s(b). Solve t(i) = 0.
-1, 0
Let k = 18 + -11. Factor k*t + 3*t**2 - t**2 - t.
2*t*(t + 3)
Let f(a) be the first derivative of 2/3*a**3 - 4/3*a - 1 - 1/6*a**4 + 1/3*a**2 - 2/15*a**5. Find r such that f(r) = 0.
-2, -1, 1
Let t(y) be the second derivative of y**4/4 + 5*y. Factor t(j).
3*j**2
Let a(j) be the second derivative of j**5/100 + j**4/30 + j. Factor a(q).
q**2*(q + 2)/5
Let k(t) be the third derivative of 1/420*t**7 + 0 - 1/96*t**6 + 1/96*t**4 - 3*t**2 - 1/24*t**3 + 0*t + 1/80*t**5. Suppose k(h) = 0. Calculate h.
-1/2, 1
Suppose -20 = -2*s + 6*s. Let u be s/2*(-5 + -1). Factor -22*t + u*t - 8 - 98*t**2 - 49*t.
-2*(7*t + 2)**2
Let r(n) be the third derivative of n**5/450 - n**4/90 - n**3/15 - 44*n**2. Factor r(z).
2*(z - 3)*(z + 1)/15
Let q = 1/156 + 1/13. Let g(u) be the second derivative of -2*u + 1/2*u**2 + 0 + 0*u**3 - q*u**4. Factor g(b).
-(b - 1)*(b + 1)
Let s(c) be the second derivative of -c**4/60 + c**3/15 + 15*c. Let s(a) = 0. What is a?
0, 2
Let j(s) be the third derivative of -1/300*s**6 - 5*s**2 + 1/150*s**5 + 0 + 0*s**4 + 0*s**3 + 0*s. Factor j(u).
-2*u**2*(u - 1)/5
Let u = 27 - 17. Suppose -u*f = -5*f. Factor 0*c**3 + f + 1/4*c**4 + 0*c**2 + 0*c.
c**4/4
Let u(x) be the first derivative of x**3 - 3/2*x**2 + 0*x + 4. Solve u(z) = 0.
0, 1
Let h be -1 - (2 + -3)*3. Find v, given that 4 - h - v**5 + 2*v**3 - 2 - v = 0.
-1, 0, 1
Let a(g) be the third derivative of 0*g + 0 - 1/70*g**5 - 1/21*g**3 + g**2 + 1/420*g**6 + 1/28*g**4. Factor a(h).
2*(h - 1)**3/7
Let i(r) be the first derivative of r**6/30 + r**5/25 - 9*r**4/20 - r**3/3 + 8*r**2/5 + 12*r/5 + 8. Let i(t) = 0. What is t?
-3, -1, 2
Let r(m) = m**2 + 2. Let i be r(0). Suppose -6*a + 26 = 2. Factor 6*s**3 + 2/3*s + 0 - 8/3*s**4 - a*s**i.
-2*s*(s - 1)**2*(4*s - 1)/3
Let s = -3 - -3. Suppose 2*p = 5*p - 15, 2*p = 4*d + 10. Determine j, given that d - 2/9*j**3 + 2/9*j + s*j**2 = 0.
-1, 0, 1
Let l = 5/12 - -1/3. Let 3/4 + l*s - 3/4*s**3 - 3/4*s**2 = 0. Calculate s.
-1, 1
Suppose 2*d + l = -0*l + 11, -4*d + l = -13. Suppose -2*z - 6 = -5*z. Factor -2*h**2 + 8*h**3 - d*h**4 - 2*h**4 - z*h**4.
-2*h**2*(2*h - 1)**2
Let y = 1 - -1. Solve 3*g**3 - g**5 + 3*g**5 - y*g**3 - 5*g**3 + 2*g = 0.
-1, 0, 1
Let m(x) be the second derivative of -2/15*x**6 + 0*x**2 + 0*x**4 + 2/5*x**5 + 0 + 0*x**3 + 7*x. Let m(h) = 0. What is h?
0, 2
Let d = -26543/46 - -577. Let u = d - -97/230. Factor 0*b**2 + u*b**3 + 0 + 0*b.
2*b**3/5
Let a = -9 + 11. Let w be 114/72 + a/(-8). Determine j so that -2/3*j**2 - 2*j - w = 0.
-2, -1
Let t(y) = y**4 + y**3 + y**2. Let r(a) = -4*a**4 - 4*a**3 - 8*a**2. Let i(q) = r(q) + 8*t(q). What is z in i(z) = 0?
-1, 0
Let i(k) be the second derivative of 0 - 6*k**2 + 7/4*k**4 + 0*k**3 + 9/20*k**5 - 6*k. Factor i(h).
3*(h + 1)*(h + 2)*(3*h - 2)
Let a be 8/(-3)*-3 + -1. Let s be a/2 - 1/2. Factor -1/5 + 1/5*i**s + 1/5*i**2 - 1/5*i.
(i - 1)*(i + 1)**2/5
Let d(i) be the third derivative of i**5/360 - 5*i**4/144 - i**3/6 + 13*i**2. Find a, given that d(a) = 0.
-1, 6
Let o be -3*((-136)/60 + (-1 - -3)). Factor 1/5 + o*m**2 + m.
(m + 1)*(4*m + 1)/5
Let v(s) be the third derivative of s**6/120 + 13*s**5/60 - s**4/24 - 5*s**3/3 - 5*s**2. Let p be v(-13). Factor -1/2*k**4 - 1/2*k**2 + 3/2*k**p + 1 - 3/2*k.
-(k - 2)*(k - 1)**2*(k + 1)/2
Suppose -6*o**3 + 3*o**3 + 9*o**4 + 193*o**2 - 193*o**2 = 0. What is o?
0, 1/3
Let h(m) be the first derivative of 3 + m + 1/3*m**3 - m**2. Factor h(s).
(s - 1)**2
Let u = 1 + 14. Suppose -4*j + j + u = 0. Factor v**j + v**4 - 3*v**5 + v**4.
-2*v**4*(v - 1)
Let c = 461/7 - 65. Find m, given that 0*m**2 + 0 - 2/7*m**4 + c*m**3 - 8/7*m = 0.
-1, 0, 2
Let f(d) be the first derivative of -d**7/945 + d**6/540 - d**2/2 + 1. Let p(n) be the second derivative of f(n). Determine m so that p(m) = 0.
0, 1
Suppose -2*h = -0*h - 3*a + 12, -3*h - 15 = -3*a. Let q be 4/(-3)*h/2. Suppose 4*g**4 - 3*g**2 + g**2 + g - g**5 - q*g**4 = 0. Calculate g.
-1, 0, 1
Suppose 0*w - 1/2 + w**3 + 3/2*w**2 = 0. What is w?
-1, 1/2
Determine m so that 0 + 3/2*m - 3*m**3 + 3/2*m**5 + 0*m**2 + 0*m**4 = 0.
-1, 0, 1
Let v(d) be the second derivative of -4*d**7/21 - d**6/3 + 3*d**5/10 + 5*d**4/6 + d**3/3 + 2*d. Solve v(z) = 0.
-1, -1/4, 0, 1
Let f(q) be the first derivative of 1/36*q**4 - 1/90*q**6 + 2*q - 1/60*q**5 - 1 + 1/18*q**3 + 0*q**2. Let i(h) be the first derivative of f(h). Factor i(z).
-z*(z - 1)*(z + 1)**2/3
Determine b, given that -8/5*b**3 + 64/5*b - 32/5 - 2/5*b**5 - 32/5*b**2 + 2*b**4 = 0.
-2, 1, 2
Determine q so that 0 + 7/2*q**4 + 5/2*q**2 + 9/2*q**3 + q**5 + 1/2*q = 0.
-1, -1/2, 0
Let s(m) = 2*m**4 - 6*m**4 - 3*m**4 + 4*m**4 - 2*m**3 + 1. Let k(i) = i**4 + i. Let g(q) = 4*k(q) + 2*s(q). Suppose g(v) = 0. What is v?
-1, 1
Let f(n) be the third derivative of n**5/15 - n**4/24 + 7*n**3/6 + n**2. Let v(s) = -s**2 - 1. Let w(z) = f(z) + 5*v(z). Find u such that w(u) = 0.
-2, 1
Let i be 1*(1 + (0 - -1)). Let h be i + 0 + -1 - -1. Solve -2*o**3 + o**2 + 2*o + h + o**2 - 4*o**2 = 0.
-1, 1
Let d(n) = n**3 + 4*n**2 + 4*n + 3. Let i be d(-3). Suppose i = 3*j + 2*j - 10. Solve m**5 + 1 + 2*m**3 - 3*m**4 + m - 4*m**j + 6*m**2 - 4*m = 0.
-1, 1
Let v(z) be the third derivative of 1/60*z**4 + 2*z**2 + 2/75*z**5 + 4/525*z**7 + 1/50*z**6 + 1/840*z**8 + 0*z**3 + 0 + 0*z. Solve v(s) = 0.
-1, 0
Let t = 31 - 31. Let h(o) be the first derivative of 1/6*o**3 + t*o + 3 + 1/4*o**2. Suppose h(f) = 0. What is f?
-1, 0
Let u(d) be the second derivative of d**6/900 + d**5/300 - d**4/30 - d**3/3 + 2*d. Let r(p) be the second derivative of u(p). Find s such that r(s) = 0.
-2, 1
Factor 10 + 11 - 19 - 2*m**2 + 0*m**2.
-2*(m - 1)*(m + 1)
Let v(j) be the first derivative of -2/7*j + 2 - 2/7*j**2 + 0*j**3 + 2/35*j**5 + 1/7*j**4. Factor v(f).
2*(f - 1)*(f + 1)**3/7
Let o = -33 + 36. Let j(p) be the third derivative of 0*p - 1/120*p**6 + 0 + 0*p**5 - 2*p**2 + 1/24*p**4 + 0*p**o. Factor j(z).
-z*(z - 1)*(z + 1)
Let z(u) = 2*u + 12. Let x be z(-6). Suppose 0*r - 6*r = x. Factor -4/7*y**2 - 2/7*y + 2/7*y**5 + 4/7*y**4 + r + 0*y**3.
2*y*(y - 1)*(y + 1)**3/7
Let r = 70/69 - 8/23. Let z be (-40)/6*(0 + 2/(-12)). Let -2*m**5 + 28/9*m**3 - 4/9*m**2 + r*m**4 - 2/9 - z*m = 0. What is m?
-1, -1/3, 1
Factor 5*l**2 + 15*l + 19*l**2 + 4*l**3 + 33*l + 32.
4*(l + 2)**3
Let c(y) = -25*y**4 + 3*y**3 + 5. Let a(h) = -h**4 - h. Let v(i) = -2*i**3 - 12*i - 2. Let x(b) = -12*a(b) + v(b). Let l(g) = -2*c(g) - 5*x(g). Factor l(n).
-2*n**3*(5*n - 2)
Let n(x) = x - 4. Let y be n(6). Determine o so that 3*o**y + 3*o**3 - o**4 - 2*o**4 + 0*o - 3*o = 0.
-1, 0, 1
Let p(x) = 3*x**5 - 2*x**4 + 11*x**3 + 5*x**2 - x. Let n(y) = 4*y**5 - 2*y**4 + 12*y**3 + 4*y**2 - 2*y. Let q(i) = 5*n(i) - 6*p(i). Factor q(o).
2*o*(o - 2)*(o + 1)**3
Suppose -n = 4*t + 24, 2*t + 10 = 4*n - 2. Let g(f) = f**3 + 6*f**2 - f - 1. Let d be g(t). Factor -y**3 - 4*y**3 + 3*y**3 + y**5 + y**d.
2*y**3*(y - 1)*(y + 1)
Let c(o) be the second derivative of 4*o**6/15 + 3*o**5/10 - 3*o**4/2 + 2*o**3/3 - 17*o. Factor c(q).
2*q*(q - 1)*(q + 2)*(4*q - 1)
Let j(h) = -6*h**2 - 24*h - 13. Let o(d) = -3*d**2 - 12*d - 6. Let g(q) = 6*j(q) - 11*o(q). Factor g(v).
-3*(v + 2)**2
Let q = 9/7 - 11/14. Factor -1/2*s - q*s**3 + s**2 + 0.
-s*(s - 1)**2/2
Suppose 2*i + 0*n - 5 = -n, 3*i = -5*n + 11. Let o(g) be the third derivative of 0*g - 1/120*g**5 - 2*g**i + 0*g**3 + 0 + 0*g**4. Factor o(x).
-x**2/2
Let z be 1 + -5 + (3 - -19). Let c be (-98)/(-693) - (-4)/z. Factor 0 - 2/11*j**2 - c*j.
-2*j*(j + 2)/11
Let d be (-14)/(-24) - 7/21. Let j(s) be the second derivative of -1/84*s**7 + 1/12*s**4 + 0*s**6 + 0 + 1/10*s**5 - 1/2*s**2 - d*s**3 - 2*s. Factor j(k).
-(k - 2)*(k - 1)*(k + 1)**3/2
Let f(y) be the first derivative of y**6/1620 + y**5/135 + y**4/27 + 2*y**3/3 + 2. Let q(o) be the third derivative of f(o). What is v in q(v) = 0?
-2
Let d(j) = 164*j**2 - 244*j - 120. Let p(z) = -33*z**2 + 49*z + 24. Let r(u) = -5*d(u) - 24*p(u). Factor r(l).
-4*(l - 2)*(7*l + 3)
Let a = 623/25740 + -8/429. Let m(q) be the third derivative of 1/360*q**6 - a*q**5 - 1/72*q**4 + 2*q**2 + 1/630*q**7 + 0*q**3 + 0*q + 0. Factor m(v).
v*(v - 1)*(v + 1)**2/3
Let c = 45/4 + -11. Let v be (-2)/(-8)*(-4)/(-4). Find p, given that v*p**2 - c + 0*p = 0.
-1, 1
Let n = -6 + 3. Let i = -3 - n. Factor i*p**4 + 3*p - 4*p**5 - 