*(d + 1)**2/9
Let z(v) be the first derivative of 4/9*v**2 + 2/27*v**3 + 8/9*v + 8. Factor z(k).
2*(k + 2)**2/9
Suppose -7*u + 5*u = 0. Let p(g) be the first derivative of 0*g**4 + 2/25*g**5 + 2/5*g - 4/15*g**3 - 3 + u*g**2. Factor p(c).
2*(c - 1)**2*(c + 1)**2/5
Let b be 6/(-18) + (-30)/(-36). Determine s, given that 3/4*s**4 - b*s**2 + 3/4*s - 1/2*s**3 - 1/4*s**5 - 1/4 = 0.
-1, 1
Let c(i) = i**2. Let w(q) be the first derivative of -q**4 + 28*q**3/3 - 48*q**2 + 64*q - 5. Let o(b) = 8*c(b) + w(b). Factor o(j).
-4*(j - 4)**2*(j - 1)
Let 6*y**3 + 38 + 12 - 58*y**2 - 682*y + 812*y = 0. Calculate y.
-1/3, 5
Let t be 1*3/(-6)*0. Suppose 0 = -5*u + 4*n, -2*u = -t*u + n - 13. Factor -2/5*v**3 - 2/5*v**u + 2/5*v + 2/5*v**2 + 0.
-2*v*(v - 1)*(v + 1)**2/5
Let w(z) be the third derivative of -z**11/665280 + z**9/60480 - z**7/10080 + z**5/15 + 4*z**2. Let t(k) be the third derivative of w(k). Factor t(j).
-j*(j - 1)**2*(j + 1)**2/2
Let t = -246749/210 + 1175. Let v(s) be the third derivative of 0 + 1/42*s**4 - 1/21*s**3 - t*s**5 + 2*s**2 + 0*s. Suppose v(x) = 0. What is x?
1
Let c(m) be the second derivative of m**9/1008 + m**8/560 - m**7/280 - m**6/120 - 2*m**3/3 + 3*m. Let v(r) be the second derivative of c(r). Factor v(z).
3*z**2*(z - 1)*(z + 1)**2
Let r be 33/(-220)*(-8 - -4). Suppose 6/5*t**2 + 0 + 0*t - r*t**3 = 0. What is t?
0, 2
Let j(k) = -k**3 - 2*k**2 + 4*k + 3. Let l be j(-3). Factor 0 + 0*u + 2/7*u**3 + l*u**2.
2*u**3/7
Let g be (-6 - 0)*(3 + (-130)/42). Factor 0 - 2/7*a**5 + g*a**3 + 0*a**4 + 0*a**2 - 2/7*a.
-2*a*(a - 1)**2*(a + 1)**2/7
Suppose 4*r - 3*f = 38, 0*r + f + 10 = r. Let y be (-1)/(-4) - (-14)/r. Factor -1 - 5*l - l**2 + l + y*l.
-(l + 1)**2
Determine d so that 30*d**4 - 56*d**4 + 2*d**2 + 4*d**3 + 28*d**4 = 0.
-1, 0
Factor -y**3 + 7/4*y**2 - 1/2*y - 1/4.
-(y - 1)**2*(4*y + 1)/4
Let k(d) be the second derivative of 0 - 2/3*d**4 - 2/21*d**7 + 0*d**2 - 5*d + 0*d**5 + 2/3*d**3 + 4/15*d**6. Factor k(t).
-4*t*(t - 1)**3*(t + 1)
Let r(s) be the second derivative of -2*s - 1/27*s**3 + 0*s**2 - 1/54*s**4 + 0. Factor r(q).
-2*q*(q + 1)/9
Let p(n) be the first derivative of -4*n**3/9 - 2*n**2 + 11. Factor p(g).
-4*g*(g + 3)/3
Suppose -4*g + 2*g**2 + 0*g**2 - 4*g**2 - 6 - 4*g = 0. What is g?
-3, -1
Let t(q) be the second derivative of -2*q**6/15 - 4*q**5/5 - 5*q**4/3 - 4*q**3/3 - 10*q. Factor t(i).
-4*i*(i + 1)**2*(i + 2)
Let h(s) be the third derivative of s**7/1260 - s**6/720 - s**5/360 + s**4/144 - 28*s**2. Find q, given that h(q) = 0.
-1, 0, 1
Suppose -3*z + 36 = 4*h, 5*z + 5*h = 4*h + 43. Let k be ((-42)/z)/7 + 1. Determine i so that k*i - 1/2*i**2 + 0 + 1/4*i**3 = 0.
0, 1
Let b(x) = -2*x**2 + 30*x + 2. Let t be b(15). Factor 0*d + 1/4*d**5 + d**t + 2*d**3 + 5/4*d**4 + 0.
d**2*(d + 1)*(d + 2)**2/4
Let g be (5/(-2))/((-3)/6). Let x(t) be the second derivative of -1/105*t**7 + 0*t**2 + 0*t**3 - 2*t + 1/15*t**4 + 0 + 0*t**6 + 3/50*t**g. Factor x(f).
-2*f**2*(f - 2)*(f + 1)**2/5
Let r(x) be the second derivative of x**6/15 + x**5/2 + 3*x**4/2 + 7*x**3/3 + 2*x**2 + 3*x. Let r(k) = 0. Calculate k.
-2, -1
Let o be 251/70 + 8/(-2). Let r = -3/14 - o. Factor -r*p**3 + 1/5*p**4 - 1/5*p**2 + 0 + 0*p + 1/5*p**5.
p**2*(p - 1)*(p + 1)**2/5
Let w(c) = 5*c**2 + 5*c - 4. Suppose 3*f - 13 = 23. Suppose f + 0 = -3*q. Let p(m) = 4*m**2 + 4*m - 3. Let x(r) = q*p(r) + 3*w(r). Solve x(u) = 0 for u.
-1, 0
Let p(h) = -h**3 + 7*h**2 - h + 6. Let o be p(7). Let c be 15/4 - o/4. Factor 3*t**2 - t + 0*t - c*t**2.
-t*(t + 1)
Let n(u) be the first derivative of -u**4/16 + u**3/4 + 2. Solve n(t) = 0 for t.
0, 3
Let b(j) be the second derivative of 6*j + 0 - 2*j**2 - 2/3*j**3 - 1/12*j**4. Determine d so that b(d) = 0.
-2
Let y(f) be the first derivative of -f**6/3 - 11*f**5/5 - 23*f**4/4 - 23*f**3/3 - 11*f**2/2 - 2*f - 8. Factor y(o).
-(o + 1)**3*(o + 2)*(2*o + 1)
Suppose z = -2*z - 9. Let w be (0*z/9)/(-2). Let 2*v**4 - v + w*v**5 - 2*v**5 + 3*v**5 - 2*v**2 = 0. Calculate v.
-1, 0, 1
Let q(m) be the third derivative of -1/168*m**8 + 0*m + 0*m**4 + 0*m**3 + 0 + 2*m**2 - 1/35*m**7 - 1/20*m**6 - 1/30*m**5. Factor q(n).
-2*n**2*(n + 1)**3
Let w(p) be the second derivative of p**7/21 + p**6/5 - 3*p**5/10 - 11*p**4/6 - 2*p**3 - 14*p. Factor w(a).
2*a*(a - 2)*(a + 1)**2*(a + 3)
Let r(b) be the second derivative of 2*b**5/45 + b**4/6 + 2*b**3/9 + b**2/9 - 8*b. Suppose r(v) = 0. Calculate v.
-1, -1/4
Let i(y) be the third derivative of -y**6/480 - y**5/60 - y**4/96 + y**3/4 - 38*y**2. Find x, given that i(x) = 0.
-3, -2, 1
Let n(h) = h**3 + 11*h**2 - h. Let v be n(-11). Suppose 4*q - 6*u + v*u = -5, 3*u + 3 = -2*q. Solve 0 + 0*w**2 + q*w - 1/5*w**5 + 0*w**4 + 1/5*w**3 = 0.
-1, 0, 1
Let s(o) be the first derivative of o**5/40 + o**4/32 - o**3/8 - o**2/16 + o/4 + 1. Suppose s(h) = 0. What is h?
-2, -1, 1
Let l(c) be the third derivative of c**8/13440 + c**7/3360 + c**5/20 - c**2. Let u(k) be the third derivative of l(k). Solve u(i) = 0.
-1, 0
Let 3/8*x**3 + 3/8*x**2 - 3/8*x - 3/8 = 0. What is x?
-1, 1
What is q in 8/5*q + 8/5*q**3 - 12/5*q**2 - 2/5 - 2/5*q**4 = 0?
1
Let u(o) be the first derivative of o**3/21 - o**2/7 + o/7 + 8. Suppose u(f) = 0. Calculate f.
1
Let i(r) = -r**2 + 8*r - 3. Let w be i(7). Factor -o**5 - 6*o**4 + 0*o - 2*o + w*o**2 + 3*o**5 + 2*o**4.
2*o*(o - 1)**3*(o + 1)
Let k(f) be the second derivative of -f**6/45 + f**4/6 + 2*f**3/9 - f. Suppose k(c) = 0. What is c?
-1, 0, 2
Let a(q) be the second derivative of q**8/3360 - q**7/560 + q**6/240 - q**5/240 + q**3/2 + 4*q. Let z(s) be the second derivative of a(s). Factor z(r).
r*(r - 1)**3/2
Let i(s) be the first derivative of 1/210*s**5 + 0*s + 1 + 4/21*s**3 - 1/21*s**4 - 1/2*s**2. Let l(m) be the second derivative of i(m). Let l(w) = 0. What is w?
2
Let h = -2/81 + 101/810. Let r(p) be the third derivative of 0*p**6 + 1/112*p**8 + 0*p**3 + 0 - 1/8*p**4 - h*p**5 + 2*p**2 + 1/35*p**7 + 0*p. Factor r(w).
3*w*(w - 1)*(w + 1)**3
Let d(x) be the third derivative of x**7/210 - x**6/60 - 23*x**5/60 + x**4 + 24*x**3 + 52*x**2. Find z, given that d(z) = 0.
-3, 4
Suppose -3*g + 15 = 4*l - 5, -3*l = 5*g - 15. Let r = g + 2. Factor -8*o**4 - r*o + 14*o**2 + 8*o - 10*o**3 - 2*o.
-2*o*(o - 1)*(o + 2)*(4*o + 1)
Factor 7/2*k**2 - 1/2*k**3 - 3*k + 0.
-k*(k - 6)*(k - 1)/2
Suppose -k + 6*k - 25 = 0. Suppose -3*t - 9 = -15. Suppose 8*g - 2 - 3*g**4 + g**4 + 8*g**3 - 10*g**t - k*g**2 + 3*g**2 = 0. What is g?
1
Suppose 0*s + 2*s - 4 = 0. What is r in -3*r**2 + 2*r**3 + 2*r**4 + r**s - 2*r**3 = 0?
-1, 0, 1
Determine f, given that -87 - 10*f**2 - 2*f**3 - 16*f + 0*f**3 + 79 = 0.
-2, -1
Let x be (-140)/(-75) - 8/(-60). Let q = 175/4 + -43. Suppose -1/4 - q*g**x + 3/4*g + 1/4*g**3 = 0. What is g?
1
Suppose 3*h = 5*t - 2, 4*h + 1 = -2*t + 7*t. Factor 1 + h + 3 - c**2 - 4.
-(c - 1)*(c + 1)
Let s(b) be the third derivative of b**6/1020 - 7*b**2. Solve s(g) = 0 for g.
0
Let p(o) be the second derivative of -1/3*o**3 - 1/10*o**5 + 1/3*o**4 + 0 + o + 0*o**2. Factor p(g).
-2*g*(g - 1)**2
Let p be (-70)/6 + (-2)/(-3). Let y be (-64)/(-110) - (-2)/p. Factor 2/5*b**3 - 2/5*b**5 + y*b**2 + 0 - 2/5*b**4 + 0*b.
-2*b**2*(b - 1)*(b + 1)**2/5
Let c(b) be the first derivative of -2/21*b**3 + 2 + 2/7*b**2 + 0*b. Factor c(m).
-2*m*(m - 2)/7
Let n = 11 - 3. Factor -32*k**2 + n*k + 98*k**4 - 16*k**2 + 52*k**3 - 10*k**3.
2*k*(k + 1)*(7*k - 2)**2
Let h(s) be the second derivative of 0*s**2 - 3/14*s**4 - 4*s + 0 + 11/70*s**5 - 2/21*s**3. What is l in h(l) = 0?
-2/11, 0, 1
Let t(n) = 3*n**3 + 27*n**2 - 19*n - 11. Let j(k) = k**3 + 7*k**2 - 5*k - 3. Let i(b) = -22*j(b) + 6*t(b). Factor i(s).
-4*s*(s - 1)**2
Let l(g) be the second derivative of 0*g**2 + 9/100*g**5 + 0 - 3/20*g**4 + 1/10*g**3 + 3*g - 1/50*g**6. Let l(q) = 0. What is q?
0, 1
Let v be -1*(17 + -3 + -2). Let a = 14 + v. Factor -4/7*t + 2/7 + 2/7*t**a.
2*(t - 1)**2/7
Let j(c) be the first derivative of -c**8/1344 + c**7/840 + c**6/480 - c**5/240 - c**2/2 + 1. Let s(y) be the second derivative of j(y). Factor s(u).
-u**2*(u - 1)**2*(u + 1)/4
Let b be (-1 + 4/3)*(2 + 10). Let c(d) be the first derivative of -1/2*d**b + 2/3*d**3 + 3 + 0*d**2 + 0*d. Solve c(m) = 0 for m.
0, 1
Suppose -5*l = b - 3, 8*b = 3*b - 3*l + 15. Solve -j**3 - 9*j**3 + j**5 - 2*j**3 + 8*j**2 + b*j**5 = 0 for j.
-2, 0, 1
Let n(z