/39*t**3. Factor g(d).
2*(d + 3)*(3*d + 2)**2/13
Let w be 88/406 + -1 - -1. Let n = w + 2/29. Factor n*z + 0 - 2/7*z**2.
-2*z*(z - 1)/7
Let u(k) be the first derivative of -8/11*k**4 + 0*k - 16/33*k**3 + 6 - 1/11*k**2. Factor u(o).
-2*o*(4*o + 1)**2/11
Factor 2/3*p**3 + 0*p + 0 - p**4 + 1/3*p**2.
-p**2*(p - 1)*(3*p + 1)/3
Let q = -7 - -11. Suppose f + 0*f - 2 = 0. Suppose -q*c**2 - c**2 + 2 + 3*c**f = 0. What is c?
-1, 1
Let o(p) be the second derivative of -3*p - 1/20*p**5 + 0 + 1/30*p**6 - 1/168*p**7 - 1/24*p**4 + 5/24*p**3 - 1/4*p**2. Factor o(i).
-(i - 2)*(i - 1)**3*(i + 1)/4
Factor -4*a**2 + 6 - 10 - 20 - 28*a.
-4*(a + 1)*(a + 6)
Let g(l) be the second derivative of -l**8/5600 - l**7/1400 + l**5/200 + 2*l**4/3 + 5*l. Let q(u) be the third derivative of g(u). Suppose q(h) = 0. What is h?
-1, 1/2
Suppose 0 = -2*n + 4*n. Let b(o) be the third derivative of 1/160*o**6 + 1/96*o**4 + 0 + n*o + 0*o**3 - 1/60*o**5 + o**2. Factor b(k).
k*(k - 1)*(3*k - 1)/4
Let z = -428/3 + 143. Factor 2/3*q**2 - 1/3*q**4 + 0*q**3 - z + 0*q.
-(q - 1)**2*(q + 1)**2/3
Let d(v) be the first derivative of 16*v**6/135 - 8*v**5/45 + v**4/9 - v**3/27 - 2*v**2 - 2. Let a(w) be the second derivative of d(w). What is c in a(c) = 0?
1/4
Let a = 41/20 + -9/5. Factor -a + 1/2*g**3 - 1/2*g + 1/4*g**4 + 0*g**2.
(g - 1)*(g + 1)**3/4
Let m(o) be the third derivative of 3*o**2 - 1/44*o**4 + 0*o - 1/330*o**5 + 0 - 2/33*o**3. Factor m(t).
-2*(t + 1)*(t + 2)/11
Let f be 1/3*(13 + 63/(-9)). Find x such that 5/4*x**4 + 0*x + 2*x**3 + x**f + 0 + 1/4*x**5 = 0.
-2, -1, 0
Let f be (-90)/54*2/(-60). Let x(u) be the second derivative of 0*u**3 - 1/45*u**6 + 0*u**2 + f*u**4 + 0 - 2*u + 0*u**5. Find n such that x(n) = 0.
-1, 0, 1
Let t be ((0 - 3/(-6))*0)/(-2). Factor -8/5*v**4 + 0 + t*v - 2/5*v**5 + 0*v**2 - 8/5*v**3.
-2*v**3*(v + 2)**2/5
Let b be (-8)/(-6)*(-6)/(-2). Factor -l**4 + l**2 + 6 - l**3 - 2 - b + l.
-l*(l - 1)*(l + 1)**2
Factor 10/7*k**3 + 18/7*k**2 + 2/7*k**4 + 2*k + 4/7.
2*(k + 1)**3*(k + 2)/7
Let b(i) be the first derivative of -i**6/540 - i**5/135 + i**4/108 + 2*i**3/27 - i**2 - 2. Let p(z) be the second derivative of b(z). Solve p(c) = 0.
-2, -1, 1
Let h(z) = -z**2 + 4*z. Let m = 7 - 4. Let n be h(m). Factor -4*t**2 + 1/3*t + 3*t**n + 2/3.
(t - 1)*(3*t - 2)*(3*t + 1)/3
Factor 4/5*x**3 + 4/5*x**2 + 0*x + 0.
4*x**2*(x + 1)/5
Let m(l) = -l**3 - l**2 - 2. Let h be m(-2). Let c be 1/(-4) + (-33)/(-36). Find p such that 2/3*p**h - c*p + 0 = 0.
0, 1
Let j(x) be the second derivative of x**5/10 + 5*x**4/3 + 25*x**3/3 - 7*x. Let j(p) = 0. Calculate p.
-5, 0
Factor -4*y + y**2 - 7*y**2 - 4*y**2 + 6*y**2.
-4*y*(y + 1)
Let t = -54 + 32. Let k(s) = -16*s**4 - 6*s**3 + 11*s. Let h(g) = 3*g**4 + g**3 - 2*g. Let f(c) = t*h(c) - 4*k(c). Factor f(z).
-2*z**3*(z - 1)
Let p(u) be the second derivative of u**7/168 + u**6/60 - 2*u. Determine d so that p(d) = 0.
-2, 0
Let x be 0*-6*(-1)/30. Let 2/5*o + 2/5*o**4 + x - 2/5*o**2 - 2/5*o**3 = 0. What is o?
-1, 0, 1
Let w be (-4)/(-3) - (24/(-9) - -2). Factor -1/4*l**w + 0*l + 1/4.
-(l - 1)*(l + 1)/4
Let m be (-6*(-2)/9)/(10/3). Let c(q) be the second derivative of 2*q - m*q**3 + 0 - 1/30*q**4 - 9/5*q**2. What is b in c(b) = 0?
-3
Let u be 10/25 - 40/225. Factor 2/9*o**4 + u + 0*o - 4/9*o**2 + 0*o**3.
2*(o - 1)**2*(o + 1)**2/9
Suppose 5*v - y = 12, 4*v = 2*v - 2*y. Solve -2 + k**2 + v = 0 for k.
0
Let x be (-1 + 3/3)*-1. Suppose 17 = 4*u - n, -3*u - 5*n = -x*n + 16. Determine o, given that 2*o**u + 2*o**4 - 3*o**4 + o**2 - 2*o**2 = 0.
0, 1
Let x(d) be the first derivative of 4*d**3/3 - 4*d**2 - 32*d - 28. Factor x(t).
4*(t - 4)*(t + 2)
Let w be (80/50)/((-2)/(-5)). Let j = -2 + w. Solve 1 + 4*c**j - 3*c - c**2 - c**3 + 0 = 0 for c.
1
Let v(d) = -d**2 + d + 3. Let h be v(0). What is t in -3*t**4 + 0 + 2*t**2 - h*t**4 - 1 + 5*t**4 = 0?
-1, 1
Let z = 650 - 1299/2. Factor 0*l**2 - 1/2*l + 0 + z*l**3.
l*(l - 1)*(l + 1)/2
Let -9/4*n - 3/4*n**2 - 3/2 = 0. Calculate n.
-2, -1
Let v(r) be the third derivative of -r**6/600 - r**5/150 + r**4/120 + r**3/15 + 5*r**2. Factor v(g).
-(g - 1)*(g + 1)*(g + 2)/5
Let j(d) be the second derivative of 0 + 1/15*d**2 - 7*d - 1/315*d**7 + 1/15*d**3 - 1/75*d**6 - 1/75*d**5 + 1/45*d**4. Factor j(r).
-2*(r - 1)*(r + 1)**4/15
Let c(a) be the first derivative of a**4/12 - a**2/2 + 2*a/3 + 4. Factor c(r).
(r - 1)**2*(r + 2)/3
Factor -5*z**2 + 51*z**4 + 4*z**2 - 50*z**4.
z**2*(z - 1)*(z + 1)
Suppose -6*b - 30 = -11*b. Let l(o) be the second derivative of -1/18*o**3 + 1/90*o**b + 0 + 1/60*o**5 + 0*o**2 - 1/36*o**4 + 4*o. Solve l(y) = 0.
-1, 0, 1
Let g = 3143/5 - 627. Suppose -4*d + 10 = 2. Factor 4/5 - 2/5*c**3 + g*c**2 - d*c.
-2*(c - 2)*(c - 1)**2/5
Find t, given that -6*t**2 - 4*t**2 - 5*t**2 + 13*t**2 + 2*t**4 = 0.
-1, 0, 1
Let p be 6/(-9)*4/(-8). Determine v so that v**3 - 8/3*v + 4/3 + p*v**2 = 0.
-2, 2/3, 1
Let z be (-1)/((-21)/9 + 2). Let f = 7 + -3. Determine p so that -1 + 5*p**2 + 1 - f*p**2 + p**z = 0.
-1, 0
Let b(z) = 2*z**4 - 8*z**3 - 8*z**2 + 8*z - 6. Let f(c) = 12*c**2 - 7*c**3 + 14*c**3 - 2*c**4 + 5 - 7*c - 5*c**2. Let y(x) = -5*b(x) - 6*f(x). Factor y(k).
2*k*(k - 1)**2*(k + 1)
Let w(g) be the third derivative of 0 - 8*g**2 - 1/96*g**4 + 0*g - 1/240*g**5 + 0*g**3. Factor w(c).
-c*(c + 1)/4
Suppose -6*t + 0*t = -18. Factor -5*u - 5 + 2*u + 3*u**2 + 5 - t*u**4 + 3*u**3.
-3*u*(u - 1)**2*(u + 1)
Let l(o) be the second derivative of 3*o**5/80 + o**4/16 - 5*o**3/8 + 9*o**2/8 - 15*o. Factor l(v).
3*(v - 1)**2*(v + 3)/4
Suppose 0 = 5*n - 3*f - 5, -n - f = -2 - 7. Suppose 0*a + 4*a = -2*t + 16, 0 = n*a + t - 12. Determine d so that -2 - 3*d**2 - 4*d + d**a + 0*d**2 = 0.
-1
Let i = 20 + -18. Let n(o) be the first derivative of -1/12*o**4 + 0*o + 0*o**i + 0*o**3 + 1/15*o**5 - 2. Factor n(d).
d**3*(d - 1)/3
Suppose 2*c + 4*h - 12 = 0, h - 7 = -2*c + 2*h. Suppose -c*a + 2*a = -6. Factor -2/3*d**2 + 2/3*d**a - 2/3*d + 2/3.
2*(d - 1)**2*(d + 1)/3
Find t such that 1/2*t**2 + 0*t - 1/4*t**5 + 1/4*t**3 - 1/2*t**4 + 0 = 0.
-2, -1, 0, 1
Let c(l) be the second derivative of l**5/60 - l**4/36 - l**3/18 + l**2/6 - 3*l. Factor c(s).
(s - 1)**2*(s + 1)/3
Factor 1/4*c**2 + 0 - 1/4*c**4 + 1/4*c**5 + 1/2*c - 3/4*c**3.
c*(c - 2)*(c - 1)*(c + 1)**2/4
Let o(r) = 4*r**4 + 6*r**3 - 18*r**2 - 4. Let n(i) = -3*i**4 - 6*i**3 + 18*i**2 + i + 5. Let u(f) = -4*n(f) - 5*o(f). Factor u(c).
-2*c*(c - 1)*(c + 2)*(4*c - 1)
Let y(m) be the third derivative of m**6/120 - m**5/20 + m**4/12 + m**3/2 - m**2. Let a(w) = 2*w**3 - 8*w**2 + 6*w + 8. Let x(f) = 3*a(f) - 8*y(f). Factor x(k).
-2*k*(k - 1)*(k + 1)
Let c be (-20)/(-110) + 2/(-11). Let t(i) be the second derivative of 0*i**2 + c + 3/25*i**5 + 1/70*i**7 + 1/30*i**3 - 1/15*i**6 - 1/10*i**4 - 4*i. Factor t(d).
d*(d - 1)**3*(3*d - 1)/5
Let o(u) be the first derivative of 4*u**3/3 - 12*u**2 + 36*u - 18. Solve o(v) = 0 for v.
3
Factor 4/7*l + 2/7*l**2 - 6/7.
2*(l - 1)*(l + 3)/7
Suppose 0 = -5*l - 3*k + 168, 3*l + 3*k = 4*k + 112. Let h be (-4)/18 - (-107)/l. Factor -4*j**2 - 1/2 + 7/4*j**3 + h*j.
(j - 1)**2*(7*j - 2)/4
Let u(k) be the third derivative of -1/180*k**6 + 0*k + 5*k**2 + 2/27*k**3 + 0 - 1/36*k**4 - 4/135*k**5. Factor u(d).
-2*(d + 1)*(d + 2)*(3*d - 1)/9
Let o(n) be the first derivative of -n**3/12 + n**2/8 + n/2 + 6. Let o(m) = 0. What is m?
-1, 2
Let l(q) be the third derivative of -q**7/280 - q**6/60 - q**5/40 - 5*q**3/6 + 4*q**2. Let h(n) be the first derivative of l(n). Factor h(t).
-3*t*(t + 1)**2
Suppose k = -3*v + 5*k + 14, 17 = -v - 3*k. Let x be v/(-5) - (-119)/15. Factor 8/3 + 8/3*y**4 + 1/3*y**5 + 38/3*y**2 + x*y**3 + 28/3*y.
(y + 1)**2*(y + 2)**3/3
Suppose -4*p + 5*f + 35 = 0, 3*p = -4*f + 5 - 2. Let l be (-8)/40 - (-1)/p. Factor 0 + l*d + 1/4*d**4 - 1/2*d**3 + 1/4*d**2.
d**2*(d - 1)**2/4
Let l(f) = -2*f - 8. Let h be l(-4). Let b(y) be the third derivative of y**2 + h*y**4 - 1/120*y**6 + 0 + 0*y**3 + 0*y + 1/60*y**5. Factor b(o).
-o**2*(o - 1)
Let n(l) = -l**3 - 8*l**2 + 10*l. Let o be n(-9). Let s(a) = a**2 + 8*a - 6. Let q be s(o). Factor -1/3*c + 5*c**2 - 19/3*c**q + 7/3*c**4 - 2/3.
(c - 1)**3*(7*c + 2)/3
Let i(h) = -6*h + 30. Let k be i(5). Find j such that 0 + 1/3*j**4 - 2/3*j**3 + k*j + 1/3*j**2 = 0.
0, 1
Let i be (4/(-6))/((-40)/30). Solve -b**3 + i*b**2 + 1/2*b**4 + 0 + 0*b = 0 f