(o + 1)/5
Let h(o) be the first derivative of 3/14*o**4 + 2/7*o**2 + 1/105*o**6 - 1/3*o**3 + 2*o - 1 - 1/14*o**5. Let y(f) be the first derivative of h(f). Factor y(u).
2*(u - 2)*(u - 1)**3/7
Let g(x) be the third derivative of 0*x - 2/15*x**3 + 0 + 1/75*x**5 + 1/300*x**6 - 2*x**2 - 1/60*x**4. Factor g(q).
2*(q - 1)*(q + 1)*(q + 2)/5
Let s(t) = t**3 - 8*t**2 + 8*t - 5. Let n = 18 - 11. Let q be s(n). Factor -q*a + 2*a**3 - a**2 + 1 + 2*a**3 - 2*a.
(a - 1)*(a + 1)*(4*a - 1)
Let s = 12 - 71/6. Suppose -s*w**3 - 1/3*w + 1/2*w**2 + 0 = 0. What is w?
0, 1, 2
Factor 4/3*z**2 - 2*z + 0 + 2/3*z**3.
2*z*(z - 1)*(z + 3)/3
Let i(z) be the third derivative of -z**7/15 + z**6/12 + 3*z**5/10 - 5*z**4/12 - 2*z**3/3 - 15*z**2. Suppose i(m) = 0. What is m?
-1, -2/7, 1
Let r(n) be the first derivative of -n**3 + 4*n**2 + 3*n + 2. Factor r(s).
-(s - 3)*(3*s + 1)
Let v(j) be the third derivative of 1/240*j**5 + 0*j - 1/480*j**6 + 0 + 2*j**2 - 1/24*j**3 + 1/96*j**4. What is b in v(b) = 0?
-1, 1
Suppose 0 = 4*y + 4*p - 4, -2 = 3*y + 5*p + 1. Suppose -7*o - 3 - y*o**2 + 15*o - o**2 = 0. Calculate o.
3/5, 1
Let j(w) = -w**3 + 8*w**2 - 7*w. Let d be j(7). Let q(z) be the first derivative of -1 + 2/9*z**3 + 7/15*z**5 + 3/4*z**4 + 0*z**2 + d*z. Factor q(x).
x**2*(x + 1)*(7*x + 2)/3
Factor -28/17*w + 30/17 - 2/17*w**2.
-2*(w - 1)*(w + 15)/17
Factor 2/9*f**2 + 0 - 4/9*f.
2*f*(f - 2)/9
Let j be ((-4)/6)/((-12)/9). Solve 0*o - j*o**2 + 1/2 = 0.
-1, 1
Let k(h) be the first derivative of 28/3*h**3 + 2 - 69/4*h**4 - 2*h**2 + 0*h - 25/6*h**6 + 14*h**5. Suppose k(v) = 0. What is v?
0, 2/5, 1
Let m(f) be the first derivative of -1/10*f**5 + 0*f**4 + 0*f + 1/6*f**3 - 