1, 1
Let k(a) be the first derivative of -a**8/280 - 8*a**7/525 - a**6/50 + a**4/60 - a**2/2 + 3. Let j(h) be the second derivative of k(h). Factor j(x).
-2*x*(x + 1)**3*(3*x - 1)/5
Let d(z) be the first derivative of 5*z**4/4 - 5*z**2/2 + 7. Find j, given that d(j) = 0.
-1, 0, 1
Let c(n) be the second derivative of -n**7/210 - n**6/30 - 9*n**5/100 - 7*n**4/60 - n**3/15 + 19*n. Factor c(k).
-k*(k + 1)**3*(k + 2)/5
Let c = -409/556 - 2/139. Let a = c + 37/28. Factor 2/7*d - a + 2/7*d**2.
2*(d - 1)*(d + 2)/7
Let j(p) = -p**2 + 9*p - 5. Let d be j(8). Let w be (-1)/d + 52/12. Factor w*h**3 - h**5 - h**3 - 2*h**3.
-h**3*(h - 1)*(h + 1)
Let l(u) = -14*u - 544. Let m be l(-39). Let -1/3*j**3 - 1/3*j**m + 0 + 0*j = 0. Calculate j.
-1, 0
Let c(f) be the second derivative of -f**8/1008 + f**6/180 - f**4/72 - f**2/2 - f. Let n(t) be the first derivative of c(t). Factor n(p).
-p*(p - 1)**2*(p + 1)**2/3
Let y(j) = 2*j**3 - j**2 - 2*j - 4. Let r(u) = u**2. Let n(h) = -10*r(h) - 2*y(h). Suppose n(m) = 0. Calculate m.
-2, -1, 1
Let b be (-20)/(-15) - 2/(-3). Let p be b*((-51)/18 - -3). Let -2/3*v - 1/3*v**2 - p = 0. Calculate v.
-1
Let j(r) be the third derivative of r**6/200 - r**5/50 + r**4/40 - 20*r**2. Find g, given that j(g) = 0.
0, 1
Suppose -7*g + 4*g = 6. Let u(o) be the first derivative of 2*o**3/3 + 2*o**2 - 2*o - 1. Let q(k) = 2*k**2 + 4*k - 3. Let c(z) = g*q(z) + 3*u(z). Factor c(b).
2*b*(b + 2)
Let z(u) = 8*u**2 - 20*u + 44. Let x(q) = -9*q**2 + 20*q - 43. Let m(k) = 6*x(k) + 7*z(k). Solve m(b) = 0 for b.
5
Let w = 554 + -2213/4. Find y, given that 0*y**2 - 3/4*y + 3/2*y**3 + 0 - w*y**5 + 0*y**4 = 0.
-1, 0, 1
Factor 0 - 1/8*k**2 + 1/8*k.
-k*(k - 1)/8
Let n(s) be the first derivative of 3/2*s**2 + 1/4*s**4 - 4 - s - s**3. Suppose n(o) = 0. What is o?
1
Factor 4/3*k**4 + 0*k + 0 - 16/3*k**3 - 20/3*k**2.
4*k**2*(k - 5)*(k + 1)/3
Let a(b) be the second derivative of -b**5/70 - 10*b. Let a(z) = 0. What is z?
0
Let j(z) be the third derivative of -2*z**2 + 0 - 4/3*z**4 - 1/15*z**5 - 32/3*z**3 + 0*z. Suppose j(y) = 0. Calculate y.
-4
Let s be (0 - 1)*(-1 - 7). Suppose -q + s = 3*q. Factor 1/2*y**2 - q*y + 2*y**3 - 1/2.
(y - 1)*(y + 1)*(4*y + 1)/2
Let w(k) be the first derivative of 4*k**3/3 - 20*k**2 + 100*k + 18. Factor w(o).
4*(o - 5)**2
Let i(h) be the third derivative of -5*h**8/168 - 23*h**7/105 - 7*h**6/12 - 17*h**5/30 + h**4/3 + 4*h**3/3 + 4*h**2. Determine y, given that i(y) = 0.
-2, -1, 2/5
Let b(k) be the first derivative of -k**4/4 + k**3 - k**2 + 5. What is d in b(d) = 0?
0, 1, 2
Let x(u) be the second derivative of -2*u**2 - 6*u**6 + 2/3*u**3 - 18/7*u**7 + 14/3*u**4 - 8*u + 0 - 6/5*u**5. Solve x(p) = 0 for p.
-1, -1/3, 1/3
Let w(q) be the first derivative of -q**3/4 + 7. Factor w(m).
-3*m**2/4
Let z(h) be the second derivative of -3*h**5/20 - 17*h**4/4 - 63*h**3/2 + 243*h**2/2 + 8*h - 3. Factor z(f).
-3*(f - 1)*(f + 9)**2
Let m(y) be the first derivative of 3*y**5/8 + 33*y**4/16 + 7*y**3/2 + 3*y**2/2 - 27. Solve m(b) = 0 for b.
-2, -2/5, 0
Let j(m) be the first derivative of 9*m**6/2 + 12*m**5 + 3*m**4 - 18*m**3 - 39*m**2/2 - 6*m - 7. Factor j(o).
3*(o - 1)*(o + 1)**3*(9*o + 2)
Let k(o) = -3*o**5 - 5*o**4 - 7*o**3 - 5*o**2 + 2. Let a(z) = -4*z**5 - 5*z**4 - 6*z**3 - 4*z**2 + z + 3. Let b(w) = -4*a(w) + 6*k(w). Let b(f) = 0. What is f?
-2, -1, 0
Let m(a) be the second derivative of -2*a**7/21 + 3*a**5/5 + 2*a**4/3 - 8*a. Factor m(s).
-4*s**2*(s - 2)*(s + 1)**2
Let n(k) be the first derivative of -k**5/25 + k**4/10 + k**3/15 - k**2/5 - 9. Determine i, given that n(i) = 0.
-1, 0, 1, 2
Suppose -2*j - 6 = -3*c, -9 = -4*j + 3. Factor 8*m**2 - 16 + 0*m**3 + 4*m**3 - 16*m - c*m**2.
4*(m - 2)*(m + 1)*(m + 2)
Let u(l) = -9*l**3 - 34*l**2 - 49*l + 4. Let j(y) = -55*y**3 - 205*y**2 - 295*y + 25. Let r(o) = 4*j(o) - 25*u(o). Factor r(g).
5*g*(g + 3)**2
Let c be (8/(-28))/(4/(-28)). Find d, given that d - 4*d - d**2 + c*d = 0.
-1, 0
Let r(u) = -3*u**3 + 3*u**2 + 4*u + 4. Let x be r(4). Let v = -487/4 - x. Factor -1/2 - 7/4*s**2 - v*s.
-(s + 1)*(7*s + 2)/4
Let v(k) be the second derivative of k**10/75600 + k**9/18900 + k**8/16800 - k**4/12 + 6*k. Let n(r) be the third derivative of v(r). Factor n(j).
2*j**3*(j + 1)**2/5
Let t(x) be the first derivative of 0*x**4 - 1 + 2/5*x**5 + 0*x**2 - 2/3*x**3 + 0*x. Determine j, given that t(j) = 0.
-1, 0, 1
Let d(w) be the first derivative of w**3/4 - w**2/2 - w + 10. Solve d(f) = 0 for f.
-2/3, 2
Let u(s) = -12*s - 30. Let z be u(-3). Let b(c) be the second derivative of 1/15*c**z + 0 + 0*c**3 - 2*c + c**2 - 1/3*c**4 + 0*c**5. Factor b(x).
2*(x - 1)**2*(x + 1)**2
Let p be (-60)/(-45)*(-3 + (-18)/(-4)). Let 1/6*k**4 - 1/3*k + 0*k**3 + 0 - 1/2*k**p = 0. What is k?
-1, 0, 2
Let z(q) be the second derivative of q**5/110 + q**4/22 - 4*q**2/11 + 9*q. Determine b so that z(b) = 0.
-2, 1
Let z(h) be the second derivative of h**8/1512 - h**7/945 - h**6/540 + h**5/270 + h**2/2 + 3*h. Let s(x) be the first derivative of z(x). Factor s(q).
2*q**2*(q - 1)**2*(q + 1)/9
Let s(p) be the third derivative of 1/192*p**8 + 0 - 2*p**2 + 3/280*p**7 + 0*p**5 + 0*p**3 + 0*p + 1/240*p**6 + 0*p**4. Let s(f) = 0. What is f?
-1, -2/7, 0
Let o(f) be the first derivative of -2*f**6/27 + 4*f**5/9 - f**4 + 28*f**3/27 - 4*f**2/9 - 45. Factor o(b).
-4*b*(b - 2)*(b - 1)**3/9
Let a be (3/(-1 + -8))/((-8)/30). Solve 1/2*w**3 + 0 + a*w**4 + 0*w**2 - 7/4*w**5 + 0*w = 0.
-2/7, 0, 1
Let t(y) be the third derivative of y**6/120 - y**4/8 - y**3/3 - 5*y**2. Factor t(f).
(f - 2)*(f + 1)**2
Let g(p) = -4*p**4 - 7*p**3 + 13*p**2 - 15*p + 8. Let l(q) = q**4 + q**2 - q. Let u(w) = -g(w) - 5*l(w). Determine n so that u(n) = 0.
1, 2
Let i = 0 - -18. Let o be 1/(-2 - (-39)/i). Factor -2*j + o*j + 5*j**2 - 3*j**2 + 2.
2*(j + 1)**2
Let o(a) = 1209*a**3 - 1479*a**2 + 111*a + 192. Let u(w) = -151*w**3 + 185*w**2 - 14*w - 24. Let g(s) = 4*o(s) + 33*u(s). Factor g(p).
-3*(p - 1)*(7*p - 4)*(7*p + 2)
Let x(r) = -r**2 - 3*r + 33. Let j be x(-7). Let f = -31/2 + 16. Determine b so that f*b**3 + 0 + b**2 + 0*b + 5/2*b**j - 4*b**4 = 0.
-2/5, 0, 1
Let x be (3/(-48)*-2)/(-1 - -4). Let k(h) be the third derivative of 0*h**4 + 0*h + 3*h**2 - 1/240*h**5 + 0 + x*h**3. Find r, given that k(r) = 0.
-1, 1
Let h(k) = k**4 + k**3 + k**2 + k - 1. Let j(m) = -27*m**3 + 3*m**2 + 60*m. Let d(q) = 12*h(q) - j(q). Find y, given that d(y) = 0.
-2, -1/4, 1
Let j = -3 + 0. Let i be ((-2)/j)/(1/6). Let -i*n**2 + 7*n**2 + 5*n**2 - 4 + 14*n = 0. What is n?
-2, 1/4
Let m(o) = -7*o. Let q(l) = -15*l. Let n(c) = 13*m(c) - 6*q(c). Let p(f) = f**2 - f - 1. Let r(u) = -3*n(u) + 3*p(u). Find y, given that r(y) = 0.
-1, 1
Suppose 5*s = 3*k + 57, 2*s = -2*k - 3 + 13. Factor s*u**4 - 7*u**4 + 2*u**4.
4*u**4
Let l(i) be the second derivative of i**7/70 + i**6/20 + i**5/20 + 5*i**2 - i. Let r(t) be the first derivative of l(t). Find z such that r(z) = 0.
-1, 0
Let r(t) = 13*t**2 + 5*t + 4. Let b(a) = -28*a**2 - 11*a - 9. Let z(f) = -6*b(f) - 13*r(f). Factor z(s).
-(s - 2)*(s + 1)
Find m such that -5*m**2 - 2*m + m**2 - 2*m + 8*m**3 = 0.
-1/2, 0, 1
Let k(b) be the third derivative of 0 + 1/180*b**6 + 0*b + 1/10*b**5 + 3*b**3 + 3/4*b**4 + 3*b**2. Factor k(o).
2*(o + 3)**3/3
Suppose -d + 2 = -k - k, 0 = -4*d + 4*k + 8. Let x(v) be the first derivative of -1/18*v**4 + 0*v**3 + 0*v + 1/9*v**d + 1. Let x(w) = 0. What is w?
-1, 0, 1
Let w be ((-3)/(-2))/3*4. Let r be -1 + -1 + (-100)/(-40). Suppose 1/2*c**w + 0*c - r = 0. What is c?
-1, 1
Let a(h) be the first derivative of 5*h**7/14 + h**6/5 - 3*h**5/4 - h**4/2 - h - 5. Let x(o) be the first derivative of a(o). Determine v so that x(v) = 0.
-1, -2/5, 0, 1
Factor 5*l**2 - 3*l**4 - 1 - 2*l**2 + 1.
-3*l**2*(l - 1)*(l + 1)
Suppose 0 = 3*l - 9*l. Determine p so that 0 + 2/3*p**3 + 0*p**2 + l*p = 0.
0
Suppose 5*v = -4*d - 0 - 3, -2*v - 6 = 0. Factor -3*j**4 + 3*j**5 + j**2 + 6*j + 2*j**2 - 9*j**d + 0*j**2.
3*j*(j - 2)*(j - 1)*(j + 1)**2
Let v(x) be the second derivative of 7*x**6/60 - 23*x**5/40 - x**4/24 + 23*x**3/12 - 3*x**2/2 - 12*x. Solve v(w) = 0 for w.
-1, 2/7, 1, 3
Let h(u) be the second derivative of -u**4/2 + u**3/4 + 9*u**2/4 - 9*u. Factor h(q).
-3*(q - 1)*(4*q + 3)/2
Suppose -2 = -3*n + 1. Let t(v) = 2*v**2 - 2*v + 1. Suppose -2*r + 20 = -6*r. Let b(s) = 1. 