, -1, 1, 2
Let x be 3 + (5/4 - 4). Factor -1/2 + 1/4*s**2 + x*s.
(s - 1)*(s + 2)/4
Let j(y) be the first derivative of -y**5/90 + y**3/9 + y**2/2 + 5. Let v(t) be the second derivative of j(t). Factor v(a).
-2*(a - 1)*(a + 1)/3
Let o(u) be the second derivative of 3*u**6/10 + 21*u**5/20 + 5*u**4/4 + u**3/2 + 2*u. Factor o(s).
3*s*(s + 1)**2*(3*s + 1)
Let r(h) = h**3 + 4*h**2 - 6*h - 3. Let x be r(-5). Suppose x = y - 3. Let a**2 - 1 + y - 3 - 2 = 0. What is a?
-1, 1
Let y be (-176)/22 - (-88)/10. Let -12/5*q**2 + y*q**3 + 6/5*q**5 - 2*q + 14/5*q**4 - 2/5 = 0. What is q?
-1, -1/3, 1
Let c = -25 - -29. Let o = c - -1. Find u such that -1 - 2*u**3 - u**2 + 2*u**4 - 1/2*u**o + 5/2*u = 0.
-1, 1, 2
Factor -735/2*b**2 - 105/2*b - 5/2 - 1715/2*b**3.
-5*(7*b + 1)**3/2
Let i(b) = b**2 + 3*b. Let v be i(0). Factor v*s**2 + 0*s**4 - 1/3*s**3 + 0 + 0*s + 1/3*s**5.
s**3*(s - 1)*(s + 1)/3
Let q(u) = 4*u**3 + u**2 - 8*u. Let v(x) = 4*x**3 - 8*x. Let o(r) = -4*q(r) + 3*v(r). Suppose o(h) = 0. What is h?
-2, 0, 1
Factor 242/7*i + 2/7*i**3 + 44/7*i**2 + 0.
2*i*(i + 11)**2/7
Let t(i) be the third derivative of -1/30*i**4 + 3*i**2 - 1/525*i**7 + 0 + 0*i**3 - 1/75*i**6 + 0*i - 1/30*i**5. Find h such that t(h) = 0.
-2, -1, 0
Find q such that -3/5 + 6*q**2 + 0*q + 9*q**4 - 12/5*q**5 - 12*q**3 = 0.
-1/4, 1
Factor -b + 1/2*b**2 + 0.
b*(b - 2)/2
Let w(y) be the third derivative of y**6/180 - y**3/2 + y**2. Let l(d) be the first derivative of w(d). What is c in l(c) = 0?
0
Suppose -4*g + g + 6 = 0. Factor 2 + 5 - 5 - 4*j**2 + g*j**4.
2*(j - 1)**2*(j + 1)**2
Solve -4*r**4 + r**4 + 0 + 3 - 9*r + 3*r + 6*r**3 = 0.
-1, 1
Let k(c) be the third derivative of -c**7/840 + c**6/90 - c**5/30 + c**3/2 - 3*c**2. Let h(s) be the first derivative of k(s). Factor h(d).
-d*(d - 2)**2
Let h = 130 + -88. Let j be (4 - 8) + h/10. Factor -4/5*y + 4/5*y**3 - j*y**2 + 1/5.
(y - 1)*(y + 1)*(4*y - 1)/5
Let q(o) be the first derivative of o**7/280 - o**6/72 + o**5/120 + o**4/24 + o**3 + 3. Let x(p) be the third derivative of q(p). Factor x(k).
(k - 1)**2*(3*k + 1)
Let s = -27 + 12. Let a = -11 - s. Suppose -4*c**2 - 5*c**3 + 4 - c**3 + a*c + 2*c = 0. What is c?
-1, -2/3, 1
Let m(l) be the third derivative of -2*l**7/105 - l**6/30 + 2*l**5/15 + 5*l**2. Solve m(a) = 0 for a.
-2, 0, 1
Let d(j) be the third derivative of -j**5/120 - j**4/12 - j**3/4 - 7*j**2. Factor d(b).
-(b + 1)*(b + 3)/2
Suppose -4*d + 1 = -3*d. Let h be (0/(-3 - -2))/d. Determine u, given that -u**2 - u + u**4 + 3*u**3 + h*u**5 + 3*u**5 - 5*u**5 = 0.
-1, -1/2, 0, 1
Let y(j) be the second derivative of -j**6/240 + j**4/48 + 5*j**2/2 - 8*j. Let h(u) be the first derivative of y(u). Factor h(p).
-p*(p - 1)*(p + 1)/2
Let j(p) be the third derivative of p**5/270 + 6*p**2. Factor j(z).
2*z**2/9
Factor 10*a**4 - 9*a**4 - 2*a**3 + a**4.
2*a**3*(a - 1)
Suppose -i - 2*i = n - 19, -n + i = -3. Suppose n*d - 22*d**2 + 11*d - 27 + 19*d**2 = 0. What is d?
3
Factor -313*w**3 + 309*w**3 + 2*w**2 - 2 + 4*w**2.
-2*(w - 1)**2*(2*w + 1)
Let v(i) = i**3 - 2*i**2 + i - 2. Let d(t) = -t + t**2 + 1 - t + t. Let p(k) = -2*d(k) - v(k). Factor p(s).
-s*(s - 1)*(s + 1)
Suppose 2*f = 5*f + 24. Let o be f/36 - 20/(-9). Suppose -2/7*b**o + 0*b + 0 - 2/7*b**3 = 0. Calculate b.
-1, 0
Let c(p) = 4*p**4 - 20*p**2 - 6*p + 10. Let g(j) = -j**4 + 0*j + 0*j + 1 + 10*j**3 - 11*j**3 - j**2. Let y(d) = -c(d) + 6*g(d). Solve y(q) = 0.
-1, 2/5, 1
Let j = 9 - 10. Let i = j + 3. Find q such that -1/2*q**4 - 1 - 9/2*q**i - 5/2*q**3 - 7/2*q = 0.
-2, -1
Let y = -2 - -4. Let m be y/(-3) - (-35)/30. Determine q, given that 1/4 + 1/4*q**2 + m*q = 0.
-1
Let h(n) be the third derivative of n**7/3780 - n**6/405 + n**5/135 - n**3/2 + 4*n**2. Let r(c) be the first derivative of h(c). Let r(y) = 0. Calculate y.
0, 2
Let u(g) be the first derivative of g**3/3 - 3*g**2/2 + 5*g - 2. Let v be u(4). Factor 9*a**3 + 2 - 1 - v*a - 5*a**2 - 3 + 7*a**4.
(a - 1)*(a + 1)**2*(7*a + 2)
Let w(i) be the third derivative of 1/336*i**8 + 1/30*i**5 + 0 - 1/105*i**7 - 1/24*i**4 + 0*i - 3*i**2 + 0*i**3 + 0*i**6. Factor w(f).
f*(f - 1)**3*(f + 1)
Let s be 7/(-9) + 9/81*9. Factor 0 + 2/9*h + s*h**3 - 4/9*h**2.
2*h*(h - 1)**2/9
Let b be ((3/8)/((-12)/(-48)))/2. Factor 3/4*n - 3/4*n**2 + 0 - 3/4*n**3 + b*n**4.
3*n*(n - 1)**2*(n + 1)/4
Let m = 7/8 + -33/56. Let x(z) be the second derivative of 0 + z + 1/10*z**5 - 8/21*z**4 - m*z**2 + 11/21*z**3. Solve x(k) = 0.
2/7, 1
Let w be 6/9 - (-87)/(-36). Let f = -5/12 - w. Find a such that 8/9*a**2 - 2/3*a**5 - 4/9 - 2/3*a + f*a**3 - 4/9*a**4 = 0.
-1, -2/3, 1
Let a(s) be the second derivative of s**5/70 - s**4/6 + 4*s**3/21 + 12*s**2/7 + 8*s. Determine o, given that a(o) = 0.
-1, 2, 6
Let m(u) be the second derivative of -u**6/30 + u**4/12 + u. Factor m(b).
-b**2*(b - 1)*(b + 1)
Suppose -6*z = -2*z - 12. Let p = 4 - 1. Factor -w**2 + 0*w**z + p*w**3 - 5*w**3 - w**4.
-w**2*(w + 1)**2
Let y(b) = -b**3 + 4*b**2 - b - 1. Let i be y(3). Suppose 0 = i*r - 2*r. Factor 2/7*q**2 + 2/7*q + r.
2*q*(q + 1)/7
Let b(v) be the first derivative of -2*v**3/13 - 5*v**2/13 + 4*v/13 + 22. Suppose b(i) = 0. What is i?
-2, 1/3
Suppose 3*i - 2*h - 6 = i, -4*i - 2*h + 12 = 0. Find l, given that -4/7*l**i + 6/7*l**4 + 0 + 0*l - 2/7*l**2 = 0.
-1/3, 0, 1
Let c = -36/13 + 134/39. What is i in -5/3*i - 1/3*i**3 - c - 4/3*i**2 = 0?
-2, -1
Let d = 1591/2685 + 4/537. Factor -1/5*p**2 - 2/5 + d*p.
-(p - 2)*(p - 1)/5
Let g(o) be the third derivative of o**8/84 - o**6/15 + o**4/6 + 7*o**2. Factor g(z).
4*z*(z - 1)**2*(z + 1)**2
Let a(s) be the second derivative of 3/50*s**5 + 1/210*s**7 + 0 + 0*s**2 + 1/15*s**4 - 3*s + 1/30*s**3 + 2/75*s**6. Factor a(y).
y*(y + 1)**4/5
Let r(t) = -5*t**4 + 4*t**3 + 5*t**2 - 4. Let o(f) = 4*f**4 - 5*f**3 - 2 - 6*f**2 + 4 + 3 + 2*f**4. Let b(p) = 4*o(p) + 5*r(p). Factor b(u).
-u**2*(u - 1)*(u + 1)
Solve 2/3*c**2 + 0*c + 0 = 0.
0
Factor -9/5*m**2 + 0*m**3 + 3/5*m**4 + 0 + 6/5*m.
3*m*(m - 1)**2*(m + 2)/5
Let d = -2 - 4. Let x be -1*(-2)/d*-7. Solve -2/3*q**2 + 0 + 0*q + x*q**4 - 5/3*q**3 = 0 for q.
-2/7, 0, 1
Suppose -4*n = 3*w - 1, 11*w + 20 = 15*w - 4*n. Find z, given that -2*z - 22/3*z**2 + 8/3*z**w + 0 = 0.
-1/4, 0, 3
Let p = -4912 - -24752/5. Factor 0 - 432/5*v**4 + 432/5*v**3 - p*v**2 + 32/5*v + 162/5*v**5.
2*v*(3*v - 2)**4/5
Suppose -5 = -5*h + 5*j, -h + 2*h - 5 = -3*j. Determine v, given that 3 + 2*v**3 + 4*v**2 + h - 5 = 0.
-2, 0
Suppose a - 20 = -3*a. Suppose -o + a - 1 = 0. Find p, given that -2/3*p + 2/3*p**3 - 2/3*p**2 + 2/3*p**o + 0 = 0.
-1, 0, 1
Factor 0 - 2/5*v**2 + 0*v + 0*v**3 + 2/5*v**4.
2*v**2*(v - 1)*(v + 1)/5
Let a(o) be the third derivative of -o**7/525 + o**6/150 - o**4/30 + o**3/15 + 4*o**2. Suppose a(z) = 0. Calculate z.
-1, 1
Let b be 97/11 - 8/(-44). Let q(j) = 2*j - 18. Let y be q(b). Let -1/2*u**3 + y + 0*u**2 + 1/4*u**5 + 1/4*u + 0*u**4 = 0. Calculate u.
-1, 0, 1
Let c = -1/20 + 1/15. Let w(a) be the third derivative of 0 - c*a**5 - 2*a**2 + 1/24*a**4 + 1/3*a**3 + 0*a. Factor w(r).
-(r - 2)*(r + 1)
Let z be 29/(-2)*2 - -1. Let l be ((-2)/7)/(12/z). Factor 0 + 0*w - 2/3*w**2 - l*w**3.
-2*w**2*(w + 1)/3
Let y = 0 + 2. Factor -2*q - y*q**2 - q - q.
-2*q*(q + 2)
Let q(p) = p**3 + 4*p**2 + 2*p + 1. Let l be q(-3). Suppose l*a = -2*o + 6, 2*a - 5*a = 3*o. Suppose -2/7*b + 2/7*b**a - 2/7*b**2 + 2/7 = 0. Calculate b.
-1, 1
Let c be (-3)/(-216)*(-2)/(-15). Let z(r) be the third derivative of 1/135*r**5 + 0*r - c*r**6 - r**2 - 1/108*r**4 + 0 + 0*r**3. Let z(u) = 0. Calculate u.
0, 1
Let o(d) be the first derivative of d**3/12 + 3*d**2/8 - d + 2. Factor o(j).
(j - 1)*(j + 4)/4
Let g(q) be the third derivative of -q**8/40320 + q**7/5040 - q**6/1440 + q**5/30 - 2*q**2. Let p(x) be the third derivative of g(x). Factor p(t).
-(t - 1)**2/2
Suppose -4 = -q - 2. Factor -q*r - 3*r + 5*r + r**2.
r**2
Suppose -34/13*r**2 + 162/13 + 126/13*r + 2/13*r**3 = 0. Calculate r.
-1, 9
Suppose -w - 5*c - 2 = -c, 2*w - 3*c - 7 = 0. Suppose 0*k = w*k. What is l in 0*l - 117/4*l**4 - l**2 + 81/4*l**5 + 10*l**3 + k = 0?
0, 2/9, 1
Suppose 0 = 4*s - 2*l - 16, -3*s = -0*l + 5*l - 12. Factor t**3 - t + 16 - 11*t**3 - 12*t**2 - 2*t**s + 9*t.
-2*(t - 1)*(t + 2)**3
Let t be -1 + 3 - 0/(-3). Factor -4*k**2 - t*k**3 + 2*k + 9 - 4 - 1.
-2*(k - 1)*(k + 1)*(k + 2)
Let b(z) be the seco