**4 + 0*a**2 + 0 - 1/27*a**6 + 1/27*a**3 + 2*a - 2/189*a**7. What is l in v(l) = 0?
-1, 0, 1/2
Let w(o) be the second derivative of -o**5/4 - 65*o**4/12 + 18*o. Factor w(k).
-5*k**2*(k + 13)
Let q(z) be the third derivative of -z**5/12 - 5*z**4/12 - 7*z**2. Factor q(v).
-5*v*(v + 2)
Find q, given that 8*q**4 + 16*q**4 + 3*q**3 - q**2 - 4*q**5 + q**3 - 23*q**4 = 0.
-1, 0, 1/4, 1
Factor -2/19*r**3 - 2/19*r**4 + 2/19*r**2 + 0 + 2/19*r.
-2*r*(r - 1)*(r + 1)**2/19
Let s(f) be the second derivative of -5*f**5/4 - 15*f**4/4 - 5*f**3/2 + 5*f**2/2 - 13*f. Factor s(x).
-5*(x + 1)**2*(5*x - 1)
Let h(r) be the second derivative of -r**7/18 - r**6/18 + r**5/30 - 8*r. Suppose h(x) = 0. Calculate x.
-1, 0, 2/7
Let q = -5 + 9. Let 3*o**q - 3*o - 1 - 22 - 1 - 9*o + 15*o**3 + 18*o**2 = 0. Calculate o.
-2, 1
Let k(t) be the first derivative of -2*t**2 - 1/20*t**5 + 1/4*t**4 + t + 1 + 0*t**3. Let i(s) be the first derivative of k(s). Factor i(d).
-(d - 2)**2*(d + 1)
Let 1/5*x**4 + 1/5*x**3 - 1/5*x - 3/5*x**2 + 2/5 = 0. What is x?
-2, -1, 1
Suppose 0 = -w + 3*w - 12. Suppose -4 = -5*a + w. Let a + 1/2*j**2 + 2*j = 0. What is j?
-2
Suppose -12/7*d**3 - 2/7*d**2 + 0 + 0*d = 0. What is d?
-1/6, 0
Let q(x) = -3*x + 8. Let b be q(4). Let d be ((-2)/(-4))/((-6)/b). Factor -1/3*w - 1/3 + 1/3*w**3 + d*w**2.
(w - 1)*(w + 1)**2/3
Let w(q) be the second derivative of -3*q - 1/25*q**5 + 1/5*q**2 + 1/15*q**3 - 1/15*q**4 + 1/75*q**6 + 0 + 1/105*q**7. Factor w(y).
2*(y - 1)**2*(y + 1)**3/5
Let q(y) be the first derivative of 0*y + 0*y**2 - 1/5*y**3 + 6. Factor q(m).
-3*m**2/5
Let g(r) = -r**3 - r**2 - 2*r + 4. Suppose 0*m = -m - 4. Let t(x) = -x + 1. Let b(y) = m*t(y) + g(y). Solve b(u) = 0 for u.
-2, 0, 1
Let f be (0 - -7) + -2 + 0. Factor 2*t**2 - f*t**2 + t**2.
-2*t**2
Suppose 0*f - 2*f = 0. Solve f*a**3 + 2*a**5 + a**5 - 4*a**3 - 4*a**4 = 0.
-2/3, 0, 2
Let c(z) be the first derivative of 3*z**5/5 - 3*z**4/4 - 2*z**3 - 8. Determine h so that c(h) = 0.
-1, 0, 2
Factor 5*u**3 + 24 - 36*u + 18*u**2 - 10*u**3 + 4*u**3 - 2*u**3.
-3*(u - 2)**3
Let v(i) be the first derivative of i**3 + 6*i**2 + 18. Determine x so that v(x) = 0.
-4, 0
Suppose 4 = -13*z + 15*z. Let o(h) be the second derivative of 0*h**z + 0 - 1/15*h**6 + 1/6*h**4 - h + 1/3*h**3 - 1/10*h**5. Factor o(l).
-2*l*(l - 1)*(l + 1)**2
Let -2*a**3 + 2*a - 1/2*a**4 + 2 - 3/2*a**2 = 0. Calculate a.
-2, -1, 1
Let s(i) be the first derivative of -1/12*i**3 + 0*i**2 + 0*i**4 - 1 + 1/40*i**5 - 5*i. Let r(t) be the first derivative of s(t). Solve r(o) = 0.
-1, 0, 1
Suppose 0 = -3*m + 5 + 1. Suppose 4*f - 5*f = -m. Factor -2/7*p**3 + 0 - 4/7*p**f - 2/7*p.
-2*p*(p + 1)**2/7
Factor -19*d**2 - 9*d + 39*d**2 - 20*d**2 + 3*d**3 - 6.
3*(d - 2)*(d + 1)**2
Let w(s) be the second derivative of s**7/840 + s**6/160 + s**5/240 - s**4/32 - s**3/12 - s**2 + 4*s. Let z(u) be the first derivative of w(u). Factor z(p).
(p - 1)*(p + 1)**2*(p + 2)/4
Let w = -2 + 8. Let m be (-2)/w - 90/(-54). Factor -2*u**2 - 2/9 - m*u.
-2*(3*u + 1)**2/9
Let k(w) be the third derivative of w**6/60 - 3*w**5/40 - w**4/4 - 2*w**3/3 + 4*w**2. Let i(m) be the first derivative of k(m). What is t in i(t) = 0?
-1/2, 2
Let z(i) be the first derivative of -i**6/480 - i**5/48 - i**4/32 + 3*i**3/8 + 3*i**2 - 3. Let d(u) be the second derivative of z(u). Factor d(l).
-(l - 1)*(l + 3)**2/4
Let z = -3517874/65 + 54120. Let q = 20/13 + z. Factor 2/5*t**2 + 0 + q*t.
2*t*(t + 1)/5
Let z be (-243 - -3)/4 - -2. Let k = 233/4 + z. Let -1 - k*m**2 - m = 0. Calculate m.
-2
Suppose 1/2*g**3 + 0*g**2 - 1 - 3/2*g = 0. What is g?
-1, 2
Factor 7*i**2 + 4*i - 6*i**2 - 8*i**3 + 13*i**2.
-2*i*(i - 2)*(4*i + 1)
Let c(x) be the third derivative of 0*x + 0 + 1/56*x**4 - x**2 + 0*x**3 + 1/140*x**5. Suppose c(h) = 0. Calculate h.
-1, 0
Let g(l) = l**3 + 14*l**2 - 15*l + 1. Let o be g(-15). Let k(q) be the first derivative of -o - 3/4*q**2 - 1/3*q**3 - 1/2*q. Factor k(v).
-(v + 1)*(2*v + 1)/2
Determine a, given that -2/9*a**2 - 4/9*a + 0 = 0.
-2, 0
Let o be 7/((-28)/(-6))*2. Factor 0 + 3/4*r**2 + 3/4*r**o + 0*r.
3*r**2*(r + 1)/4
Let x be 1/2*6*1. Let w(z) = -z**2 - 9*z - 12. Let a be w(-7). Factor 0 - 1/3*b**x - 2/3*b - b**a.
-b*(b + 1)*(b + 2)/3
Let u = 760/7 + -108. Find f such that 2/7*f - u + 2/7*f**2 = 0.
-2, 1
Let t(o) = o**2 + 2*o + 1. Let y(i) = i + 8. Let x be y(-11). Let g be t(x). Factor 1/4*u**5 + u**g + u**2 + 1/4*u + 0 + 3/2*u**3.
u*(u + 1)**4/4
Let q(t) = -t**3 + 4*t**2 - 3*t - 4. Let n(b) be the third derivative of b**5/20 - b**4/8 - b**3/2 + b**2. Let l(w) = -4*n(w) + 3*q(w). What is i in l(i) = 0?
-1, 0, 1
Let a = 19/21 + -4/7. Let g(y) be the second derivative of 0 - 1/4*y**2 + 3*y - 11/24*y**3 - a*y**4 - 7/80*y**5. Factor g(i).
-(i + 1)**2*(7*i + 2)/4
Let a(r) be the third derivative of r**8/392 + 4*r**7/245 - 8*r**5/35 - 4*r**4/7 + 38*r**2 + 2*r. Factor a(d).
6*d*(d - 2)*(d + 2)**3/7
Suppose 13 = s - 2*s + 5*l, 2*s - 19 = -5*l. Suppose 2/7*w + 2/7*w**s - 2/7 - 2/7*w**3 = 0. Calculate w.
-1, 1
Let o(d) be the first derivative of d**7/35 + d**6/15 + d**5/30 + 3*d**2/2 - 1. Let b(l) be the second derivative of o(l). Suppose b(r) = 0. What is r?
-1, -1/3, 0
Let p = 731/2 - 365. Factor r + p + 1/2*r**2.
(r + 1)**2/2
Suppose -6*g - 636 = -654. Factor -3/7*k + 0 + 18/7*k**2 - 27/7*k**g + 12/7*k**4.
3*k*(k - 1)**2*(4*k - 1)/7
Let f(n) = 10*n**2 - 10*n - 12. Let o(a) = 0*a + 0*a - 1 + a**2 - a. Let p(m) = -f(m) + 12*o(m). Determine u, given that p(u) = 0.
0, 1
Factor 396/13*m**2 + 54/13*m**4 + 270/13*m**3 + 232/13*m + 48/13.
2*(m + 3)*(3*m + 2)**3/13
Let -20*d - 4/9*d**3 + 200/9 + 16/3*d**2 = 0. What is d?
2, 5
Let y = -2 + 4. Factor y - 10*l**3 + 9*l**3 - 2 - l**4.
-l**3*(l + 1)
Find a, given that 0*a**2 - 1 - 4*a + 1 - 6*a**2 - 2*a**3 = 0.
-2, -1, 0
Factor -2/3*o**3 + 4/3*o**2 + 0*o - o**4 + 2/3*o**5 - 1/3.
(o - 1)**3*(o + 1)*(2*o + 1)/3
Let d(v) = -2*v + 37. Let u be d(17). Solve -11/4*s**4 - 3/2*s + 0*s**u + 5/2*s**2 + 3/2*s**5 + 1/4 = 0 for s.
-1, 1/3, 1/2, 1
Let i(b) be the first derivative of -3*b**5/20 - b**4 - 2*b**3 + 3*b + 8. Let p(n) be the first derivative of i(n). Let p(v) = 0. What is v?
-2, 0
Let m(u) = u**2 + u - 8. Let f be m(7). Let k = f - 334/7. Factor 0 - k*v**3 + 4/7*v + 2/7*v**2.
-2*v*(v - 2)*(v + 1)/7
Factor 0 + 0*t + 2/5*t**2 + 1/5*t**3.
t**2*(t + 2)/5
Let t(q) be the second derivative of -1/30*q**6 - 1/10*q**5 - 2*q + 0 + 1/12*q**4 + 0*q**2 + 1/3*q**3. Solve t(z) = 0 for z.
-2, -1, 0, 1
Let i(a) be the first derivative of a**4 + 4*a**3/3 - 2*a**2 - 4*a + 3. Factor i(w).
4*(w - 1)*(w + 1)**2
Let j = 4 + -2. Suppose 12 = j*y + 2*y. Solve -2/5*r**y - 2/5*r + 4/5*r**2 + 0 = 0 for r.
0, 1
Factor 6/7 - 2/7*t**3 + 2/7*t**2 + 10/7*t.
-2*(t - 3)*(t + 1)**2/7
Factor 0*m + 0*m**2 + 5/4*m**4 - 1/2*m**3 + 0.
m**3*(5*m - 2)/4
Let s(x) be the first derivative of 2*x**2 - x**4 - 5 + 6 + 4 + 1. Solve s(b) = 0.
-1, 0, 1
Let p(d) = 4*d + 78. Let n be p(-18). Let i(x) be the second derivative of -7/6*x**4 + 7/15*x**n + 0*x**2 + 2/3*x**3 - 1/5*x**5 + x + 0. Factor i(q).
2*q*(q - 1)*(q + 1)*(7*q - 2)
Let q(w) be the first derivative of 2/25*w**5 + 4/5*w**2 + 4 - 2/5*w**4 + 2/5*w**3 - 8/5*w. Factor q(r).
2*(r - 2)**2*(r - 1)*(r + 1)/5
Let a(p) be the second derivative of 1/21*p**3 + 5*p - 1/70*p**5 + 0 + 1/105*p**6 + 0*p**2 - 1/42*p**4. Factor a(x).
2*x*(x - 1)**2*(x + 1)/7
Let y(v) be the second derivative of 7/6*v**3 + 7*v + 0 + 1/30*v**6 + 1/4*v**5 + v**2 + 3/4*v**4. Factor y(a).
(a + 1)**3*(a + 2)
Let d(s) = 2*s**2 - 5*s + 12. Let b(q) = -q. Let i(l) = -10*b(l) - 2*d(l). Factor i(z).
-4*(z - 3)*(z - 2)
Let w(u) = -u**3 - 5*u**2 + 4*u - 10. Let c be w(-6). Factor -1/2*o**4 + 0 - 1/2*o**3 + 1/2*o**c + 0*o + 1/2*o**5.
o**2*(o - 1)**2*(o + 1)/2
Suppose 3*s - 5*v = 27, -4*s - s = 2*v - 14. Let c(k) = k**2 - 2*k + 2. Let m be c(2). Factor b**3 + 5*b + m*b**5 + 3*b**3 - s*b**5 - 7*b.
-2*b*(b - 1)**2*(b + 1)**2
Suppose 0 = 3*o + 3*n - 9, -6*n = o - 3*n - 5. Let u = -199 - -998/5. Let -3/5*r + u*r**o - 6/5 = 0. Calculate r.
-1, 2
Let o(n) be the second derivative of -n**4/18 - n**3/9 + 3*n. Factor o(j).
-2*j*(j + 1)/3
Let g(h) = h + 4. Let p be g(4). Factor q - 6*q**3 - 12*q**2 + 8*q**2 + q + p*q**5 + 8*q**4.
2*q*(q + 1)**2*(2*q - 1)**2
Let z(v) be the third derivative of -v**8/47040 - v*