7
Let v be -9*(10/(-6) - -2) + 3. What is w in 2/5*w**4 + 0*w**3 + v*w + 0 - 2/5*w**2 = 0?
-1, 0, 1
Factor -1/2*p**2 + 3/2*p + 1 - 1/2*p**4 - 3/2*p**3.
-(p - 1)*(p + 1)**2*(p + 2)/2
Let n(y) be the second derivative of y**5/70 + y**4/42 - y**3/21 - y**2/7 - 11*y. Find u such that n(u) = 0.
-1, 1
Let o = 13 - 37. Let l be 8/o + 15/9. Factor 2/3*a - 2/3*a**2 + l.
-2*(a - 2)*(a + 1)/3
Factor 4*l**4 - 3*l**3 + 4*l**3 - 3*l**3 - 2*l**5.
-2*l**3*(l - 1)**2
Suppose 0 = -h + 4. Let r(o) be the third derivative of 0*o**5 - o**2 + 1/180*o**6 + 1/630*o**7 - 1/36*o**h + 0 - 1/18*o**3 + 0*o. Factor r(w).
(w - 1)*(w + 1)**3/3
Factor -2 - 1/3*r**2 + 5/3*r.
-(r - 3)*(r - 2)/3
Let m = -2/21 + -13/84. Let k = m + 11/12. Let -k*b - 2/3*b**2 + 4/3 = 0. What is b?
-2, 1
Let z be (6/5)/((-4)/10). Let m = -3 - z. Let 10/9*j**3 + 0 - 4/9*j**2 + m*j + 4/9*j**4 - 10/9*j**5 = 0. Calculate j.
-1, 0, 2/5, 1
Let g(v) be the third derivative of -1/4*v**4 + 0 + 0*v - 7/20*v**5 + 0*v**3 - 7*v**2. Factor g(h).
-3*h*(7*h + 2)
Let d = 73/2 + -36. Let -d*h**3 - 5/2*h - 2*h**2 - 1 = 0. What is h?
-2, -1
Let b be 3 - (-1 + 2)*-1. Let l(o) = o - 4. Let x be l(7). Factor t - 2*t**5 + 0*t + b*t**3 - x*t.
-2*t*(t - 1)**2*(t + 1)**2
Let c = 1 - -1. Factor 0*x**2 + x + 6*x**2 - 5*x**c.
x*(x + 1)
Suppose 5*k + 0*k + 13 = 4*u, 4*u = -3*k + 5. Let l(g) be the first derivative of -2/3*g + 1 + 1/6*g**4 - 1/3*g**u + 2/9*g**3. Find y, given that l(y) = 0.
-1, 1
Let t(o) be the first derivative of -1 + 1/15*o**3 + 0*o**2 - 1/5*o. Let t(p) = 0. Calculate p.
-1, 1
Factor 2 - 5*b**2 + 18 + 0.
-5*(b - 2)*(b + 2)
Let d(r) = r**3 - r + 4. Let t be d(0). Let b(q) be the first derivative of 0*q**2 + 1/8*q**t + 0*q + 0*q**3 + 2. Let b(h) = 0. Calculate h.
0
Let z(r) be the first derivative of r**3/5 - 3*r**2/5 + 3*r/5 - 2. Let z(y) = 0. What is y?
1
Let x(a) be the first derivative of -a**4/16 - a**3 - 6*a**2 - 16*a - 26. Factor x(y).
-(y + 4)**3/4
Let k = -467 + 469. Determine u so that -3/7*u + 0 + 3/7*u**3 + 0*u**k = 0.
-1, 0, 1
Let o(w) = 16*w - 16. Let v be o(1). Factor 1/4*u**2 - 3/4*u + v.
u*(u - 3)/4
Let r(x) = -8*x**2 - 9*x - 1. Let j(n) = -7*n**2 - 8*n - 1. Let v(l) = 7*j(l) - 6*r(l). Solve v(q) = 0.
-1
Let s(m) be the first derivative of 5*m**9/12096 + m**8/3360 - 7*m**3/3 - 7. Let t(i) be the third derivative of s(i). Factor t(d).
d**4*(5*d + 2)/4
Let l = 4 - 4. Suppose -4*m - 21 + 129 = l. Find c, given that 14*c - 6 + 2 - m*c**2 + 11*c**2 + 6*c**3 = 0.
2/3, 1
Suppose -5*m = -34 - 1. Suppose 0 = m*b - 8*b + 2. Factor 1/3*u**b + 1/3*u + 0.
u*(u + 1)/3
Let c(x) be the second derivative of x**4/60 + 5*x. Factor c(k).
k**2/5
Let y(x) be the first derivative of -7*x**5/10 + 5*x**4/6 + 2*x**3/3 - 2*x + 3. Let k(h) be the first derivative of y(h). Factor k(d).
-2*d*(d - 1)*(7*d + 2)
Let s(y) = -3*y**4 + 8*y**3 + 9*y**2 - 8*y - 1. Let g(b) = -3*b**4 + 9*b**3 + 9*b**2 - 9*b. Let k(q) = -5*g(q) + 6*s(q). What is z in k(z) = 0?
-1, 1, 2
Let y(s) be the third derivative of 0*s + 1/60*s**5 + 1/12*s**4 + 0 + 0*s**3 + 4*s**2. Solve y(a) = 0 for a.
-2, 0
Let j be (-68)/(-8)*(-2 + 0). Let v(f) = f**2 + 3*f + 2. Let m(d) = -3*d**2 - 9*d - 6. Let u(s) = j*v(s) - 6*m(s). Factor u(k).
(k + 1)*(k + 2)
Factor 0 - 1/3*k**3 + 1/6*k**5 + 0*k**4 + 0*k**2 + 1/6*k.
k*(k - 1)**2*(k + 1)**2/6
Suppose 1/3*t**3 + 2/3 + 0*t**2 - t = 0. What is t?
-2, 1
Let b(d) be the third derivative of -d**6/40 - d**5/20 + d**2. Determine a so that b(a) = 0.
-1, 0
Let d(v) = -v**2. Let x(w) = -18*w**2 + 9*w. Let y be 58/(-4) + 6/(-12). Let q(f) = y*d(f) + x(f). Factor q(h).
-3*h*(h - 3)
Suppose 8*g - 150 = 42. Let q = -24 + g. Let -2/5*z**3 + 2/5*z + q + 0*z**2 = 0. Calculate z.
-1, 0, 1
Let o(t) be the second derivative of t**6/75 + t**5/10 + 3*t**4/10 + 7*t**3/15 + 2*t**2/5 - 4*t. Let o(i) = 0. Calculate i.
-2, -1
Suppose -1/6*o**5 - 1/6 - 1/6*o**4 - 1/6*o + 1/3*o**2 + 1/3*o**3 = 0. Calculate o.
-1, 1
Suppose 0 = -p + 3*i - 10, -3*p = -5*i + 4*i - 2. Factor -2/11 - 2/11*z**p + 4/11*z.
-2*(z - 1)**2/11
Let n be -2*(0 + 6/4). Let q be (6/9)/(5 + n). Factor q*j**2 + j + 2/3.
(j + 1)*(j + 2)/3
Let h(c) be the first derivative of -c**4/3 - 4*c**3/3 - 2*c**2 + 8*c - 5. Let b(k) be the first derivative of h(k). Suppose b(a) = 0. What is a?
-1
Let j(f) be the first derivative of f**4/10 - 2*f**3/5 + 8*f/5 - 5. Determine y so that j(y) = 0.
-1, 2
Let j(d) be the second derivative of d**6/120 - d**5/40 + d**4/48 + d. Solve j(k) = 0 for k.
0, 1
Suppose -3*o = -2*o + 3, 0 = 3*i - 5*o - 15. Let c = i - -9. Factor c*q**2 - 12*q + 5 + q - 3.
(q - 1)*(9*q - 2)
Let f(s) be the second derivative of -5*s**7/42 - 2*s**6/3 - 3*s**5/4 + s. Let f(v) = 0. Calculate v.
-3, -1, 0
Let f(l) = 18*l**4 - 18*l**3 - 9*l + 15. Let s(b) = -110*b + b**2 - b**3 + 110*b + 1 + b**4. Let j(d) = -f(d) + 15*s(d). Factor j(w).
-3*w*(w - 3)*(w + 1)**2
Let d(s) be the third derivative of 1/5*s**5 + 4/3*s**3 + 0 + 1/420*s**7 + 0*s + 1/30*s**6 + 4*s**2 + 2/3*s**4. Suppose d(j) = 0. What is j?
-2
Let c be 3/(3/(-2) + 3). Factor 3*b**3 + 3*b**3 + 3*b**c + 8*b**4 - 5*b**4.
3*b**2*(b + 1)**2
Let y be (-7)/(-4) + 1457/(-940). Let -1/5*o**2 - y*o + 0 = 0. Calculate o.
-1, 0
Let j(m) be the second derivative of m**5/100 - 3*m**4/10 + 18*m**3/5 - 108*m**2/5 - 10*m. Suppose j(h) = 0. Calculate h.
6
Let u(j) be the first derivative of j**7/525 + j**6/300 - j**5/75 + 3*j**2/2 + 5. Let x(v) be the second derivative of u(v). Find o such that x(o) = 0.
-2, 0, 1
Factor -2/3*b**2 - 2/3*b**3 + 0 + 2/3*b + 2/3*b**4.
2*b*(b - 1)**2*(b + 1)/3
Solve -90*p**3 - 5/2*p**5 + 160*p + 40*p**2 + 0 + 55/2*p**4 = 0.
-1, 0, 4
Factor 12*j**2 - 12*j**4 - 10*j + 18*j + 2*j**3 - 10*j.
-2*j*(j - 1)*(j + 1)*(6*j - 1)
Let j(l) be the second derivative of -l**6/40 + l**5/5 - 5*l**4/8 + l**3 - l**2 - 3*l. Let q(v) be the first derivative of j(v). Determine f so that q(f) = 0.
1, 2
Let i = 32 + -15. Factor -17*b - 10*b**3 + i*b + 8*b**4 - 2*b**5 + 4*b**2.
-2*b**2*(b - 2)*(b - 1)**2
Let f(d) be the second derivative of -2*d**7/21 - 2*d**6/15 + d**5/5 + d**4/3 - 9*d. Determine n, given that f(n) = 0.
-1, 0, 1
Let w(y) be the first derivative of y**6/12 - y**5/5 - 5*y**4/8 + 5*y**3/3 + y**2 - 4*y + 7. Determine c so that w(c) = 0.
-2, -1, 1, 2
Suppose -c + 21 - 19 = 0. Solve 2/5*v - 2/5*v**c + 0 = 0.
0, 1
Let d(x) be the second derivative of x**7/8820 + x**6/630 + x**5/105 - x**4/4 - 2*x. Let b(t) be the third derivative of d(t). Factor b(o).
2*(o + 2)**2/7
Let r(c) be the first derivative of c**8/840 - c**6/180 + 4*c**3/3 + 2. Let j(z) be the third derivative of r(z). Factor j(x).
2*x**2*(x - 1)*(x + 1)
Suppose -39*u**5 - 19*u**5 + 8*u**5 + 40*u**4 - 8*u**3 = 0. What is u?
0, 2/5
Let m(y) be the first derivative of -1/12*y**4 + 1/9*y**3 - 1/15*y**5 - 2 + 0*y + 1/6*y**2. Let m(c) = 0. What is c?
-1, 0, 1
Suppose 2 = -a + 3*a. Let x be a - 3 - (-7)/2. Let -3/2*l - x*l**2 + 0 = 0. Calculate l.
-1, 0
Let w(l) = -l**2 + l. Let n(h) = h**3 + 18*h**2 + 100*h + 81. Let y(d) = -5*n(d) + 5*w(d). Factor y(f).
-5*(f + 1)*(f + 9)**2
Let d(j) = -7*j**2 - 5*j + 3. Let a(v) = -34*v**2 - 26*v + 14. Let m(i) = 3*a(i) - 14*d(i). Determine w, given that m(w) = 0.
-2, 0
Let -21/2*j - 30*j**2 - 33/2*j**3 + 3 = 0. What is j?
-1, 2/11
Let a be 3*(1 + (-7)/(-3)). Let w be 1/3 + a/6. Factor -4*m - 4*m**3 + 0*m**2 + 2*m - 6*m**w.
-2*m*(m + 1)*(2*m + 1)
Factor 4/3*j - 4/3*j**3 + 2/3 + 0*j**2 - 2/3*j**4.
-2*(j - 1)*(j + 1)**3/3
Let x = -3 - -1. Let h = 2 + x. Solve -12*n**3 - 10*n**4 - 2*n**5 + h*n**2 + 0*n**4 - 6*n**2 - n - n**5 = 0 for n.
-1, -1/3, 0
Suppose -a**3 - 25*a**2 + 6*a**3 - 55*a - 15 + 7*a**3 + 3*a**3 = 0. Calculate a.
-1, -1/3, 3
Factor 0 + 3/2*b**2 + 0*b.
3*b**2/2
Factor 4*h**2 - 5 - 5 - 4*h + 0*h + 2.
4*(h - 2)*(h + 1)
Solve -9/2*b**3 + 3 - 3/2*b**4 + 9/2*b - 3/2*b**2 = 0 for b.
-2, -1, 1
Factor -18*f**2 - 34 + 17*f**2 + 9 - 10*f.
-(f + 5)**2
Let s(w) = w**3 + 22*w**2 - 20*w + 69. Let z be s(-23). Factor 0*k**2 + z + 1/3*k**3 - 1/3*k.
k*(k - 1)*(k + 1)/3
Let w = 3 - -5. Factor -l**2 - 62 + 54*l + 2*l**3 - 17*l**2 + w.
2*(l - 3)**3
Suppose 28*r**2 + 4*r + 100/3*r**3 - 8/3 + 12*r**4 = 0. Calculate r.
-1, 2/9
Let g(z) = 5*z**4 + 17*z**3 + 33*z**2 + 23*z + 5. Let d(r) = -10*r**4 - 33*r**3 - 67*r**2 - 47*r - 10. Let f(u) = -3*d(u) - 7*g(