2 + 560*r - 265. Let n(q) = 6*a(q) - 25*u(q). Factor n(g).
5*(g - 3)*(g - 2)**2*(g - 1)
Let b(h) be the second derivative of 11/12*h**4 + 4/5*h**5 - 2*h + 7/30*h**6 + 1/3*h**3 + 0 + 0*h**2. Factor b(d).
d*(d + 1)**2*(7*d + 2)
Let v(x) be the first derivative of -2/9*x**3 + 2 + x**2 - 4/3*x. Suppose v(u) = 0. What is u?
1, 2
Let u(j) be the third derivative of 0*j - 5*j**2 + 0*j**4 - 2/105*j**7 + 1/30*j**6 + 0 - 1/84*j**8 + 0*j**3 + 1/15*j**5. Factor u(a).
-4*a**2*(a - 1)*(a + 1)**2
Let k(c) be the second derivative of c**6/120 + c**5/40 - c**4/4 + 5*c**3/6 - 6*c. Let a(o) be the second derivative of k(o). Suppose a(b) = 0. Calculate b.
-2, 1
Let c be 0 - -6*2/28. Solve -3/7*y - c*y**2 + 0 = 0 for y.
-1, 0
Let b = 20 - 18. Suppose 0 = -b*o - o. Factor o + 0*u + 1/4*u**2.
u**2/4
Let x(c) be the second derivative of -c**5/5 + c**4/3 + 2*c**3/3 - 2*c**2 + 19*c. Let x(f) = 0. Calculate f.
-1, 1
Let g(c) be the first derivative of 4*c**3/3 + 8*c**2 - 18. Factor g(f).
4*f*(f + 4)
Let d(k) = -2*k + 1. Let x be d(6). Let w = x + 11. Factor 1/2*c**2 + 1/2*c + w.
c*(c + 1)/2
Suppose 5*j - 203 = -193. Let -15/2*r**3 - 9/2*r**j + 6*r**4 + 15/2*r - 3/2 = 0. What is r?
-1, 1/4, 1
Let p(u) be the first derivative of -u**6/6 + u**4 - 21. Factor p(s).
-s**3*(s - 2)*(s + 2)
Let t(r) = 32*r**2 - 47*r - 23. Let i(k) = 11*k**2 - 16*k - 8. Let h(b) = 11*i(b) - 4*t(b). Determine d so that h(d) = 0.
-2/7, 2
Let b be (-6)/1*10/(-20). Determine h, given that 2/5*h**b + 6*h + 14/5*h**2 + 18/5 = 0.
-3, -1
Let s = -1208 - -1210. Find y, given that 1/6 - 1/6*y + 1/6*y**3 - 1/6*y**s = 0.
-1, 1
Let q(p) be the first derivative of -2*p**5/25 - p**4/10 + 2*p**3/15 + p**2/5 + 6. Factor q(y).
-2*y*(y - 1)*(y + 1)**2/5
Let n be 2/9 - (-21)/27. Solve n + k**4 - k**2 + 2 - 3 = 0.
-1, 0, 1
Let h(o) = 2*o**2 + 11*o + 32. Let y(z) = 3*z**2 + 16*z + 48. Let d(f) = 8*h(f) - 5*y(f). Factor d(i).
(i + 4)**2
Let i(c) be the first derivative of c**6/360 + c**5/180 + 3*c**2/2 - 4. Let z(q) be the second derivative of i(q). Factor z(t).
t**2*(t + 1)/3
Solve 1/8*o**4 + 0*o + 0*o**2 - 1/8*o**3 + 0 = 0 for o.
0, 1
Let b(t) be the third derivative of t**8/168 - t**6/20 + t**5/15 + 10*t**2. Factor b(r).
2*r**2*(r - 1)**2*(r + 2)
Let v(t) be the second derivative of -2*t + 0 - 1/28*t**4 + 3/7*t**3 - 27/14*t**2. Solve v(b) = 0.
3
Let h = -1/488 - -981/2440. Factor -h*m + 2/5*m**4 - 2/5*m**2 + 0 + 2/5*m**3.
2*m*(m - 1)*(m + 1)**2/5
Let m(x) = -x**2 + 5*x - 1. Let j be m(1). Let a(q) be the first derivative of 4 - 1/12*q**j + 1/8*q**2 + 0*q. Let a(o) = 0. Calculate o.
0, 1
Let n(x) = x**3 + x**2 + x + 2. Let o be n(0). Suppose -u = 4*l - 16, 2*u - 4*u = -l - 5. Factor 3/4*m**l - 1/4*m + 0 - 1/2*m**o.
m*(m - 1)*(3*m + 1)/4
Let w = -1 + 1. Let v(t) be the second derivative of -t**3 + w + t - 3/4*t**4 - 1/2*t**2. Factor v(i).
-(3*i + 1)**2
Suppose -5*g + 3*f = -53, f - 1 - 8 = -g. Let w be g/16*8/20. Let w*d + 0 + 1/4*d**2 = 0. What is d?
-1, 0
Let y(t) be the first derivative of 7*t**6/2 + 6*t**5/5 + 3*t**4/28 - 7. Solve y(d) = 0.
-1/7, 0
Factor 0*d + 4/5*d**3 + 4*d**2 + 0.
4*d**2*(d + 5)/5
Suppose 2*w + v - 16 = 1, -5*v + 8 = -w. Suppose w*k**2 + 0*k + 2*k - 8*k**2 - 3*k = 0. What is k?
-1, 0
Let x(u) be the first derivative of -u**5/5 + 3*u**4/4 - u**3 + 3*u**2/2 + 7. Let b(d) = -d**4 + 4*d**3 - 4*d**2 + 4*d. Let y(s) = 3*b(s) - 4*x(s). Factor y(z).
z**4
Let z(s) be the second derivative of -2*s**5/65 - s**4/78 - 33*s. Factor z(o).
-2*o**2*(4*o + 1)/13
Let d = 47 + -23. Let f be (6/(-4))/(d/(-4)). Solve -f*m**5 + 1/2*m**2 + 1/2*m**3 - 1/4*m - 1/4*m**4 - 1/4 = 0 for m.
-1, 1
Let j(q) be the first derivative of 2/3*q**3 + 4*q + 1 + 3*q**2. Solve j(t) = 0 for t.
-2, -1
Let g(f) be the third derivative of 1/60*f**6 + 0*f + 1/30*f**5 + 0 + 0*f**3 + 0*f**4 + f**2. Suppose g(i) = 0. What is i?
-1, 0
Let n(t) be the first derivative of -t**5/10 - t**4/6 - 2*t - 1. Let k(p) be the first derivative of n(p). Factor k(l).
-2*l**2*(l + 1)
Let m(b) be the second derivative of -b**9/45360 + b**4/2 + 6*b. Let c(t) be the third derivative of m(t). Factor c(n).
-n**4/3
Factor -4/9 + 2/9*q**2 + 2/9*q.
2*(q - 1)*(q + 2)/9
Let g(o) be the first derivative of -o**4/8 - o**3/8 + 3*o - 3. Let r(t) be the first derivative of g(t). Factor r(n).
-3*n*(2*n + 1)/4
Let v(n) be the second derivative of 0*n**2 + n + 0*n**3 + 0 - 1/30*n**4. Factor v(c).
-2*c**2/5
Let k(w) be the second derivative of w**7/14 + w**6/10 - 3*w**5/10 + 7*w. Determine s so that k(s) = 0.
-2, 0, 1
Factor 0*c + 16/3 - 4/3*c**3 - 4*c**2.
-4*(c - 1)*(c + 2)**2/3
Suppose 3 = b - 2. Solve b*s**4 + 6*s**3 + 2*s**4 - s**4 + 2*s**2 + 2*s**5 = 0.
-1, 0
Suppose 0 = -4*l - 20. Let d(m) = -m - 1. Let c(n) = n**4 + n**3 - n**2 + 4*n + 5. Let a(v) = l*d(v) - c(v). Suppose a(k) = 0. Calculate k.
-1, 0, 1
Solve 2/3 + 6*t + 27/2*t**2 = 0 for t.
-2/9
Determine x, given that 6*x - x**3 + x**4 - 7*x - x**2 + 2*x = 0.
-1, 0, 1
Factor 0*j**4 + 2/3*j**3 + 0*j + 0 + 2/9*j**2 - 8/9*j**5.
-2*j**2*(j - 1)*(2*j + 1)**2/9
Let t = -32/5 + 101/15. Let -t*y**4 + 0 + 1/3*y**2 + 2/3*y**3 - 2/3*y**5 + 0*y = 0. What is y?
-1, -1/2, 0, 1
Let h(g) be the second derivative of 0 + 1/8*g**5 - 2/3*g**3 + g**2 + g - 7/24*g**4. Factor h(v).
(v - 2)*(v + 1)*(5*v - 2)/2
Suppose -5*s = -2*a - 6*s + 12, -2*a = -2*s. Factor -3/5*z**a - 3/5*z**3 - 1/5*z**5 - 1/5*z**2 + 0 + 0*z.
-z**2*(z + 1)**3/5
Determine b, given that 3*b**3 - 9*b**2 + 23 - 23 + 6*b = 0.
0, 1, 2
Let n(d) = -d**2 - 6*d - 5. Let t be n(-5). Let b = 0 + t. Factor b - 1/3*z**2 + 1/3*z.
-z*(z - 1)/3
Suppose -3*z + 3 = 2*l - 13, z + 18 = 4*l. Find r such that -2*r**z - 1 - 10*r**3 + r**3 + 9*r + 3 = 0.
-1, -2/9, 1
Let o(n) be the second derivative of 0 + 0*n**2 + 7*n + 1/14*n**3 + 1/28*n**4. Suppose o(m) = 0. What is m?
-1, 0
Let w(o) be the third derivative of o**8/6720 + o**7/560 + o**6/120 - o**5/60 + 4*o**2. Let h(f) be the third derivative of w(f). Factor h(n).
3*(n + 1)*(n + 2)
Let c be 3/(-3) - (-2 + 1). Let s be (-8)/(-14)*(-21)/(-6). What is k in -1/2*k + c - 7/4*k**s = 0?
-2/7, 0
Let r(p) be the first derivative of -4 - 2/3*p - 1/9*p**3 - 1/2*p**2. Factor r(q).
-(q + 1)*(q + 2)/3
Let r(g) = -2*g**5 - 2*g**4 - 3*g**2 + 3*g. Let m(u) = 2*u**5 + 2*u**4 + 2*u**2 - 2*u. Let y(k) = -6*m(k) - 4*r(k). Find x, given that y(x) = 0.
-1, 0
Let p = 11 + -5. Suppose 6*n - 3*n = p. Factor 4*q + q - n*q**3 - 3*q.
-2*q*(q - 1)*(q + 1)
Factor 4*f**3 - 1 - 4*f - 3 + 18*f**2 - 10*f**2 - 4*f**2.
4*(f - 1)*(f + 1)**2
Let h(k) be the first derivative of k**6/2 + 6*k**5/25 - 6. Suppose h(v) = 0. What is v?
-2/5, 0
Let x = -48 - -50. Let h(t) be the second derivative of 2*t - 1/4*t**x + 0*t**3 + 0 + 1/24*t**4. Suppose h(y) = 0. Calculate y.
-1, 1
Let b(n) be the second derivative of n**6/50 - 3*n**5/50 - 7*n**4/20 - 2*n**3/5 + 28*n. Factor b(l).
3*l*(l - 4)*(l + 1)**2/5
Suppose -2*m**3 - 243*m**5 - 3*m**4 + 249*m**5 - m**3 = 0. Calculate m.
-1/2, 0, 1
Let d be 600/216 - (-2)/9. Let k(i) be the first derivative of 2 + 0*i + 1/8*i**4 - 1/8*i**6 - 1/5*i**5 + 1/3*i**d + 1/8*i**2. Solve k(f) = 0 for f.
-1, -1/3, 0, 1
Let z(a) be the second derivative of -a**4/4 + 3*a**2/2 - 13*a. Factor z(f).
-3*(f - 1)*(f + 1)
Let d(n) be the third derivative of -n**5/360 + n**4/24 - n**3/4 - 29*n**2. Factor d(o).
-(o - 3)**2/6
Determine p so that 1/2*p**2 - 1/2 + 0*p = 0.
-1, 1
Let p(u) be the third derivative of 1/100*u**5 - 3*u**2 + 0*u + 7/600*u**6 + 0 - 1/40*u**4 + 1/350*u**7 - 1/15*u**3. Factor p(j).
(j + 1)**3*(3*j - 2)/5
Factor 0 - 4/9*o + 2/9*o**2.
2*o*(o - 2)/9
Factor 32/11 + 16/11*c + 2/11*c**2.
2*(c + 4)**2/11
Let r(w) = -6*w**5 + 9*w**4 - 4*w**3 - 6*w**2 + 4*w - 3. Let s(p) = p**5 + p**3 - p**2 + p + 1. Let y(j) = -r(j) - 2*s(j). Factor y(i).
(i - 1)**3*(i + 1)*(4*i - 1)
Factor 2/5*r**2 + 0*r - 1/5*r**4 - 1/5 + 0*r**3.
-(r - 1)**2*(r + 1)**2/5
Let x(o) be the first derivative of o**6/40 + 3*o**5/40 + o**4/16 + 3*o + 3. Let p(a) be the first derivative of x(a). Factor p(d).
3*d**2*(d + 1)**2/4
Factor -213*s**3 + 204*s**3 + 2 - 5 - 21*s**2 - 15*s.
-3*(s + 1)**2*(3*s + 1)
Suppose -2*l + 5*u + 4 = -0*l, -2*l + 2*u = -4. Let x(t) be the second derivative of -1/42*t**4 + 2*t - 4/7*t**l - 4/21*t**3 + 0. Determine z so that x(z) = 0.
-2
Let r(o) be the third derivative 