1
Let w(u) be the third derivative of 0 + 1/840*u**8 - 2/75*u**5 + 0*u**3 + 1/50*u**6 - 4/525*u**7 + 0*u - u**2 + 1/60*u**4. Factor w(q).
2*q*(q - 1)**4/5
Let x(j) be the first derivative of j**5/60 + 3*j**2/2 + 1. Let r(u) be the second derivative of x(u). Factor r(s).
s**2
Let k be 65/(-2) + 10/5. Let o = 31 + k. Suppose -1/2*x**3 + o*x + 1/2 - 1/2*x**2 = 0. What is x?
-1, 1
Let i(x) be the third derivative of 1/420*x**7 + 0*x + 0 + 0*x**4 + 1/160*x**6 + 4*x**2 + 0*x**3 + 1/240*x**5. Determine k so that i(k) = 0.
-1, -1/2, 0
Let p = -4 + 7. Factor -4/7*b**p + 4/7*b**2 + 8/7*b + 0.
-4*b*(b - 2)*(b + 1)/7
Let l(o) = -2*o**3 - 4*o**2 + 6*o + 4. Let h(t) be the first derivative of t**4/4 + 5*t**3/3 - 7*t**2/2 - 5*t + 2. Let j(z) = 2*h(z) + 3*l(z). Factor j(k).
-2*(k - 1)*(k + 1)*(2*k + 1)
Let c be 0 + (2/2)/4. Suppose -2 - 8 = -2*u. Let 1/2*j**2 + 0*j + c*j**u + 5/4*j**3 + j**4 + 0 = 0. Calculate j.
-2, -1, 0
Factor 4*k**4 + k**4 - 10*k**2 + 131*k**3 - 131*k**3 + 5.
5*(k - 1)**2*(k + 1)**2
Factor 54/7*f**4 - 54*f**3 + 990/7*f**2 + 500/7 - 1150/7*f.
2*(f - 2)*(3*f - 5)**3/7
Let v = -80 + 86. Let p(h) be the second derivative of -1/45*h**v - 1/15*h**5 + 0*h**2 + 0 - 1/18*h**4 + h + 0*h**3. Factor p(a).
-2*a**2*(a + 1)**2/3
Let l(p) = -p**2 + 13*p - 19. Let q(u) = u**2 - u - 1. Let y(o) = l(o) - 3*q(o). Factor y(v).
-4*(v - 2)**2
Let w(p) be the second derivative of 0 - 1/3*p**3 + 2*p**2 - 1/6*p**4 + 4*p. Find u, given that w(u) = 0.
-2, 1
Let a(i) be the second derivative of 4*i - 1/18*i**4 + 0 + 0*i**2 - 2/9*i**3. Determine s, given that a(s) = 0.
-2, 0
Let w(o) be the first derivative of 2 + 1/4*o**3 + 3*o + 3/2*o**2. Let w(x) = 0. What is x?
-2
Let l(d) be the second derivative of 0 + 1/5*d**2 + 3*d + 1/10*d**3 - 1/100*d**5 + 0*d**4. Suppose l(r) = 0. Calculate r.
-1, 2
Let b(p) = 4 - 6*p**3 + p**4 + p - 2 + p + p**4. Let r(x) = -3*x**3 - 1 + x**2 + 4*x**3 - x + 0. Let d(c) = -b(c) - 2*r(c). Find h such that d(h) = 0.
0, 1
Let q(b) = 4*b. Let z be q(-1). Let v = -2 - z. Let 2*l**3 - v*l**5 - 4*l + 2*l**3 + 2*l = 0. Calculate l.
-1, 0, 1
Suppose 0*i + 45 = -5*i + 4*v, 2*i = 2*v - 18. Let k = -4 - i. Determine q so that -4*q**2 + 5*q**3 + q**k - q**3 + 2*q**3 + q - 4*q**4 = 0.
0, 1
Let m be (9 + -12)*(-1 + 0). Factor 2/9*c**5 + 4/9*c**4 + 0*c**m - 4/9*c**2 - 2/9*c + 0.
2*c*(c - 1)*(c + 1)**3/9
Suppose -4*o + p = -4, 0 = -5*o - 5*p + 10 + 20. Let q be -40*2/(-90)*o. Factor 0 + q*b + 4/3*b**3 - 2/9*b**4 - 8/3*b**2.
-2*b*(b - 2)**3/9
Let b(m) be the first derivative of m**6/120 + m**5/80 - m**4/48 - m**3/24 - 5*m - 5. Let h(l) be the first derivative of b(l). Factor h(i).
i*(i - 1)*(i + 1)**2/4
Let o(r) be the first derivative of -r**4/2 - 4*r**3/3 - r**2 + 1. Factor o(w).
-2*w*(w + 1)**2
Let a = 2 - 32. Let k be (-11)/a + (-4)/24. Solve 1/5*h**5 - 1/5*h**3 - k*h**4 + 0*h + 0 + 1/5*h**2 = 0 for h.
-1, 0, 1
Let a(j) = 3*j + 1. Let c be a(1). Let s = 7 - c. Suppose 0*t - t**2 - s*t + 4*t = 0. Calculate t.
0, 1
Suppose 1 + 1 = 4*v - 2*t, -4*t = v - 14. Find n such that -v + 9*n + 0 + 8 - 3*n**2 - 3*n**4 - 9*n**3 = 0.
-2, -1, 1
Factor 10/3*x**2 - 14/3*x + 4/3.
2*(x - 1)*(5*x - 2)/3
Let p(n) be the second derivative of -n**9/3024 + n**7/420 - n**5/120 - 7*n**3/6 - 9*n. Let z(c) be the second derivative of p(c). Factor z(s).
-s*(s - 1)**2*(s + 1)**2
Let c be (-4)/10 - 231/(-15). Suppose 0 = r + 4*r - 20. Find p, given that c*p**4 - 14*p**5 - 23*p**2 - 2 + r*p + 13*p + 10*p**4 + p**3 - 4*p = 0.
-1, 2/7, 1/2, 1
Let p(w) be the first derivative of w**8/1512 + w**7/945 - w**6/540 - w**5/270 - 2*w**2 + 3. Let m(k) be the second derivative of p(k). Factor m(h).
2*h**2*(h - 1)*(h + 1)**2/9
Let z = 2687 - 18710/7. Factor z*m**2 + 120/7*m**3 + 48/7*m**4 + 30/7*m + 3/7.
3*(m + 1)**2*(4*m + 1)**2/7
Let n(c) be the first derivative of -1/2*c + 3 - 1/8*c**2 + 1/12*c**3. Factor n(r).
(r - 2)*(r + 1)/4
Let h(d) be the first derivative of 4*d**5/5 + 2*d**4 + 4*d**3/3 - 5. Factor h(q).
4*q**2*(q + 1)**2
Let s be (-35)/(-30)*(-3)/(-42). Let a(b) be the third derivative of 0*b**3 + s*b**4 + 0*b + 1/30*b**5 + 0 - b**2. What is j in a(j) = 0?
-1, 0
Let i = 9 + -6. Factor -6*d**2 - d + i*d**2 - 2*d + 12*d.
-3*d*(d - 3)
Let z(v) be the second derivative of -49*v**6/180 - 21*v**5/20 - 109*v**4/72 - v**3 - v**2/3 + 8*v - 1. Let z(o) = 0. What is o?
-1, -2/7
Solve -6*h**2 + 16*h - 20*h**3 - 19*h**2 - 11*h**2 + 4*h**2 = 0.
-2, 0, 2/5
Let n(d) be the first derivative of d**5/35 + d**4/14 - d**3/21 - d**2/7 - 16. Let n(b) = 0. What is b?
-2, -1, 0, 1
Let t(d) be the third derivative of -1/18*d**3 - 1/180*d**6 + 0*d**4 + 0 + 0*d + 1/60*d**5 - d**2. Determine a so that t(a) = 0.
-1/2, 1
Let c(a) be the third derivative of a**7/210 + a**6/120 - a**5/10 - a**4/6 + 4*a**3/3 + 11*a**2. Suppose c(o) = 0. What is o?
-2, 1, 2
Let y(a) = 2*a - 10. Let m be y(7). Let r(h) be the first derivative of 4/15*h**3 + 1/20*h**m - 2 + 1/2*h**2 + 2/5*h. Factor r(u).
(u + 1)**2*(u + 2)/5
Let l(k) be the third derivative of -k**7/210 + k**6/15 - 11*k**5/30 + k**4 - 3*k**3/2 - 33*k**2. Let l(i) = 0. Calculate i.
1, 3
Let m be (12/63)/(-1*30/(-35)). Suppose -m*v**2 - 2/3*v - 4/9 = 0. What is v?
-2, -1
Let r = 518 - 1553/3. Factor 0 - 1/3*x**2 + 0*x - 1/3*x**5 + r*x**4 + 1/3*x**3.
-x**2*(x - 1)**2*(x + 1)/3
Suppose 7 = -2*i + 33. Suppose -n = -2*a + 4, 4*a + n = 1 + i. Solve 3*y**2 - y - y**2 - 2*y**3 + y**a = 0.
0, 1
Let c be ((-6)/9)/(0 - 2). Solve -1/3*q**2 - c*q**4 - 2/3*q**3 + 0*q + 0 = 0 for q.
-1, 0
Suppose 3 = -2*h + 15. Suppose 21*u - 24*u + h = 0. Let 9/5*z**u + 12/5 - 24/5*z = 0. What is z?
2/3, 2
Let z(t) = 35*t**2. Let p be z(-1). Let c be 4/p - (-18)/63. Factor 4/5*j**2 - c*j - 2/5*j**5 + 4/5*j**3 - 2/5 - 2/5*j**4.
-2*(j - 1)**2*(j + 1)**3/5
Let f(b) = -b**3 + b**2 - 1. Let u(a) = -6*a**3 + 27*a**2 - 36*a - 3. Let c(y) = -3*f(y) + u(y). Factor c(p).
-3*p*(p - 6)*(p - 2)
Let j = 5 + -3. Suppose -2*s - 4*v + 14 = -2*v, 0 = j*s - 5*v + 14. Factor 2*a**5 + 2*a**5 - 5*a**5 + 4*a**3 - s*a**3.
-a**3*(a - 1)*(a + 1)
Let o(z) be the second derivative of 81*z**5/10 - 21*z**4 + 20*z**3 - 8*z**2 - 4*z. Factor o(w).
2*(3*w - 2)**2*(9*w - 2)
Let m(c) be the first derivative of c**6/9 + 2*c**5/15 + 9. Factor m(b).
2*b**4*(b + 1)/3
Let t(n) be the first derivative of 1/2*n**3 + 0*n + 0*n**2 - 1. Solve t(o) = 0 for o.
0
Let b(m) be the third derivative of 49*m**6/780 - 77*m**5/390 + 8*m**4/39 - 4*m**3/39 - 16*m**2. Factor b(r).
2*(r - 1)*(7*r - 2)**2/13
Let 2/19 - 4/19*w + 2/19*w**2 = 0. Calculate w.
1
Suppose -x + 4*x - 18 = 0. Let p = -3 + x. Solve -k**3 + 5*k + 2*k**2 + 2*k**2 + k - k**p = 0 for k.
-1, 0, 3
Let t(g) be the third derivative of -g**7/70 - 3*g**6/40 + g**4/2 + 12*g**2. Factor t(v).
-3*v*(v - 1)*(v + 2)**2
Let x(m) = -38*m + 342. Let j be x(9). Factor j + 2/3*k**2 - 2/3*k**4 - 2/3*k**3 + 2/3*k.
-2*k*(k - 1)*(k + 1)**2/3
Let 2/11*z**2 - 8/11*z + 0 = 0. What is z?
0, 4
Factor -4/3*x**2 + 1/3*x**4 + 0 - 2*x**3 + 1/3*x**5 + 8/3*x.
x*(x - 2)*(x - 1)*(x + 2)**2/3
Let p be -3 - (-2)/((-4)/(-42)). Factor -p*z**2 - 9*z**3 - 3*z**4 - 3 - 3*z**3 + 97*z - 109*z.
-3*(z + 1)**4
Let y = -1 + 3. Suppose -4*i + y = -6. Factor 5*n**2 - 2*n**4 - 4 + i - n**2.
-2*(n - 1)**2*(n + 1)**2
Solve 2/5*t**3 + 0*t**2 + 0 + 0*t = 0 for t.
0
Let s = -6 - -13. Let z(t) be the third derivative of 0*t**3 - 1/105*t**s + 0*t + 0*t**6 + 1/30*t**5 + 0 + t**2 + 0*t**4. Suppose z(p) = 0. What is p?
-1, 0, 1
Let a = 3 - 1. Let c(v) = v**2 + 3*v - 4. Let u be c(-5). Factor 2*k**2 + a*k**3 - 2*k**4 + k**4 - u*k - k**5 - 1 + 5*k.
-(k - 1)**2*(k + 1)**3
Suppose 3*z = 4*f - 36, 0*z - 45 = -5*f + z. Let h = 14 - f. Determine l, given that 2/3*l + 0 - 16/3*l**2 + 16/3*l**4 - 32/3*l**h + 10*l**3 = 0.
-1, 0, 1/4, 1
Solve 225/7*p**3 + 4/7*p + 60/7*p**2 + 0 = 0 for p.
-2/15, 0
Let v(b) be the second derivative of -14*b**6/15 - 16*b**5/5 - 11*b**4/3 - 4*b**3/3 + 5*b. Factor v(c).
-4*c*(c + 1)**2*(7*c + 2)
Let z be (-3)/27 + 51/216. Let g(n) be the first derivative of 0*n - 1/12*n**3 - z*n**2 - 2. Factor g(i).
-i*(i + 1)/4
Let m(q) = 8*q**2 + 23*q + 22. Let o(a) = -9*a**2 - 24*a - 21. Let b(s) = -6*m(s) - 5*o(s). Let b(j) = 0. What is j?
-3
Let u(d) be the first derivative of -d**7/2520 + d**6/540 + d**5/360 - d**4/36 + d**3/3 + 2. Let m(j) be 