*2 - h + 2. Let m be x(0). Factor 2*d**3 + m*d**5 + 0*d**5 - 3*d**5 - d.
-d*(d - 1)**2*(d + 1)**2
Let v(s) be the second derivative of s**7/42 + s**6/30 - 7*s. Factor v(t).
t**4*(t + 1)
Let p(h) be the third derivative of 1/12*h**4 + 0*h + 0*h**3 + 1/105*h**7 - 1/30*h**5 - 1/60*h**6 + h**2 + 0. Solve p(w) = 0 for w.
-1, 0, 1
Let t = 6 - 9. Let w = t + 6. Suppose 6*x**3 + x**2 + x**2 - 4*x**w = 0. What is x?
-1, 0
Let w(r) be the third derivative of -r**5/20 + 3*r**4/8 - r**3 - 15*r**2. Factor w(f).
-3*(f - 2)*(f - 1)
Let h(a) = a**3 + 5*a**2 + a + 9. Let j be h(-5). Let y(i) be the second derivative of 2*i**2 - 1/40*i**5 + 0 + 1/4*i**j - i**3 - i. Factor y(q).
-(q - 2)**3/2
Let w(z) be the third derivative of -z**6/30 - z**5/15 + z**4/6 + 2*z**3/3 + 9*z**2. Find v, given that w(v) = 0.
-1, 1
Let p(i) be the first derivative of i**8/84 - i**7/30 - i**6/30 + 7*i**5/30 - i**4/3 - 7*i**3/3 - 3. Let s(t) be the third derivative of p(t). Factor s(x).
4*(x - 1)**2*(x + 1)*(5*x - 2)
Let d = 20 - 77/4. Let r(b) be the first derivative of -d*b**2 - 1/6*b**3 - b + 1. Factor r(n).
-(n + 1)*(n + 2)/2
Suppose i - 4*i + x = -5, -3*i - 3 = -3*x. Let h**i - h + 10 - 10 = 0. What is h?
-1, 0, 1
Suppose 0 = 3*n - w + 3*w - 10, n + 5*w + 1 = 0. Factor 0*h**4 + 4*h + 2*h**2 - 5*h**3 + h**3 - 2*h**n.
-2*h*(h - 1)*(h + 1)*(h + 2)
Let g(m) = -m**2 - m - 1. Let k(a) = a**3 + 2*a**2 + 2*a + 4. Let j(q) = 3*g(q) + k(q). Factor j(u).
(u - 1)**2*(u + 1)
Suppose 4 = v + 2. Let 3*f**v - 4*f + 3*f**2 + 0*f**2 - 4*f**3 + 1 + f**4 = 0. Calculate f.
1
Let y be 2/(10 - 12) - 10/(-6). Factor -1/3 - 1/3*v + y*v**3 - 1/3*v**4 + 2/3*v**2 - 1/3*v**5.
-(v - 1)**2*(v + 1)**3/3
Determine z, given that 8/5*z + 2/5*z**2 - 2 = 0.
-5, 1
Suppose 3*b = 6, 5*t + 5*b + 0*b = 30. Let q = -1 + t. Factor -1 + d**4 + 6*d**2 + 5*d**4 + 6*d - 3 - 14*d**q.
2*(d - 1)**3*(3*d + 2)
Let y(b) be the third derivative of 1/180*b**5 - 3*b**2 + 1/360*b**6 - 1/630*b**7 + 0*b - 1/1008*b**8 + 0*b**3 + 0 + 0*b**4. Suppose y(t) = 0. Calculate t.
-1, 0, 1
Solve -12*l**2 + 18*l - 27/4 = 0.
3/4
Let v(n) be the first derivative of -n**6/60 + 3*n**5/40 - n**4/8 + n**3/12 - 2*n - 1. Let g(u) be the first derivative of v(u). Factor g(y).
-y*(y - 1)**3/2
Suppose 2*v = -2, 3*v + 0*v + 3 = -2*f. Let b be (1/6)/(1/4). Solve 0*s + 0 - 2/3*s**4 + f*s**2 - b*s**3 = 0.
-1, 0
Let q be (-140)/(-36) + 8/((-40)/15). Factor q - 8/9*k + 2/9*k**2.
2*(k - 2)**2/9
What is i in -3 + 2*i + 6*i**2 - 16*i**2 + 4*i + 7*i**2 = 0?
1
Let b(p) be the second derivative of p**4/4 + p**3/2 - 3*p**2 + 2*p. Find d such that b(d) = 0.
-2, 1
Let y(f) be the first derivative of f**3/7 + 3*f**2/14 + 18. Let y(i) = 0. What is i?
-1, 0
Factor 12*u + 27*u**2 + 4/3.
(9*u + 2)**2/3
Let v = -5 + 7. Let q be v/(-7) + (-405)/(-21). Factor -q*b**2 - 4/3 + 12*b**3 + 28/3*b.
(3*b - 2)**2*(4*b - 1)/3
Factor 2/7*h**3 - 4/7*h + 2/7*h**2 + 0.
2*h*(h - 1)*(h + 2)/7
Let c = 8 - 38/5. What is m in 0*m - c*m**2 - 8/5*m**3 + 0 = 0?
-1/4, 0
Let f(i) = 9*i**2 + 8*i + 2. Let t(l) = 8*l**2 + 8*l + 2. Let w = 5 + -5. Suppose -3*r + 4 + 2 = w. Let c(p) = r*f(p) - 3*t(p). Let c(h) = 0. What is h?
-1, -1/3
Let k = 23/3 - 7. Factor -2/3*d**2 + 0 + k*d**3 - 4/3*d.
2*d*(d - 2)*(d + 1)/3
Let m(h) be the first derivative of -h**6/45 - h**5/60 + h**3 - 1. Let q(x) be the third derivative of m(x). Factor q(l).
-2*l*(4*l + 1)
Let d(j) = 2*j**3 + j**2 - 11*j + 4. Let n(a) = 7*a**3 + 3*a**2 - 45*a + 17. Let s(k) = 18*d(k) - 4*n(k). Factor s(h).
2*(h - 1)*(h + 2)*(4*h - 1)
Let z(h) = h - 1. Let x be z(4). Factor -10*p**x + p**2 - 5*p**2 + 23*p**4 - 9*p**4.
2*p**2*(p - 1)*(7*p + 2)
Let o(z) be the second derivative of z**4/15 + 56*z**3/15 + 392*z**2/5 + 10*z. Find g such that o(g) = 0.
-14
Factor 3*t + 2*t - 20*t**2 - 15 + 25 + 10 - 5*t**3.
-5*(t - 1)*(t + 1)*(t + 4)
Suppose -3*u + 13 = l, -4*u + 25 - 6 = 3*l. Suppose 4*b = 2*s + 18, 5*b = s - 2*s + 19. Factor -b*k**2 + 6*k**2 - 2 + 2*k**2 + 2*k**4 - 4*k**u.
-2*(k - 1)**2*(k + 1)**2
Suppose 0*a + 2*v + 2 = 3*a, 0 = -4*a + 3*v + 3. Let c(q) be the second derivative of a*q**3 - 2*q + 0*q**2 + 1/18*q**4 + 0 - 1/30*q**5. Factor c(f).
-2*f**2*(f - 1)/3
Let r(b) = -b**3 + 8*b**2 - 6*b - 6. Let g be r(5). Let n be -1 + (-3 - g/(-9)). Factor 2/3*q - 2/3*q**3 + 1/3*q**4 + 0*q**2 - n.
(q - 1)**3*(q + 1)/3
Let x(v) be the first derivative of -3 + 0*v**3 - 4/3*v - 1/6*v**4 + v**2. Determine w, given that x(w) = 0.
-2, 1
Let r = 585/4 - 146. Let i(g) be the first derivative of -1/3*g**3 + 3 - 1/15*g**5 - r*g**4 + 0*g - 1/6*g**2. Solve i(v) = 0.
-1, 0
Let t be ((-36)/(-270) - 17/15)*0. Let 1/2*d**2 - 1/2*d**3 + 0*d + t = 0. What is d?
0, 1
Let i(a) be the first derivative of a**6/1980 + a**5/660 - a**4/66 - 4*a**3/3 + 3. Let y(u) be the third derivative of i(u). Factor y(r).
2*(r - 1)*(r + 2)/11
Let s = -26168/7 + 134319/35. Let l = -99 + s. Suppose 0*f - l*f**2 + 0 + 1/5*f**3 = 0. What is f?
0, 2
Let z(s) be the third derivative of -s**6/60 + s**5/15 + s**4/4 + 5*s**2. Factor z(p).
-2*p*(p - 3)*(p + 1)
Let r(c) = 4*c**3 - c**2 - 20*c - 12. Let m(o) = 44*o**3 - 12*o**2 - 220*o - 132. Let d(y) = -3*m(y) + 32*r(y). Factor d(g).
-4*(g - 3)*(g + 1)**2
Let v(i) be the third derivative of i**10/30240 + i**9/15120 - i**8/6720 - i**7/2520 + i**4/12 + i**2. Let b(w) be the second derivative of v(w). Factor b(f).
f**2*(f - 1)*(f + 1)**2
Let f(r) = 7*r - 7. Let k be f(1). Let 0 + 6/7*l**3 - 2/7*l**4 - 4/7*l**2 + k*l = 0. Calculate l.
0, 1, 2
Let i(b) be the first derivative of -b**4 + 2*b - 1/3*b**6 - 6/5*b**5 + 1 + 3*b**2 + 4/3*b**3. Solve i(w) = 0.
-1, 1
Let o = 9 - 19. Let m = 12 + o. Suppose 0 - 2/3*j**3 + 2/3*j + 0*j**m = 0. Calculate j.
-1, 0, 1
Let o(g) = g**2 + 4*g + 10. Let d(h) = 2*h**2 + 8*h + 21. Suppose -5*f + 5*x - 45 = 0, f - 3*x + 25 = 10. Let z(r) = f*d(r) + 13*o(r). Factor z(s).
(s + 2)**2
Let l(j) = j**2 + j - 1. Let z(u) = 1 - 4*u - 2*u + 2*u - 2*u**2. Let v(n) = 3*l(n) + z(n). Factor v(w).
(w - 2)*(w + 1)
Factor -8*w + 5*w**3 + 3*w**2 - 4*w**3 - 5*w**2.
w*(w - 4)*(w + 2)
Let d(y) be the third derivative of -y**7/17640 + y**6/5040 + y**5/420 + y**4/8 + y**2. Let h(x) be the second derivative of d(x). Determine c so that h(c) = 0.
-1, 2
Factor -17*g**3 + 218*g**2 - 203*g**2 + 38*g**3 + 12 - 48*g.
3*(g - 1)*(g + 2)*(7*g - 2)
Let g = -111 - -337/3. Factor -2*m - 2/3*m**2 - g.
-2*(m + 1)*(m + 2)/3
Find g such that 8/13*g**2 - 6/13*g**5 + 16/13*g**3 + 2/13*g**4 + 0*g + 0 = 0.
-1, -2/3, 0, 2
Suppose 0 = 4*p - k - 2*k - 12, p - 3*k = 3. Factor -4*d - p*d - 10*d**3 - 4 - 18*d**2 + d**4 - 7*d - 3*d**4.
-2*(d + 1)**3*(d + 2)
Suppose 4*y + d - 12 = 2*d, y - d = 6. Find l, given that -l**2 + 2*l - 4 + 2 + 0*l**2 + 3*l**2 - y*l**3 = 0.
-1, 1
Let a(y) = y**3 + y**2 + 3*y + 1. Let z(m) = -2*m**3 - m**2 - 4*m - 2. Suppose 0 = -3*g + 5*g + 4. Let n(q) = g*z(q) - 3*a(q). Determine w so that n(w) = 0.
-1, 1
Let -5*n - 6*n - 6*n + 2*n**2 + 11*n = 0. What is n?
0, 3
Factor 134*b - 24 - 266*b + 114*b - 3*b**2.
-3*(b + 2)*(b + 4)
Let x(g) = -g + 7. Let q be x(5). Let j(m) be the second derivative of -m - 5/3*m**3 + 0 - 7/6*m**4 + 2*m**q. Let j(t) = 0. Calculate t.
-1, 2/7
Let s = -5/74 - -203/814. Suppose 0 = -2*z - d + 2*d + 2, 0 = 4*z - 5*d - 10. Factor s*r + z + 6/11*r**2.
2*r*(3*r + 1)/11
Suppose 0 = 3*b - b + r - 3, -3*b + 8 = 5*r. Let t(w) = -w**2 + w. Let p(u) = u**2 - 6*u - 3. Let i(k) = b*p(k) + 2*t(k). Factor i(y).
-(y + 1)*(y + 3)
Let m(p) be the first derivative of -4/11*p + 1/22*p**4 + 4 + 0*p**3 - 3/11*p**2. Factor m(h).
2*(h - 2)*(h + 1)**2/11
Let z(b) be the third derivative of -b**9/45360 - b**8/20160 + b**7/7560 + b**6/2160 + b**4/8 + 3*b**2. Let w(g) be the second derivative of z(g). Factor w(h).
-h*(h - 1)*(h + 1)**2/3
Let a = -30652/7 + 4386. Let z = 2104/77 + -288/11. Factor 0 + a*m**3 + z*m + 40/7*m**2.
2*m*(5*m + 2)**2/7
Factor 3*u**4 - 5*u**2 + 16*u**4 + 10*u**3 - 4*u**4.
5*u**2*(u + 1)*(3*u - 1)
Let k(j) be the first derivative of -j**6/7 - 9*j**5/35 + j**3/7 - 15. Let k(w) = 0. Calculate w.
-1, 0, 1/2
Let g(j) = 3*j**5 + 9*j**4 + 13*j**3 - 7*j**2 + 7. Let c(w) = -2*w**5 - 6*w**4 - 9*w**3 + 5*w**2 - 5. Let p(a) = 7*c(a) + 5*g(a). Let p(k) = 0. Calculate k.
-2, -1, 0
Let u(a) be the first derivative of 1/240*a**5 + 1/2*a**2 + 1/24*a**3 - 1/48*