1, 5
Let z(v) = -v**2 + 5*v + 8. Let c be z(6). Let j(x) be the third derivative of -3*x**c - 1/240*x**5 + 0 + 0*x - 1/24*x**3 + 1/48*x**4. Factor j(s).
-(s - 1)**2/4
Let n(y) = y**2 - 4*y + 4. Let q(m) = -4*m**2 + 16*m - 16. Let o(u) = 9*n(u) + 2*q(u). Factor o(g).
(g - 2)**2
Factor -1/2*s + 1/6*s**3 + 1/3*s**2 + 0.
s*(s - 1)*(s + 3)/6
Let k(o) be the third derivative of 0*o**3 - 1/210*o**7 + 1/336*o**8 + 0*o**4 + 0 + 1/60*o**5 - 4*o**2 - 1/120*o**6 + 0*o. Factor k(t).
t**2*(t - 1)**2*(t + 1)
Let m be ((-4)/6)/(12/(-126)). Suppose -12*a**4 - 31*a**4 + 15*a**4 - 9*a**5 - m*a**5 + 8*a**3 = 0. Calculate a.
-2, 0, 1/4
Let f = 15 + -13. Let v be 5/(-15)*(1 - f). What is n in 1/3*n**4 + 1/3*n**3 - v*n - 1/3*n**2 + 0 = 0?
-1, 0, 1
Let j(s) be the first derivative of s**5/150 - s**4/15 + 4*s**3/15 + 5*s**2/2 + 6. Let z(w) be the second derivative of j(w). Factor z(a).
2*(a - 2)**2/5
Let f(l) be the first derivative of l**6/30 + l**5/5 + 7*l**2/2 + 3. Let y(n) be the second derivative of f(n). Solve y(h) = 0.
-3, 0
Let n(f) be the third derivative of -f**5/150 - f**4/60 + 6*f**2. Solve n(a) = 0 for a.
-1, 0
Let j be 24/14 - 28/(-49). Factor 3*l**3 - j*l**2 + 0 - 9/7*l**4 + 4/7*l.
-l*(l - 1)*(3*l - 2)**2/7
Suppose 0 = -m + 2*g + 6, -2*m - 2*g - 3*g = 15. Let a(u) be the third derivative of m*u**3 + 1/6*u**5 + 0*u - 1/6*u**4 + 0 - 2*u**2. Factor a(l).
2*l*(5*l - 2)
Determine f so that -3 - 47*f + 2*f - 50*f**2 + 5 + 3 = 0.
-1, 1/10
Factor 128/3 + 16/3*g + 1/6*g**2.
(g + 16)**2/6
Let t(d) be the third derivative of 0*d**3 + 1/360*d**6 + 1/180*d**5 + 0*d + 0*d**4 + 5*d**2 + 0. Solve t(q) = 0.
-1, 0
Factor -2/3*g**3 - 32/3*g - 16/3*g**2 + 0.
-2*g*(g + 4)**2/3
Let r = -6 + 10. Let i be (8/(-3))/r*-3. Factor -1 + 4*n**3 + 1 + 2*n**i - 4*n - 2.
2*(n - 1)*(n + 1)*(2*n + 1)
Let t be (2 + (-36)/8)/(-1 + -4). Let a(b) be the first derivative of 0*b - 1 + 2/3*b**3 + 1/4*b**4 + t*b**2. Factor a(i).
i*(i + 1)**2
Let i = 29 + -21. Let s = i + -6. Determine j, given that -4*j**5 - s*j**4 + 3*j**5 - j**3 + 0*j**3 = 0.
-1, 0
Let i(q) be the third derivative of q**5/270 + q**4/36 + 2*q**3/27 + 3*q**2. Find v such that i(v) = 0.
-2, -1
Let x(m) be the first derivative of -m**5/35 - m**4/28 + m**3/21 + m**2/14 + 20. Factor x(v).
-v*(v - 1)*(v + 1)**2/7
Suppose 5*k + 107 = 3*z, -4*z - 5*k = -97 + 1. Let l = z - 86/3. Let 1/3*n + 1/3*n**4 - 1/3*n**2 + 0 - l*n**3 = 0. Calculate n.
-1, 0, 1
Let z be (-42)/(-12) + 2/4. Factor 10*m**z - 3*m**4 - 4*m**4 - 2*m**3 - m**3.
3*m**3*(m - 1)
Suppose -33 = -3*p + 3*w, -4*w = -p - w + 21. Suppose p*d - d = 0. Solve 6/5*z - 4/5 + d*z**2 - 2/5*z**3 = 0 for z.
-2, 1
Let r(k) = 2*k**2 + 3*k + 4. Let n(x) be the third derivative of -x**4/24 - x**2. Let q(f) = 3*n(f) - r(f). Factor q(h).
-2*(h + 1)*(h + 2)
Suppose -4*q = r - 6 - 4, -6 = -3*q. Factor 1/6*s**3 + 1/6*s**r - 1/6*s - 1/6.
(s - 1)*(s + 1)**2/6
Let q(b) = 3*b**4 - 12*b**3 - 20*b**2 - 36*b - 20. Let x(l) = 5*l**4 - 23*l**3 - 41*l**2 - 71*l - 39. Let i(v) = -7*q(v) + 4*x(v). Solve i(z) = 0.
-2
Let r be ((-2)/25)/(21/(-10)). Let x(k) be the second derivative of 1/21*k**3 + 1/147*k**7 + 0*k**2 - r*k**6 - 2/21*k**4 + 3/35*k**5 + 0 + k. Factor x(w).
2*w*(w - 1)**4/7
Let f be (-6)/2*80/(-24). Let u be 8/(-6)*(-15)/f. Determine p, given that 3*p**2 + 3 - 2 - 4 + 0*p**u = 0.
-1, 1
Let g(y) be the third derivative of 0*y**3 + 1/20*y**5 + 0*y**4 + 3/70*y**7 + 0*y + 0 - 1/112*y**8 - 3*y**2 - 3/40*y**6. Factor g(p).
-3*p**2*(p - 1)**3
Let j(o) be the second derivative of 0 + 9/20*o**4 - 7/10*o**3 - 3/5*o**2 - 4*o. Determine a, given that j(a) = 0.
-2/9, 1
Suppose -4 = b - 0*l + 2*l, b = 5*l + 10. Factor 0 - 2/3*d**3 + b*d - 2/3*d**2.
-2*d**2*(d + 1)/3
Suppose -6 = -4*a - 62. Let i = a + 43/3. Factor -1/3*o + i*o**3 - 1/3*o**2 + 0 + 1/3*o**4.
o*(o - 1)*(o + 1)**2/3
Factor 1 - 1/2*v**2 + 1/2*v.
-(v - 2)*(v + 1)/2
Let u(t) = t**3 + 2*t**2 - 4*t - 4. Let r be 0/(3*1/3). Let z = -5 + r. Let p(h) = h**3 + 2*h**2 - 5*h - 5. Let x(d) = z*u(d) + 4*p(d). Factor x(q).
-q**2*(q + 2)
Suppose 2/3*p**3 + 0 - 2/3*p + 0*p**2 = 0. What is p?
-1, 0, 1
Factor 1/5 - 13/5*t + 12/5*t**2.
(t - 1)*(12*t - 1)/5
Suppose -4*j + 11 = -4*q + 35, 0 = j + 4. Let a(y) be the second derivative of 0 - 1/60*y**6 + 2*y + 1/12*y**3 + 0*y**q + 1/24*y**4 - 1/40*y**5. Solve a(g) = 0.
-1, 0, 1
Let y(z) be the second derivative of z**4/4 - 7*z**3/6 - 3*z**2 + 2*z. Factor y(d).
(d - 3)*(3*d + 2)
Factor -41*w**2 - 16*w**3 + 11783*w - 2*w**4 + 7*w**2 - 11803*w.
-2*w*(w + 1)*(w + 2)*(w + 5)
Factor -3*d**4 + 16*d**3 + 63*d**4 + 324*d**5 + 84*d**4.
4*d**3*(9*d + 2)**2
Let a(f) = -f**2 - 3*f + 2. Let i(m) = 33 - 22*m**2 + 7*m**2 - 58*m + 10*m. Let l(u) = -33*a(u) + 2*i(u). What is k in l(k) = 0?
-1, 0
Let b = -4 + -1. Let n be (-18)/b + (-3)/5. Factor 0*w**2 + 2/3 + 1/3*w**n - w.
(w - 1)**2*(w + 2)/3
Let g = -3715487/672 + 5529. Let x(u) be the third derivative of 0*u**5 - g*u**8 + 0*u**3 - 1/210*u**7 + 0*u**4 + 0*u - 1/240*u**6 + 0 - u**2. Factor x(j).
-j**3*(j + 1)**2/2
Suppose 0 = 15*x - 17*x. What is i in 0*i + x + 2/5*i**2 + 2/5*i**3 = 0?
-1, 0
Let n = -118 + 120. Factor 0*b + 49/5*b**5 + 0 - 28/5*b**4 + 0*b**n + 4/5*b**3.
b**3*(7*b - 2)**2/5
Let t(x) = -10*x**3 - 10*x**2 + 5*x + 25. Let w(o) = -11*o**3 - 9*o**2 + 6*o + 26. Let d(b) = -6*t(b) + 5*w(b). Find h, given that d(h) = 0.
-2, 1
Let f be 0/(-1) + -1 + 13. Let a(k) = k**2 - 2*k - 2. Let q be a(-4). What is p in f*p**2 - 6*p**5 - 2 - p + 0*p + 3*p - 28*p**3 + q*p**4 = 0?
-1/3, 1
Let y(o) be the third derivative of o**7/70 + 3*o**6/40 + o**5/20 - 3*o**4/8 - o**3 + o**2. Find k, given that y(k) = 0.
-2, -1, 1
Let w(r) = r**2 + 2*r - 3. Let o = 2 - 0. Let n be w(o). Factor -h**3 - 2*h**5 + h**n - 3*h**4 + 5*h**4.
-h**3*(h - 1)**2
Let q be (-2 - -7)*-1*(-3 - -2). Let b(x) be the second derivative of 0 - 1/165*x**6 + 3/110*x**q + 0*x**2 - 3*x - 1/22*x**4 + 1/33*x**3. Factor b(s).
-2*s*(s - 1)**3/11
Suppose 0 = 22*j - 10 - 34. Let q(u) be the third derivative of 1/84*u**4 + 1/210*u**5 + 0*u**3 - 4*u**j + 0 + 0*u. Suppose q(v) = 0. Calculate v.
-1, 0
Let w = 4 - 10. Let z be (-20)/w*(-6)/(-15). Factor 4/3*m**3 - 2/3 + 0*m**2 + 2/3*m**4 - z*m.
2*(m - 1)*(m + 1)**3/3
Let o(w) be the first derivative of 0*w**3 - 1/90*w**5 + 1/36*w**4 + 0*w + w**2 + 2. Let f(t) be the second derivative of o(t). Determine a so that f(a) = 0.
0, 1
Find x, given that 0*x + 2*x**3 + 0 + 2/3*x**2 = 0.
-1/3, 0
Let d(l) be the second derivative of l**4/18 - 8*l. Factor d(g).
2*g**2/3
Suppose -2*i = i - 15. What is a in 5*a**3 + 30*a**4 + 4*a + 38*a**3 + 11*a**i - 4*a**5 + 24*a**2 = 0?
-2, -1, -2/7, 0
Suppose 0 = 2*u - 3*p - 4, 3*u + p - 5 = 1. Suppose -4*t + 3*t = -4*q, q - 2*t = 0. Suppose 0 + q*i - 1/3*i**3 - 1/3*i**u = 0. Calculate i.
-1, 0
Determine v, given that -2/3*v**3 - 2/9*v**4 - 4/9*v**2 + 0*v + 0 = 0.
-2, -1, 0
Let k(c) = -2*c**2 - 1 - 2 + 7*c**3 + 9*c**2 + 2*c - c. Let z(t) = -6*t**3 - 7*t**2 + 2. Let w(y) = -4*k(y) - 6*z(y). Determine v so that w(v) = 0.
-2, 0, 1/4
Let a(b) be the first derivative of b**4 - 28*b**3/3 - 17. Let a(t) = 0. What is t?
0, 7
Let a(i) be the first derivative of -i**3/18 + i**2 + 13*i/6 - 34. Let a(w) = 0. What is w?
-1, 13
Suppose s + 3*s = 20. Let w be (-2)/(-5) - 2/s. Let 0*o**4 + w*o**5 + o**4 + o**5 = 0. Calculate o.
-1, 0
Let w(x) = 5*x**2 - 15*x - 7. Let i(v) = -7*v**2 + 23*v + 10. Let g(q) = 5*i(q) + 8*w(q). Let t(r) = 4*r**2 - 4*r - 5. Let n(m) = -5*g(m) + 6*t(m). Factor n(h).
-h*(h - 1)
Let k(f) be the third derivative of -f**8/3360 - f**7/630 - f**6/360 + 5*f**4/24 - 6*f**2. Let t(a) be the second derivative of k(a). What is b in t(b) = 0?
-1, 0
Suppose -18 - 57 = 5*k. Let x be 4*(k/(-6))/5. Factor 3*t + 0 + 2 - 3*t**2 + x*t.
-(t - 2)*(3*t + 1)
Let p be (-6)/10 + 40/25. Let f = p + 2. Factor -6*s**2 - 3*s + f*s**4 + s - 5*s**4 - 6*s**3.
-2*s*(s + 1)**3
Suppose 3 = 4*a - 9, -5*d = a - 78. Let z = d - 13. Factor 2/9*b**z + 2/9*b**4 + 0 - 4/9*b**3 + 0*b.
2*b**2*(b - 1)**2/9
Let g(k) be the second derivative of k**7/42 + k**6/15 - k**4/6 - k**3/6 - 13*k. Factor g(j).
j*(j - 1)*(j + 1)**3
Suppose 2*x - 22*r = -18*r + 12, 4*r + 4 = -2*x. What is k in 2/3 + 2*k**x - 2/3*k**3 - 2*k = 0?
1
Factor 3/2*t + 0 - 3/8*t**2.
-3*t*(t - 4)/8
Let c = 37 + -30. Suppose 0 = -2*m + c*m.