(s - 1)**2*(s + 1)*(2*s + 1)
Suppose f = -3*z - 17, f - 5*z = 4*f + 31. Let k = f - -12. Suppose 4*s**2 - k*s**2 + 5*s**2 = 0. What is s?
0
Let k(g) be the second derivative of g**5/20 + 7*g**4/60 + g**3/15 - 13*g. Factor k(j).
j*(j + 1)*(5*j + 2)/5
Let g(h) be the third derivative of -h**7/280 - h**6/80 + h**4/16 + h**3/8 - 26*h**2. Factor g(t).
-3*(t - 1)*(t + 1)**3/4
Let i = -142 - -142. Factor -4/3*j + i - 5/3*j**4 + 8/3*j**2 + 7/3*j**3.
-j*(j - 2)*(j + 1)*(5*j - 2)/3
Let m(u) = -u**5 - u**4 - u**3 - u**2 - u - 1. Let j(t) = 2*t**5 + 7*t**4 - 3*t**3 + 7*t**2 + 2*t + 3. Let b(f) = -4*j(f) - 12*m(f). Factor b(n).
4*n*(n - 1)**4
Suppose -7 = 5*m - 22. Factor -2*o**2 + 0*o**2 - o - 2*o + o**m + 2*o**4 + 2*o.
o*(o - 1)*(o + 1)*(2*o + 1)
Factor -13*h + 45 - 17*h - 9*h**2 + 14*h**2.
5*(h - 3)**2
Let 27/2*s**2 + 3/2*s**3 + 33/2*s + 6 - 3/2*s**4 = 0. What is s?
-1, 4
Let s(f) = 9*f**3 + 8*f**2 - f - 8. Let m(o) = -3*o**3 - 3*o**2 + 3. Let j be (3 - 5 - 0)*-4. Let n(h) = j*m(h) + 3*s(h). Determine i so that n(i) = 0.
-1, 0, 1
Let o(z) = z**2 + 8*z - 1. Let g(w) = -w**2 - w. Suppose 3*p - 3 = -0*p. Let x be 2/(-6) - (-13)/3. Let r(j) = p*o(j) + x*g(j). Factor r(s).
-(s - 1)*(3*s - 1)
Let m = 1 + 3. Find x, given that 2*x**4 - 3*x**4 + 0*x**4 + 3*x**m = 0.
0
Let o be (-8 + -1)*(-2 + 1). Let d = o - 7. What is w in -4/7*w - 2/7 - 2/7*w**d = 0?
-1
Suppose 12 = 2*r + 4. What is f in 2*f**3 - f - 3*f**2 - 15*f**r + 19*f**3 - 5*f + 3*f**3 = 0?
-2/5, 0, 1
Let z(t) be the third derivative of t**8/448 + t**7/140 - 3*t**6/160 - t**5/10 - t**4/8 + 7*t**2. What is c in z(c) = 0?
-2, -1, 0, 2
Let o(t) be the second derivative of -t**4/24 - t**3/12 + 11*t. Factor o(n).
-n*(n + 1)/2
Factor -1/4*t + 3/4*t**2 + 0.
t*(3*t - 1)/4
Let u(a) be the first derivative of a**4/10 + 8*a**3/15 + a**2/5 - 12*a/5 - 7. Factor u(j).
2*(j - 1)*(j + 2)*(j + 3)/5
Factor 29*d + 16 - 5*d - 2*d**2 + 2*d**3 + 14*d**2.
2*(d + 2)**3
Let l be 6/(-10)*4/(-6). Suppose 3 = -2*p + 9. Factor 0*a - 2/5*a**4 + 0*a**p + 0 + l*a**2.
-2*a**2*(a - 1)*(a + 1)/5
Factor 3*a + 1/2*a**2 + 2 - 1/4*a**4 - 3/4*a**3.
-(a - 2)*(a + 1)*(a + 2)**2/4
Let j(x) be the third derivative of 1/30*x**4 - 1/150*x**6 - 4/15*x**3 + 0 + 0*x - 6*x**2 + 2/75*x**5. Suppose j(c) = 0. What is c?
-1, 1, 2
Let v(m) = -8*m**2 - 10*m. Let u(x) = x**2 + x. Let o(w) = 36*u(w) + 4*v(w). Factor o(j).
4*j*(j - 1)
Factor 4/9 - 2/3*c + 2/9*c**2.
2*(c - 2)*(c - 1)/9
Let j be 1/3 + (-174)/(-126). Factor -8/7*d - 8/7*d**3 - 2/7 - 2/7*d**4 - j*d**2.
-2*(d + 1)**4/7
Let y be 5/(-330) - (-4)/22. Let m be (-4 + 1)*(-8)/12. Factor 0 - y*w**m - 1/6*w.
-w*(w + 1)/6
Let y = -489 - -3426/7. Factor y*v**2 + 18/7*v + 27/7.
3*(v + 3)**2/7
Let t(y) be the third derivative of -y**8/560 - y**7/150 - y**6/120 - y**5/300 - 4*y**2. Factor t(w).
-w**2*(w + 1)**2*(3*w + 1)/5
Let s be 14/36*(-52)/(-109). Let l = 4/109 + s. Factor 0 - 2/3*p**3 + 4/9*p - l*p**2.
-2*p*(p + 1)*(3*p - 2)/9
Let v be 12/1 + (-2)/(-1). Let -210*r**4 - 47*r**5 - 30*r**5 - 207*r**3 - 84*r**2 + 16*r**5 - v*r**5 - 12*r = 0. What is r?
-1, -2/5, 0
Suppose 22 = -8*z + 22. Factor -2/11*y + z - 16/11*y**3 - 12/11*y**2.
-2*y*(2*y + 1)*(4*y + 1)/11
Let a(z) be the second derivative of z**5/40 + z**4/24 - z**2/2 - 3*z. Let n(p) be the first derivative of a(p). Solve n(o) = 0 for o.
-2/3, 0
Let j = 10 - 0. Suppose j = -3*z - 2, 5*d + 2 = -3*z. Factor d*h + 2*h**2 + 2/3*h**3 + 2/3.
2*(h + 1)**3/3
Let o(f) = -16*f**4 - 50*f**3 + 20*f**2 + 14*f + 14. Let z(s) = 3*s**4 + 10*s**3 - 4*s**2 - 3*s - 3. Let t(j) = -3*o(j) - 14*z(j). Factor t(n).
2*n**2*(n + 2)*(3*n - 1)
Let c(g) = g**2 - g + 3. Let q be c(0). Suppose j + q = -2*y + 2, -4*y + 28 = -4*j. Factor 4*f - 6*f**3 + 2 - 2 - 2*f**y.
-2*f*(f + 1)*(3*f - 2)
Let u(f) = -f**2 + 6*f - 3. Let b be u(5). Factor -x**2 + 2*x - 4*x + x**2 - x**b.
-x*(x + 2)
Let n = -523 - -3665/7. Factor -2/7 + n*a - 2/7*a**2.
-2*(a - 1)**2/7
Let t(v) = -2*v**4 - 3*v**3 + 25*v**2 - 3*v - 20. Let s(b) = -3*b**4 - 7*b**3 + 50*b**2 - 7*b - 40. Let g(d) = 3*s(d) - 7*t(d). Solve g(l) = 0 for l.
-2, -1, 1, 2
Let a(b) be the first derivative of -b**6/33 + 24*b**5/55 - 24*b**4/11 + 128*b**3/33 + 36. Determine d so that a(d) = 0.
0, 4
Let u be 3/(-12) - (-68)/16. Let r = 7 - u. Factor -a**4 + a + a**r + a**2 - 2*a**3 + 0*a**4.
-a*(a - 1)*(a + 1)**2
Let i(n) be the third derivative of -n**7/280 + n**5/40 - n**3/2 - n**2. Let y(q) be the first derivative of i(q). Solve y(c) = 0 for c.
-1, 0, 1
Determine m so that -1/2 - 1/2*m**2 - m = 0.
-1
Let r(q) be the second derivative of q**6/720 - q**5/480 - q**4/96 - q**3/2 + 3*q. Let y(i) be the second derivative of r(i). Determine o, given that y(o) = 0.
-1/2, 1
Let p(b) be the third derivative of -1/480*b**6 + 0*b**5 + 0*b**3 + 0 + 1/96*b**4 - 2*b**2 + 0*b. Factor p(h).
-h*(h - 1)*(h + 1)/4
Let s(b) be the first derivative of -b**3/9 + b/3 + 4. Suppose s(r) = 0. Calculate r.
-1, 1
Suppose -6 = -2*v - 0*v. Suppose -8 = -7*j + v*j. Suppose b + 2*b + 3*b + 3*b**j + 3 = 0. What is b?
-1
Suppose -6*h + 18 = -5*h. Suppose -5*m = 2*q - h, -4*m + 10 = 2*q - 6. Factor 2/3*x**m - 1/3*x + 0.
x*(2*x - 1)/3
Let t be 1 + -3 + 20/8. Let k = t - 1/6. Let k*l**3 - l + 2/3 + 0*l**2 = 0. What is l?
-2, 1
Let r(u) be the second derivative of u**5/150 - u**4/60 - 2*u**3/15 + u**2/2 + 2*u. Let p(j) be the first derivative of r(j). Factor p(m).
2*(m - 2)*(m + 1)/5
Factor -b + 0 - 1/4*b**2.
-b*(b + 4)/4
Let l = 18 - 7. Factor -6*v - 2*v**2 - l*v - 6 - 19*v**2 - 10*v.
-3*(v + 1)*(7*v + 2)
Let u(j) be the third derivative of j**8/672 + j**7/105 + j**6/48 + j**5/60 - 2*j**2. Factor u(h).
h**2*(h + 1)**2*(h + 2)/2
Let p(k) be the third derivative of -k**8/112 - 3*k**7/35 - 3*k**6/20 + k**5 + 39*k**4/8 + 9*k**3 + k**2. Determine s, given that p(s) = 0.
-3, -1, 2
Let x(z) be the second derivative of 5*z**5/4 + 15*z**4/4 + 5*z**3/2 - 5*z**2/2 - 29*z. Determine v, given that x(v) = 0.
-1, 1/5
Factor 2/11*a**2 - 4/11*a + 0.
2*a*(a - 2)/11
Let q(p) be the third derivative of -p**7/42 + p**5/12 + 12*p**2. Factor q(l).
-5*l**2*(l - 1)*(l + 1)
Let w = 94 + -94. Find p such that -6/5*p**3 + w*p**2 - 3/5*p**4 + 6/5*p + 3/5 = 0.
-1, 1
Let t(q) be the first derivative of -1/42*q**4 + 1/21*q**3 + 1 + 2/7*q**2 - 2*q. Let b(u) be the first derivative of t(u). Factor b(o).
-2*(o - 2)*(o + 1)/7
Let x(n) = -5*n + 225. Let d be x(44). Let -9/7*j**3 + 3/7*j**2 + 3/7*j**d + 0 - 3/7*j**4 + 6/7*j = 0. What is j?
-1, 0, 1, 2
Let r be (117/12)/((-27)/15). Let c = -19/4 - r. Suppose -4/3 + c*o**2 + 2/3*o = 0. Calculate o.
-2, 1
Solve 95/4*a + 25/4 - 5*a**2 = 0.
-1/4, 5
Let f(r) be the second derivative of r**4/3 - 2*r**3/3 - 4*r**2 + r. Factor f(c).
4*(c - 2)*(c + 1)
Let j(k) be the third derivative of k**5/60 - k**4/12 - k**3/2 - 15*k**2. Factor j(r).
(r - 3)*(r + 1)
Suppose 4*w - 3*w - 5 = 0. Suppose -w*o - 5*g = 0, -2*o + 6*g - g + 14 = 0. Factor 0 + 1/3*l + 1/3*l**o.
l*(l + 1)/3
Let l be (-2)/(-12) - (-552)/144. Let v(r) be the first derivative of 0*r**2 + 0*r + 2 + 2/21*r**3 + 18/35*r**5 + 3/7*r**l. Factor v(q).
2*q**2*(3*q + 1)**2/7
Suppose 0 = 3*v + 2*v - 20. What is p in 3*p**4 + 0*p**3 - 3*p**5 + 0*p**3 + 0*p**v = 0?
0, 1
Let j = 8 - 6. Factor -3*t**2 + 0*t**j + 6*t**2 - 3*t**3.
-3*t**2*(t - 1)
Factor -1/4 + 2*g - 4*g**2.
-(4*g - 1)**2/4
Let o be ((-2)/(-10))/((-32)/(-96)). Factor 3/5*w**4 - 6/5*w - o + 0*w**2 + 6/5*w**3.
3*(w - 1)*(w + 1)**3/5
Let 9/2 + 1/8*d**2 - 3/2*d = 0. What is d?
6
Factor 4/3*c**3 - 4/3*c**2 - 32/3*c + 16.
4*(c - 2)**2*(c + 3)/3
Let y(r) be the first derivative of -r**4/10 + 2*r**3/15 + r**2 + 6*r/5 - 14. Let y(f) = 0. What is f?
-1, 3
Let z(t) be the first derivative of 2*t**6/3 - 4*t**5 + 9*t**4 - 28*t**3/3 + 4*t**2 - 6. Factor z(w).
4*w*(w - 2)*(w - 1)**3
Suppose -2*o + 12 = y, 6 = -4*y + 22. Let m(g) be the second derivative of 1/12*g**o + 1/2*g**2 - 2*g + 0 + 1/3*g**3. Determine d, given that m(d) = 0.
-1
Let u be (-2)/(-4)*(-58)/2. Let c = 17 + u. Factor 1 + 2*m**4 - 1/2*m**3 - c*m - 6*m**2.
(m - 2)*(m + 1)**2*(4*m - 1)/2
Let f be 5/(-2)*(-8)/10. Suppose -f = -m - 0*m. Factor -w**2 - 3 + 2*w**m + 3.
w**2
Let f = -102 - -1531/15. Let t(x) be the second derivative of f*x**6 + 0*x**3 + 1/5*x**5 + 3*x + 0*x**2 + 1/6*x**4 + 0. Factor t(v).
2*v**2*(v + 1)**2
Let 