/4*x**3 = 0.
-2, 0
Suppose -p + 112 = 3*p. Let a = 32 - p. Find r such that -55/4*r**3 + r + 25*r**a + 0 - r**2 = 0.
-1/4, 0, 2/5
Let d(x) be the first derivative of 0*x + 0*x**2 + 2 - 1/2*x**3 - 3/8*x**4. Factor d(n).
-3*n**2*(n + 1)/2
Let l(x) = 12*x**5 + 8*x**4 - 12*x**3 + 16*x**2 - 8*x - 8. Let j(h) = -h**5 - h**4 - h**2 + h + 1. Let t(g) = -8*j(g) - l(g). Factor t(o).
-4*o**2*(o - 1)**2*(o + 2)
Let a(m) be the third derivative of m**6/30 + m**5/15 + 2*m**2. Determine l, given that a(l) = 0.
-1, 0
Let a(r) be the first derivative of 1 + 2/9*r**3 + 0*r**2 + 2*r + 1/18*r**4. Let k(y) be the first derivative of a(y). Suppose k(j) = 0. What is j?
-2, 0
Let i = 1394/7 - 199. Solve -1/7*u**2 + 0*u + 0 - i*u**3 + 1/7*u**4 + 1/7*u**5 = 0.
-1, 0, 1
Let a(d) be the third derivative of d**5/24 - 25*d**4/24 - 55*d**3/12 - 13*d**2. Suppose a(k) = 0. Calculate k.
-1, 11
Let m be 4 + 3 + (-120)/18. Factor 0*p + 1/3*p**2 - 2/3*p**4 + 0 + m*p**3.
-p**2*(p - 1)*(2*p + 1)/3
Let j be 2 - (-32)/(-20) - 0. What is u in 24/5*u**2 + j - 14/5*u = 0?
1/4, 1/3
Let q = 1381/7 - 197. Let d(t) be the second derivative of -1/42*t**4 + 1/21*t**3 - 3*t + q*t**2 + 0. Factor d(z).
-2*(z - 2)*(z + 1)/7
Let w(d) = 3*d**3 + 5*d**2 - 12*d. Let x(g) = 3*g**3 + 4*g**2 - 12*g. Let b(j) = -4*w(j) + 5*x(j). Let b(p) = 0. What is p?
-2, 0, 2
Let d(v) be the second derivative of 0*v**2 + 0*v**3 + 3*v + 1/36*v**4 + 0. Factor d(l).
l**2/3
Let z = -542 - -542. Let p be 1 - (-4)/(-3) - -33. Solve 0*y + p*y**4 + z - 8/3*y**2 - 8/3*y**3 + 98/3*y**5 = 0.
-1, -2/7, 0, 2/7
Let u(g) = g**2 - 14*g + 51. Let n be u(7). Factor 0 + 0*h**n + 2/9*h**4 + 0*h + 0*h**3.
2*h**4/9
Let u(m) = -m**5 - m**4 + m**2 - m - 1. Let b(r) = 2*r**5 - 2*r**3 + r**2 + 2*r. Let c(l) = 4*b(l) + 4*u(l). Factor c(t).
4*(t - 1)**3*(t + 1)**2
Suppose 14/5*f**2 + 1/5*f**5 - 6/5*f**3 - 1/5*f**4 + 3/5 - 11/5*f = 0. What is f?
-3, 1
Let q = 124 - 124. Let v = 66/5 + -13. Factor 1/5*i**2 - v + q*i.
(i - 1)*(i + 1)/5
Factor -1 - 8 + 8*j**2 - 8 + 17*j + j**3 + 27.
(j + 1)*(j + 2)*(j + 5)
Suppose -9 = 4*w + 3*o, -1 = -w + 4*o + 11. Let t(m) be the second derivative of 1/30*m**5 + 0 - 1/18*m**4 + 0*m**3 + m + w*m**2. Factor t(p).
2*p**2*(p - 1)/3
Factor 3*x - 12 + 3*x**2 + 13 + 0*x - 7.
3*(x - 1)*(x + 2)
Let c = -53 - -54. Let u(q) be the first derivative of -c + 1/2*q**2 + 0*q + q**3. Factor u(n).
n*(3*n + 1)
Let s(o) be the first derivative of 2/5*o**5 + 3 + 4/15*o**6 + 0*o + 0*o**2 + 1/10*o**4 + 0*o**3. Factor s(r).
2*r**3*(r + 1)*(4*r + 1)/5
Let l(i) = -i**2 - 4*i + 2. Let x(z) = -2*z**2 - 5*z + 2. Let n(o) = -3*l(o) + 2*x(o). Let w(r) = -3*r**2 + 4*r - 5. Let a(d) = 10*n(d) - 4*w(d). Factor a(k).
2*k*(k + 2)
Let k = -43 - -42. Let n(x) = -6 + 4*x**3 - 4*x + 0 + 2*x**2 - 6*x**3 - 2*x**4. Let h(b) = -b**3 - 1. Let g(o) = k*n(o) + 6*h(o). Factor g(l).
2*l*(l - 2)*(l - 1)*(l + 1)
Let x(w) be the third derivative of w**5/80 + 3*w**4/16 + 9*w**3/8 + 3*w**2. Solve x(i) = 0 for i.
-3
Let d(h) be the third derivative of -h**6/120 - h**5/10 - 3*h**4/8 - 2*h**3/3 - 8*h**2. Factor d(u).
-(u + 1)**2*(u + 4)
Let y(t) = -188*t**4 + 232*t**3 + 110*t**2 - 198*t + 78. Let p(h) = 17*h**4 - 21*h**3 - 10*h**2 + 18*h - 7. Let g(k) = 68*p(k) + 6*y(k). Factor g(x).
4*(x - 1)**2*(x + 1)*(7*x - 2)
Factor 0*b + 3/4*b**5 + 3/8*b**3 + 0*b**2 + 0 - 9/8*b**4.
3*b**3*(b - 1)*(2*b - 1)/8
Let i = -311 + 313. Factor -1/3*d**5 - 1/3*d + 1/3*d**4 - 2/3*d**i + 1/3 + 2/3*d**3.
-(d - 1)**3*(d + 1)**2/3
Let t(c) = -2*c - 14. Let g be t(-10). Find f such that -2 + 2*f**2 + 4*f**3 - 2*f - g*f**3 + 2*f**3 + 2*f**3 = 0.
-1, 1
Let p(c) be the third derivative of 0*c**6 + 0*c**3 + 0*c + 0 + 1/672*c**8 - 1/48*c**4 + 1/60*c**5 - 4*c**2 - 1/210*c**7. Factor p(g).
g*(g - 1)**3*(g + 1)/2
Let l(r) = 3*r**4 + 13*r**2 + 3*r - 19. Let p(o) = -4*o**4 - 12*o**2 - 2*o + 18. Let g(x) = 6*l(x) + 5*p(x). Suppose g(z) = 0. Calculate z.
-2, 1, 3
Let j = 13/5 - 73/30. Let m(d) be the third derivative of 0*d + j*d**4 + 1/30*d**5 + 0 + 1/3*d**3 + 2*d**2. Suppose m(t) = 0. What is t?
-1
Let z(a) be the third derivative of a**8/420 + 8*a**7/525 + a**6/50 - 4*a**5/75 - 2*a**4/15 + 16*a**2. Suppose z(t) = 0. Calculate t.
-2, -1, 0, 1
Let l(w) = -2*w**3 + w + 1. Let v(s) = s**4 + s**2 - s - 1. Let d(x) = 3*l(x) + 3*v(x). Solve d(j) = 0 for j.
0, 1
Let p(c) = 2*c**2 + 13*c - 8. Let m(h) = h. Let g(a) = -14*m(a) + 2*p(a). Find y such that g(y) = 0.
-4, 1
Suppose -5*a + 3*a = -2*y - 2, 0 = -a + 2*y + 2. Suppose 0*c - 2*c = a. Factor 4*f**4 - 2*f**4 + c*f**4.
2*f**4
Let s = -122 + 253/2. Determine x so that -6*x - 2 - s*x**2 = 0.
-2/3
Let s be (-4)/(-2)*45/210. Factor 0 - 3/7*f**5 - 3/7*f**2 + 0*f + 3/7*f**3 + s*f**4.
-3*f**2*(f - 1)**2*(f + 1)/7
Let r(c) be the third derivative of -c**8/2184 + 4*c**7/1365 - c**6/130 + 2*c**5/195 - c**4/156 + 13*c**2. What is w in r(w) = 0?
0, 1
Suppose 3*d = f + 8, f = 4*d - 5*d. Let l be (-7 - -5)*3/(-2). Determine n, given that -1 - 3*n + 3*n**2 - n**l - d - 2*n**4 + 2 + 4*n = 0.
-1, 1/2, 1
Factor 2*z**3 - z**2 + 0*z**3 - 7*z**3 - 5*z - 9*z**2.
-5*z*(z + 1)**2
Let m(t) be the third derivative of -1/9*t**3 + 0 - 3*t**2 + 0*t + 1/90*t**5 + 0*t**4. Factor m(s).
2*(s - 1)*(s + 1)/3
Suppose -11 = -8*f + 29. Let z(j) be the first derivative of -4/15*j**3 - 1 + 1/5*j**4 + 2/25*j**f + 2/5*j - 1/15*j**6 - 1/5*j**2. Solve z(o) = 0.
-1, 1
Suppose -25 = -5*n + 3*k, -2*k = 2*k + 20. Factor -6/5 + 3/5*j + 9/5*j**n.
3*(j + 1)*(3*j - 2)/5
Let x be (42/(-189))/((-2)/18). Factor 0*k + 0 - 1/5*k**x.
-k**2/5
Let a = 425978/15 - 28411. Let w = a + 38/3. Let -w*h**2 - 4/5 + 4/5*h = 0. Calculate h.
2
Suppose 4*i - 13 - 3 = -4*m, 20 = -i + 5*m. Factor -5*f**3 - 2*f**2 + 6*f**3 + i*f**2 - 4*f**3.
-f**2*(3*f + 2)
Let c(m) be the third derivative of 0 + 1/60*m**4 + 2*m**2 + 0*m**3 + 0*m - 1/150*m**5. Solve c(g) = 0 for g.
0, 1
Let a be 4/14 + (-26)/(-7). Suppose i + 3*i**4 + 9*i**3 + 2*i + 9*i**2 + 0*i**a = 0. Calculate i.
-1, 0
Let w = -8187 + 24262/3. Let k = 101 + w. Solve 2*q**4 + 0 + k*q - 2*q**2 - 4/3*q**3 = 0 for q.
-1, 0, 2/3, 1
Let t(d) be the second derivative of d**4/66 + 2*d**3/33 - 5*d. Factor t(k).
2*k*(k + 2)/11
Let i(z) be the second derivative of -z**7/27 + 16*z**6/135 - 11*z**5/90 + z**4/27 + z. Factor i(l).
-2*l**2*(l - 1)**2*(7*l - 2)/9
Let u(p) = 29 + 0*p - 3*p**2 + p + 6*p**2 - 2*p**2. Let b be u(0). Factor -5*z**2 + 28*z**5 - b*z**5 + 3*z**2 + 2*z**4 + z.
-z*(z - 1)**3*(z + 1)
Let d = 11 - 9. Factor -u**2 + 2*u**2 + 2*u + u**d.
2*u*(u + 1)
Let f(n) be the third derivative of 0*n**4 - 1/480*n**6 + 1/120*n**5 + 0 + 0*n - 3*n**2 + 0*n**3. Suppose f(z) = 0. Calculate z.
0, 2
Solve -31*c + 6 + 67*c**2 - 8*c - 13*c**2 = 0 for c.
2/9, 1/2
Let w(q) be the second derivative of 0 - 8/15*q**5 - 64/9*q**3 + 2/45*q**6 + 8/3*q**4 + 32/3*q**2 - 6*q. Factor w(u).
4*(u - 2)**4/3
Let c(a) be the first derivative of -1/2*a**2 + 1/4*a**4 - a - 3 + 1/3*a**3. Factor c(b).
(b - 1)*(b + 1)**2
Let o(t) be the second derivative of -t**5/70 - t**4/14 - 2*t**3/21 - 60*t. Find u, given that o(u) = 0.
-2, -1, 0
Let m(n) be the second derivative of n**4/54 - n**2/9 - 5*n. Factor m(i).
2*(i - 1)*(i + 1)/9
Let m be ((-1)/(-3))/(((-38)/12)/(-19)). Determine z, given that m - 3/2*z**2 + 0*z - 1/2*z**3 = 0.
-2, 1
Let k = -69479/26 + 2673. Let u = -3/13 + k. Let -1 - 1/2*q + q**2 + u*q**3 = 0. Calculate q.
-2, -1, 1
Let a(d) be the first derivative of 1/16*d**6 + 0*d - 7 + 3/16*d**2 + 0*d**3 + 0*d**5 - 3/16*d**4. Factor a(j).
3*j*(j - 1)**2*(j + 1)**2/8
Let i = 16/15 - 2/3. Let a(x) be the first derivative of 0*x**4 - 1/3*x**6 + 0*x**2 + 2 + 0*x + 0*x**3 + i*x**5. Factor a(w).
-2*w**4*(w - 1)
Let b(z) be the first derivative of -7 + 0*z**5 + 0*z**3 + 0*z + 0*z**2 + 0*z**4 - 1/18*z**6. Factor b(j).
-j**5/3
Let g(p) = p**3 + 4*p**2 - 14*p - 9. Let k be g(-6). Factor -5/3*t**3 + 4*t**2 + 2/3 - k*t.
-(t - 1)**2*(5*t - 2)/3
Suppose 5*q - 8 = 7. Let n be ((-1)/q)/((-5)/30). Let 16/7 + 24/7*f + 2/7*f**3 + 12/7*f**n = 0. What is f?
-2
Let s(k) = k**3 + 13*k**2 - 17*k - 21. Let p be s(-14). Factor 4*d**2 + p*d - 17*d + 4 - 12*d.
4*(d - 1)**2
Suppose -4/5 + 3/5*p**2 + 0*p + 1/5*p**3 = 0. Calculate p.
-2, 1
Let u(q) be the first derivative of -q**5/90 - q**4/12 - 2*q**3/9 + 2*q**2 + 6. Let h(l) be the second der