
Let t(b) be the third derivative of -b**8/112 - 11*b**7/210 - 3*b**6/40 + 7*b**5/60 + b**4/2 + 2*b**3/3 + 35*b**2. Determine k, given that t(k) = 0.
-2, -1, -2/3, 1
Suppose -5*b + 5 = -10. Suppose -4*i + 6 = -6. Factor -2*y**4 - 2*y**i - y**b - 3*y**3 - 4*y**2.
-2*y**2*(y + 1)*(y + 2)
Let p(v) be the first derivative of -1 + 1/6*v**3 + 0*v - 1/2*v**2. Determine s, given that p(s) = 0.
0, 2
Let c(r) be the first derivative of 4*r**7/105 + r**6/12 - r**5/10 - 5*r**4/12 - r**3/3 - r**2 + 2. Let a(i) be the second derivative of c(i). Factor a(k).
2*(k - 1)*(k + 1)**2*(4*k + 1)
Let j = 6 + -3. Suppose 2*i = -5*x + 21, 0 = 2*i - 4*x + 3 + j. Factor 4/7*z**2 + 2/7*z + 2/7*z**i + 0.
2*z*(z + 1)**2/7
Find a such that 2*a**2 + 8 - 11*a + 7 - 3 + a = 0.
2, 3
Let c(f) = f**2 - 4*f - 1. Let j be c(5). Suppose 9*s = j*s. Factor 0 + 1/2*r**4 + 1/4*r**3 - 1/4*r**2 + s*r.
r**2*(r + 1)*(2*r - 1)/4
Let g(u) be the first derivative of 3/10*u**5 + 0*u**4 - 1/10*u**6 + 3/2*u**2 - 2 - u**3 - 4*u. Let w(v) be the first derivative of g(v). Factor w(c).
-3*(c - 1)**3*(c + 1)
Let j(t) be the second derivative of t**6/720 + t**5/30 + t**4/3 + t**3/2 + 5*t. Let d(o) be the second derivative of j(o). Factor d(g).
(g + 4)**2/2
Let j(i) be the third derivative of -1/3*i**3 + 1/60*i**5 + 1/24*i**4 + 0*i + 8*i**2 + 0. Factor j(m).
(m - 1)*(m + 2)
Suppose l - 4 = 2*y - y, 0 = 2*y. Factor -1/4*s**l + 0*s - 1/4*s**2 + 1/2*s**3 + 0.
-s**2*(s - 1)**2/4
Let u = 33/5 + -6. Solve -3/5*o + 0 + 3/5*o**4 + 3/5*o**3 - u*o**2 = 0.
-1, 0, 1
Let q(h) = h**4 - h**2 - h - 1. Let f be 36/(-15)*10/(-4). Let x(p) = -16*p**4 + 26*p**3 - 12*p**2 + 4*p + 10. Let a(n) = f*q(n) + x(n). Factor a(g).
-2*(g - 1)**3*(5*g + 2)
Let n(x) = -x**4 + 5*x**3 - 4*x**2 + 3*x + 3. Let s(h) = -5*h + 7*h**2 + 1 - 2 - 9*h**3 - 4 + 2*h**4. Let c(j) = -5*n(j) - 3*s(j). Factor c(y).
-y**2*(y - 1)**2
Let q be (4 - 4)*(-3)/(-6). Factor 3*h**2 + 8*h + 4*h + q*h**2 - h**2 + 18.
2*(h + 3)**2
Solve 109/5*g**2 + 16/5*g**5 + 88/5*g**4 + 153/5*g**3 + 31/5*g + 3/5 = 0 for g.
-3, -1, -1/4
Let a(u) be the first derivative of 0*u**2 + 1/4*u**3 - 3/4*u + 3. Factor a(y).
3*(y - 1)*(y + 1)/4
Let f = 15 - 11. Suppose 0 = -3*u + f*u + 2, 0 = -4*w + 5*u + 30. Let 0*n**2 + 7*n**2 + 18*n**3 + 5*n**2 - n**w + 3*n + 4*n**5 + 12*n**4 = 0. Calculate n.
-1, 0
Let x = 31 + -92/3. Factor -x*r**2 + 2/3 - 1/3*r.
-(r - 1)*(r + 2)/3
Let h = -1698/5 - -340. What is n in -h*n**2 - 2/5*n + 0 = 0?
-1, 0
Let z(o) = -4*o**2 - 5. Let u(k) = -3 + k**2 + k**2 - 8*k**2 - 4. Let h(s) = 5*u(s) - 7*z(s). Let h(q) = 0. Calculate q.
0
Let l(m) = -m - 1. Let n(k) = -4*k - 8. Let w(t) = -2*l(t) + n(t). Let p be w(-5). Factor -2/7*y**2 - 2/7*y + 0 + 2/7*y**p + 2/7*y**3.
2*y*(y - 1)*(y + 1)**2/7
Factor 3*x**4 + 0*x**4 - 6*x**3 - 13*x**2 + 24*x + 25*x**2 - 24*x**2.
3*x*(x - 2)**2*(x + 2)
Let m(v) be the second derivative of v**6/45 - v**4/3 - 8*v**3/9 - v**2 + 7*v. Factor m(s).
2*(s - 3)*(s + 1)**3/3
Suppose 8 = 4*d + 5*x, 2*x + 4 = -3*d + 10. Let p be d + 2 + (-1 - 0). Let 3*q**2 + 2*q**5 + 2*q**3 - 6*q**4 + 4*q**p - 5*q**2 = 0. What is q?
0, 1
What is p in -2/15*p**2 + 0 + 0*p = 0?
0
Let p(k) be the first derivative of -2/3*k**3 + 0*k + k**2 + 2. Suppose p(i) = 0. What is i?
0, 1
Suppose 0 = -5*t + 2*n + 24, 4*t - n + 4 = 25. Let b be ((-10)/15)/((-20)/t). Factor 1/5*w**4 + 0*w + 0 - b*w**2 - 1/5*w**3 + 1/5*w**5.
w**2*(w - 1)*(w + 1)**2/5
Factor 0 - 2/3*q**2 + 4*q.
-2*q*(q - 6)/3
Let q be 4/(-18) + 22/99. Let t(n) be the second derivative of 0*n**4 + 1/105*n**6 + 0*n**2 - n + 0 - 1/70*n**5 + q*n**3. Suppose t(w) = 0. What is w?
0, 1
Suppose -5*a + 0*a = 40. Let u be (a/6)/((-2)/6). Find b, given that 4*b**2 + 0*b**4 - 3*b**2 + u*b**4 - 5*b**4 = 0.
-1, 0, 1
Let t = 83 + -47. Let k = t + -178/5. Determine r so that -k*r**3 + 0*r**2 - 4/5 + 6/5*r = 0.
-2, 1
Let o be (1/(-21))/((-2)/24). Factor 22/7*p + 18/7*p**2 + o.
2*(p + 1)*(9*p + 2)/7
Solve r**4 - 2*r + 0 + 3/2*r**3 - 2*r**2 - 1/2*r**5 = 0 for r.
-1, 0, 2
Let k be 116/30 + (-12)/(-90). Let q(u) be the third derivative of -u**2 - 1/60*u**5 + 0 - 1/6*u**3 + 1/12*u**k + 0*u. Suppose q(l) = 0. What is l?
1
Let c = 31 + -185/6. Let u(g) be the first derivative of -2*g - c*g**3 + 2 - g**2. Factor u(o).
-(o + 2)**2/2
Let b(s) be the first derivative of 4*s**5/5 - s**4 - 8*s**3 + 8*s**2 + 32*s + 42. Factor b(w).
4*(w - 2)**2*(w + 1)*(w + 2)
Let n(w) be the first derivative of -4*w**6/21 + 8*w**5/35 + 9*w**4/14 - 2*w**3/21 - 2*w**2/7 - 4. Suppose n(a) = 0. What is a?
-1, -1/2, 0, 1/2, 2
Suppose -4*x - 20 = -24. Factor -1/2*w**2 - 3/2*w - x.
-(w + 1)*(w + 2)/2
Let p be 3*75/(-90) + (0 - -3). Factor 0 + 0*f + 0*f**3 - p*f**4 + 1/2*f**2.
-f**2*(f - 1)*(f + 1)/2
Let b(j) = -6*j**4 + 18*j**3 - 12*j**2 + 7*j - 7. Let l(n) = -3*n**4 + 9*n**3 - 6*n**2 + 4*n - 4. Let c(v) = -4*b(v) + 7*l(v). Factor c(d).
3*d**2*(d - 2)*(d - 1)
Let i(h) be the second derivative of -h**8/672 + h**7/420 + h**6/240 - h**5/120 - 3*h**2/2 + 5*h. Let l(a) be the first derivative of i(a). Factor l(c).
-c**2*(c - 1)**2*(c + 1)/2
Let g be 16 - (-1 + 3) - -1. Suppose -3*z + k + g = 0, 5*z - 4*k - 33 = -5*k. Factor j**3 - 2*j + j - j**2 - 5 + z.
(j - 1)**2*(j + 1)
Let d(h) be the second derivative of 0 - 2/7*h**2 + 1/3*h**4 - 2*h - 1/7*h**3. Factor d(c).
2*(2*c - 1)*(7*c + 2)/7
Let t be 3/(-6)*16/(-4). Factor 2*y**2 - 4*y**t + 0*y**2.
-2*y**2
Let f(j) be the second derivative of -1/6*j**4 - 8*j + 0 - 9*j**2 + 2*j**3. Find a, given that f(a) = 0.
3
Let j = -52 + 157/3. Solve 0*o**2 - j*o**4 + 1/3 - 2/3*o + 2/3*o**3 = 0 for o.
-1, 1
Factor -28/3*j**2 + 11*j + 6 + 5/3*j**3.
(j - 3)**2*(5*j + 2)/3
Let r(j) be the third derivative of -1/180*j**5 + 1/72*j**4 + 0 - 7*j**2 - 1/360*j**6 + 0*j**3 + 0*j + 1/630*j**7. Factor r(b).
b*(b - 1)**2*(b + 1)/3
Let i(j) = 91*j**3 - 171*j**2 + 87*j - 25. Let q(x) = -46*x**3 + 86*x**2 - 44*x + 12. Let t be (-1)/(1*(-4)/36). Let w(h) = t*q(h) + 4*i(h). Factor w(a).
-2*(a - 1)*(5*a - 2)**2
Factor 5*w**3 + 13*w**2 - 12*w**2 - 21*w**2 + 20*w.
5*w*(w - 2)**2
Let s(n) be the third derivative of 1/4*n**4 + 2/3*n**3 + 1/30*n**5 - 3*n**2 + 0 + 0*n. Determine a, given that s(a) = 0.
-2, -1
Solve -2/9*c**3 + 2/9*c + 2/9 - 2/9*c**2 = 0 for c.
-1, 1
Let v(d) be the first derivative of -d**6/240 - d**5/30 - d**4/12 + 2*d**2 - 1. Let f(m) be the second derivative of v(m). Solve f(w) = 0.
-2, 0
Let m(g) = 23*g**3 - g**2 + 17. Let x(l) = 3*l**3 + 2. Let i(j) = -6*m(j) + 51*x(j). Factor i(u).
3*u**2*(5*u + 2)
Let z(g) = g + 1. Let a(m) = 2*m - 2. Let q be a(3). Let j be z(q). Let -f**4 + 4*f**2 - 2*f + 2*f**5 - 3*f**4 + 0*f**j = 0. What is f?
-1, 0, 1
Let d(h) be the third derivative of h**7/10080 - h**4/24 + 5*h**2. Let x(o) be the second derivative of d(o). Factor x(n).
n**2/4
Let a = -4 - -7. Solve 6*h**3 + 0*h**3 - 4*h + 2*h**2 - 2*h**a + 2*h = 0.
-1, 0, 1/2
Let f(x) = -x**4 + x**2. Let l(d) = -4*d**5 - 21*d**4 + 4*d**3 + 21*d**2. Let p(s) = f(s) - l(s). Factor p(t).
4*t**2*(t - 1)*(t + 1)*(t + 5)
Let k(t) = -t**3 + t**2 - t - 1. Let i(m) = -m**5 - m**4 - 5*m**3 + 9*m**2 - 8*m - 8. Let j(x) = 4*i(x) - 28*k(x). Factor j(n).
-4*(n - 1)**2*(n + 1)**3
Suppose -4*r + 6*u = 3*u - 21, 12 = -4*u. Factor -4/3*m + 0*m**2 + 2/3*m**4 + 4/3*m**r - 2/3.
2*(m - 1)*(m + 1)**3/3
Let l(j) = j**5 + j**2. Let w(d) = -30*d**3 - 2*d**5 + 26*d**2 - 4*d - 5*d**2 - d**5 + 22*d**4. Let v(n) = -3*l(n) + w(n). Factor v(p).
-2*p*(p - 1)**3*(3*p - 2)
Let y(s) be the third derivative of -s**8/336 - s**7/42 - 7*s**6/120 - s**5/20 - 5*s**2. Factor y(u).
-u**2*(u + 1)**2*(u + 3)
Let q(x) be the second derivative of -x**7/56 + 3*x**6/20 - 21*x**5/40 + x**4 - 9*x**3/8 + 3*x**2/4 + 4*x. Suppose q(p) = 0. What is p?
1, 2
Factor 6 - 2 - q - 2*q - 3*q + 2*q**2.
2*(q - 2)*(q - 1)
Let y(b) = -2*b**3 + 8*b**2 - 11*b. Let p(d) = -d**3 + 4*d**2 - 6*d. Let z(q) = -5*p(q) + 3*y(q). Factor z(g).
-g*(g - 3)*(g - 1)
Suppose -3*m + 3*r = -6*m - 210, -r = 0. Let k be (4/m)/(10/(-50)). Suppose 2/7*q - 2/7*q**2 - k*q**3 + 2/7 = 0. Calculate q.
-1, 1
Let n(q) be the second derivative of -q**5/130 + 5*q**4/78 + 20*q. What is i in n(i) = 0?
0, 5
Suppose -3*m + 0*m = 0. Suppose 3*h - 2*f - 17 + 0 = m, h - 2*f - 11 = 0. Factor 3/2*l**4 + 3/4*l**5 + 0*l + 0*l**2 + 3/4*l**h + 0.
3*l**3*(l + 1)**2/4
Let t