Factor 2/3*y**2 + 0 - 2/3*y**4 - 10/3*y + 10/3*y**3.
-2*y*(y - 5)*(y - 1)*(y + 1)/3
Factor -3*s**5 + 9*s**2 - 13*s**2 - s**5 + 4*s**3 + 4*s**4.
-4*s**2*(s - 1)**2*(s + 1)
Suppose 0 = 2*k - 4*m, -2*k - 3*m + 3 = -4. Factor 12*i**2 + 20*i - 9*i**2 + 20 + 2*i**k.
5*(i + 2)**2
Let p = 485/24 - 241/12. Determine m so that -13/8*m**2 + p - 3/2*m = 0.
-1, 1/13
Suppose -26 = 6*y - 80. Factor 6*i + 11 + 22*i**2 - 18*i**2 - y.
2*(i + 1)*(2*i + 1)
Let l be (-5)/(-45)*6 - 5/12. Factor -9/4 + 3/2*c - l*c**2.
-(c - 3)**2/4
Factor -29*z + 21 + 51 + 9*z + 4*z**2 + 56*z.
4*(z + 3)*(z + 6)
Let p(m) = 2*m + 2. Let f be p(3). Factor l + f*l**3 + 6*l + l + 12*l**3 + 28*l**2.
4*l*(l + 1)*(5*l + 2)
Let a = 9 + -15. Let p = 9 + a. Factor 0*x - x**p + 6 + 4*x**3 + 21*x - 30*x**3.
-3*(x - 1)*(3*x + 1)*(3*x + 2)
Factor 1422*h**2 + 8*h**3 - 3*h**3 - 5*h - 4*h**4 - 1419*h**2 + 1.
-(h - 1)**2*(h + 1)*(4*h - 1)
Factor 1/9*d**2 + d + 14/9.
(d + 2)*(d + 7)/9
Let u(i) be the second derivative of -9*i**5/140 + 62*i**4/7 - 5207*i**3/14 + 5043*i**2/7 - 103*i. Factor u(r).
-3*(r - 41)**2*(3*r - 2)/7
Let d(s) be the second derivative of 3*s**5/160 - 7*s**4/8 - s + 44. Determine x, given that d(x) = 0.
0, 28
Let -9/5*j**2 + 0 + 6/5*j + 3/5*j**3 = 0. What is j?
0, 1, 2
Let x(a) be the second derivative of 1/70*a**5 + 0 - 5/42*a**4 + 1/3*a**3 - 15*a - 3/7*a**2. Suppose x(s) = 0. Calculate s.
1, 3
Let p be (2/3)/((-4)/(-300)). Factor -p*a**2 + 13*a**2 - 12*a + 4*a**3 - 4 - 8*a**3 + 25*a**2.
-4*(a + 1)**3
Let z(h) = -8*h**3 - 2*h**2 + 2*h - 4. Let j(n) = 6*n**3 + n**2 - n + 4. Let d(s) = 6*j(s) + 5*z(s). Suppose d(x) = 0. What is x?
-1, 1
Let m = -40825/2 + 20414. Suppose -m - 7/4*d**2 + 17/4*d = 0. What is d?
3/7, 2
Let h be (680/30 - 22)*(-24)/(-7). Determine o so that 2/7*o**4 - 8/7*o**3 - 16/7*o**2 + 32/7 + h*o + 1/7*o**5 = 0.
-2, 2
Let a = 1/1422 + 35/158. Find u, given that 2/3*u**2 - 2/9*u**3 - 2/3 + a*u = 0.
-1, 1, 3
Let c be 52/16*(-40)/(-260). Let k(t) be the second derivative of 1/60*t**5 + 7/18*t**3 - 5/36*t**4 + 0 - c*t**2 - t. Find z, given that k(z) = 0.
1, 3
Let x(y) be the second derivative of 4/15*y**6 - 2*y**4 + 1/21*y**7 + 0 + 0*y**2 - 6*y - 1/5*y**5 + 3*y**3. Find i, given that x(i) = 0.
-3, 0, 1
Let r(n) = -n**2 + 12*n + 18. Let p be r(13). Determine w so that p*w**5 + 26*w**3 - 23*w**3 - 8*w**5 = 0.
-1, 0, 1
Let a = -410 + 413. Factor -2/3*d**a + 0 + 2/3*d**2 + 0*d.
-2*d**2*(d - 1)/3
Solve 3/2*q**2 + 0 + 9/2*q = 0 for q.
-3, 0
Suppose -4 = -3*k + 5. Solve 0*a**2 + 3*a**k - 5*a**2 - 6*a**3 - a**2 = 0 for a.
-2, 0
Let q = 22088/27605 - 4/27605. Determine w so that -2/5*w + 2/5*w**2 - q = 0.
-1, 2
Suppose -2*o = 29 - 39. Let x(b) be the third derivative of -5*b**2 - b**3 + 0*b + 0 + 1/20*b**o - 1/8*b**4. Find q, given that x(q) = 0.
-1, 2
Factor 1/2*p**2 - p - 3/4 + 1/4*p**4 + p**3.
(p - 1)*(p + 1)**2*(p + 3)/4
Let z = 304 - 304. Factor 0*l**4 + 0*l**3 + 0*l**2 + 0 - 1/3*l**5 + z*l.
-l**5/3
Solve -22*i - 7 - 24*i - 22*i + 46 + 4*i**2 + 25 = 0 for i.
1, 16
Suppose -8*a - 8 = -11*a - p, 4*a - 5*p + 2 = 0. Find u such that 5 + 12*u**a - 7*u**2 - 5 - 15*u = 0.
0, 3
Let 175*w**3 + 185*w**3 + 14*w**4 - 356*w**3 = 0. What is w?
-2/7, 0
Let w(x) be the first derivative of x**5/70 + x**4/14 - x**3/21 - 3*x**2/7 + 24*x + 7. Let b(f) be the first derivative of w(f). Factor b(q).
2*(q - 1)*(q + 1)*(q + 3)/7
Suppose -1/4*u + 1/4*u**2 - 1/2 = 0. Calculate u.
-1, 2
Let p(n) be the first derivative of 21/2*n**2 + 9*n + 2*n**3 - 9/2*n**4 - 3*n**5 - 1/2*n**6 - 20. Factor p(u).
-3*(u - 1)*(u + 1)**3*(u + 3)
Let u = -1956 - -1959. Let m(n) be the second derivative of -1/2*n**4 + 4*n**2 + 0 - 1/10*n**5 + 6*n + 0*n**u. Solve m(q) = 0.
-2, 1
Find w such that -w - 1 + w**3 + w**2 + 6*w - 6*w = 0.
-1, 1
Let z be (150/(-141) - -1)*(-20)/(-90). Let y = 133/564 - z. Solve 1/4*c**3 - 1/4*c - y + 1/4*c**2 = 0 for c.
-1, 1
Factor 4*c**2 + 4*c**2 - 8 - 218*c**3 + 4*c + 214*c**3.
-4*(c - 2)*(c - 1)*(c + 1)
Suppose 3*q + q = -16. Let h be 97/5 + q/10. Let 4*u**2 + 27 + 9*u + 0 + 3*u**3 - h*u**2 = 0. Calculate u.
-1, 3
Let o(c) be the third derivative of c**7/525 + 7*c**6/150 + 6*c**5/25 + 17*c**4/30 + 11*c**3/15 + c**2 - 17*c. Factor o(i).
2*(i + 1)**3*(i + 11)/5
Factor o**2 + 19*o**2 - 211*o + 2*o**3 - 210*o - 20 + 419*o.
2*(o - 1)*(o + 1)*(o + 10)
Suppose -a + 37 = 3*j, 5*j + 19 - 86 = a. Let i = -10 + j. Factor -g**2 - 6*g**3 + g**5 - 2*g**5 - i*g**4 + 3*g**3.
-g**2*(g + 1)**3
Let k(t) = -2*t**2 + 15*t + 8. Let j(h) = h + 12. Let l be j(-4). Let g be k(l). Solve -4*i + 0*i**2 + 4*i**3 + g*i**3 - i**2 - 4*i**4 + 5*i**2 = 0 for i.
-1, 0, 1
Let y(n) be the third derivative of -n**9/7560 - n**8/672 - n**7/315 - n**4/8 - 2*n**2. Let z(v) be the second derivative of y(v). Factor z(j).
-2*j**2*(j + 1)*(j + 4)
Let h(q) = 10*q**3 - 13*q**2 - 16*q + 7. Let u(w) = -9*w**3 + 12*w**2 + 15*w - 6. Let a = -23 - -29. Let o(r) = a*h(r) + 7*u(r). Determine c so that o(c) = 0.
-1, 0, 3
Let p(f) be the second derivative of -f**8/1176 + f**7/735 + 15*f**2/2 - 4*f. Let t(d) be the first derivative of p(d). Solve t(j) = 0 for j.
0, 1
Suppose -8/5*w**2 + 14/5 - 1/5*w**3 - w = 0. What is w?
-7, -2, 1
Let c be 4/6*(7/2 - -1). Let g(z) be the second derivative of 0 + 0*z**2 - 3*z + 1/6*z**c + 1/6*z**4 + 1/20*z**5. Solve g(p) = 0 for p.
-1, 0
Let b(o) = 12*o**3 + 126*o**2 - 24*o - 126. Let w(i) = -i**4 - 46*i**3 - 505*i**2 + 98*i + 506. Let p(v) = -13*b(v) - 3*w(v). Determine q, given that p(q) = 0.
-4, -1, 1, 10
Let w(f) be the third derivative of -f**7/5460 - f**6/2340 + f**5/780 + f**4/156 + 11*f**3/6 + 2*f**2. Let y(o) be the first derivative of w(o). Factor y(c).
-2*(c - 1)*(c + 1)**2/13
Let l(c) be the first derivative of -c**6/3780 + c**5/210 - 4*c**3 - 14. Let q(w) be the third derivative of l(w). Find p such that q(p) = 0.
0, 6
Suppose -4*k + 28 = 5*z, -3*k = -z + 5 + 12. Let a be (-6)/z - (-30)/8. Let 1/9*t**2 + 2/9*t**a + 0*t + 0 + 1/9*t**4 = 0. What is t?
-1, 0
Let y be (4 + (-5 - -1))*(2 - 3). Factor 1/4*z**2 + 0 + y*z + 1/4*z**3.
z**2*(z + 1)/4
Let j = -2/65507 - -120938/65507. Determine f, given that -58/13*f**4 - 8/13 - j*f**5 + 8/13*f**3 + 66/13*f**2 + 16/13*f = 0.
-2, -1, -2/3, 1/4, 1
Suppose a = -a + 6. Factor -6*y**3 - a*y**4 + 6*y**2 - 3*y**3 + 12*y**4 - 6*y**4.
3*y**2*(y - 2)*(y - 1)
Solve -33/8*j - 9/4 - 9/4*j**2 - 3/8*j**3 = 0 for j.
-3, -2, -1
Suppose -2*t + 15 = 3*k - 24, 0 = -k + 3*t + 24. Let i = k + -15. Determine o so that -2/7*o**5 - 10/7*o**3 + i + 0*o + 4/7*o**2 + 8/7*o**4 = 0.
0, 1, 2
Let f = -4 + 8. Suppose 4*j - 105 = h, -4*j + 7*j - 5*h = 66. Factor -48*p**3 + 0*p**2 + j*p**2 + 17*p**2 + 2 - 16*p + 18*p**f.
2*(p - 1)**2*(3*p - 1)**2
Let w(x) be the first derivative of x**9/6048 - x**8/3360 - 6*x**3 - x - 54. Let c(t) be the third derivative of w(t). Factor c(h).
h**4*(h - 1)/2
Let z = -4342 + 4342. Find r, given that 2/9*r**4 + 0*r**3 - 10/9*r**2 + 8/9 + z*r = 0.
-2, -1, 1, 2
Let f(i) be the second derivative of i**7/210 + 2*i**6/45 + i**5/6 + i**4/3 + 7*i**3/6 - 3*i. Let b(v) be the second derivative of f(v). Factor b(n).
4*(n + 1)**2*(n + 2)
Solve 46/9*h**2 - 14/9*h**3 - 40/9 + 128/9*h = 0 for h.
-2, 2/7, 5
Let x(y) = y**3 + 4*y**2 + 2*y. Let l be x(-3). Let m be (12/(-16))/((-9)/24). Factor -4*g**2 + l - 3 + 2*g**4 + m.
2*(g - 1)**2*(g + 1)**2
Let r be (3 + 0)*(2 + 375/(-9)). Let o be r/(-21) + -6 - 13/(-21). Factor -o*p**3 - 12/7*p**2 - 16/7 - 24/7*p.
-2*(p + 2)**3/7
Let g be ((-27)/45)/((-2)/40). Factor -32*j**4 - 28*j + 18*j**5 + 24*j**2 + 16*j**3 + g*j**5 - 18*j**5 + 8.
4*(j - 1)**3*(j + 1)*(3*j - 2)
Let b(a) = -2*a - 67. Let q be b(-35). Let l = -15787/13 - -1215. Factor 8/13*z - l + 10/13*z**q + 2*z**2.
2*(z + 1)*(z + 2)*(5*z - 2)/13
Solve 18*l**2 + 19*l**2 + 6*l**2 - l**3 + 4*l**2 - 36*l**2 - 10*l = 0 for l.
0, 1, 10
Suppose 4*u - 2 = 26. Suppose 1 - u = -3*k. Factor -8/7 - 24/7*p + 2*p**k.
2*(p - 2)*(7*p + 2)/7
Suppose -3*i = -b + 21, -4*b + 2*b + 4*i = -34. Suppose 4*c + b = 7*c. Suppose -56*w**2 - 4*w**4 + c*w**4 + 55*w**2 + 2*w**3 = 0. What is w?
0, 1
Factor -2/17*q + 2/17*q**3 - 2/17 + 2/17*q**2.
2*(q - 1)*(q + 1)**2/17
Let u(v) be the third derivative of v**9/15120 + v**8/1680 + v**7/504 + v**6/360 + v**4/6 + 20*v**2. Let d(q) be the second derivative of u(q). Factor 