p(n) = -n**2 - n. Let k(j) = -i(j) - 5*p(j). Factor k(x).
-x**2*(x + 1)
Let o(r) be the first derivative of r**6/21 - 8*r**5/35 + 5*r**4/14 - 4*r**3/21 + 14. Factor o(b).
2*b**2*(b - 2)*(b - 1)**2/7
Let d(h) be the first derivative of -6 + 1/10*h**4 - 2/5*h + 26/15*h**3 - 1/5*h**2 - 24/25*h**5. Solve d(k) = 0.
-1, -1/4, 1/3, 1
Suppose z - 4 + 2 = 0. Solve 3*w**4 + 2*w**3 - 3*w**4 + w**4 + 0*w**4 + w**z = 0.
-1, 0
Suppose -6 = -3*h + i, 5*h - 6 = -2*i + 4. Factor -4 - 5*u**2 + u**2 + 6*u**2 + h*u.
2*(u - 1)*(u + 2)
Let x = -16 + 216/13. Solve -x - 2/13*f**2 - 8/13*f = 0 for f.
-2
Suppose 5*o + 231 = -14. Let f be o/(-70) + 2/4. Suppose -2/5*q + 2/5*q**4 - 6/5*q**3 + f*q**2 + 0 = 0. What is q?
0, 1
Factor -f**3 + 1/2*f**5 - 4*f**2 + f**4 - 7/2*f - 1.
(f - 2)*(f + 1)**4/2
Factor -1/7*t**4 + 4/7*t + 5/7*t**3 - 8/7*t**2 + 0.
-t*(t - 2)**2*(t - 1)/7
Let l(v) be the second derivative of -v**7/840 - v**6/240 - v**5/240 + 3*v**2/2 + 2*v. Let j(f) be the first derivative of l(f). Factor j(x).
-x**2*(x + 1)**2/4
Let a(l) = -15*l**4 + 9*l**3 + 21*l**2 + 3*l. Let v(d) = 14*d**4 - 8*d**3 - 20*d**2 - 2*d + 1. Let n(f) = 5*a(f) + 6*v(f). Factor n(j).
3*(j - 1)**2*(j + 1)*(3*j + 2)
Let u(w) be the first derivative of w**3/5 + 9*w**2/5 - 26. Factor u(i).
3*i*(i + 6)/5
Let u(k) = -5*k**3 - k**2 - 3*k + 1. Let n(b) = -6*b**3 - b**2 - 4*b + 1. Let c be 1*(-4)/(-10)*-10. Let p(y) = c*n(y) + 5*u(y). Factor p(f).
-(f - 1)*(f + 1)**2
Let w = -3 + 6. Let j = w + -1. Determine z, given that 0*z**2 + z**3 - 2*z**j + 6*z - 5*z = 0.
0, 1
Factor 0*o - 1/2*o**2 + 0 + 1/2*o**3.
o**2*(o - 1)/2
Let x(m) be the second derivative of -m**6/15 + m**4/2 + 2*m**3/3 - 3*m. Find z such that x(z) = 0.
-1, 0, 2
Suppose 3*j - 80 = -j. Let x be (j/(-6))/((-4)/6). Solve 1/4*o**2 + 1/4*o**3 - 1/4*o**4 + 0*o - 1/4*o**x + 0 = 0.
-1, 0, 1
Suppose -4*y + 9 = -y. Suppose -4*d**2 + 2*d**5 - d**2 + 6*d**4 + 6*d**y + 4*d**2 + 3*d**2 = 0. Calculate d.
-1, 0
Suppose -16 = -2*d - 4. Find k, given that k + d*k**4 - 3*k**5 - 3*k**3 + 0*k**5 - k = 0.
0, 1
Let a(b) = -b**3 + b**2 + 1. Let r(w) = -5*w**3 - 5*w**2 - 27*w + 12. Let t(d) = -4*a(d) + r(d). Let s(q) be the first derivative of t(q). Factor s(o).
-3*(o + 3)**2
Suppose 0 = 3*a + 60 - 51. Let y be 6*((-11)/(-3) + a). Find f such that 0*f**3 + 1/3*f**y - 2/3*f**2 + 0*f + 1/3 = 0.
-1, 1
Let q(h) = -2*h**5 - 4*h**4 - 3*h**3 - 3*h**2 - 3. Let b(v) = 10*v**5 + 20*v**4 + 14*v**3 + 14*v**2 + 14. Let t(x) = -6*b(x) - 28*q(x). Solve t(j) = 0 for j.
-2, 0
Suppose -20 = 3*k - 7*k. Suppose 2*n + 1 - k = 0. Determine s so that -s + 1 - 2*s**2 - s - s**n = 0.
-1, 1/3
Suppose -2 = -4*b + l, 4 = b - 3*l - 2. Suppose 9*n - 4*n = b. What is z in 1/2*z**2 + n - z = 0?
0, 2
Let k(a) be the second derivative of a**7/1260 + a**6/180 - a**4/3 - a. Let l(m) be the third derivative of k(m). Factor l(u).
2*u*(u + 2)
Suppose -f**3 + 1/4*f**5 + 0*f - 2*f**2 + 1/2*f**4 + 0 = 0. Calculate f.
-2, 0, 2
Let z(i) be the first derivative of -4*i**3/3 + 20*i**2 - 100*i + 4. Solve z(j) = 0.
5
Let k(o) be the second derivative of -54/5*o**6 - 24*o**3 + 6*o + 77/3*o**4 + 8*o**2 + 0 + 36/5*o**5. Suppose k(q) = 0. Calculate q.
-1, 2/9, 1
Let g(o) be the second derivative of -o**4/14 + 5*o**3/21 - 2*o**2/7 + 5*o. Factor g(i).
-2*(i - 1)*(3*i - 2)/7
Let l be (-32)/(-8) + 78/(-20). Let q(g) be the third derivative of g**2 + 0*g + 1/3*g**3 + 0 + l*g**5 + 1/4*g**4 + 1/60*g**6. What is x in q(x) = 0?
-1
Let k = 1717/75 + -353411/17475. Let q = k + -2/699. Factor 0 + q*l + 98/3*l**4 + 64/3*l**2 + 154/3*l**3.
2*l*(l + 1)*(7*l + 2)**2/3
Let c(x) be the third derivative of x**6/660 + x**5/66 + 7*x**4/132 + x**3/11 + 10*x**2. Let c(u) = 0. Calculate u.
-3, -1
Let s(f) = 3*f**3 + 9*f**2 - 25*f - 31. Let z(g) = -3*g**3 - 9*g**2 + 24*g + 30. Let h(a) = 6*s(a) + 7*z(a). Suppose h(l) = 0. Calculate l.
-4, -1, 2
Let u be (-4)/(-24)*-9 + 2. Factor 0*p + u*p**2 - 3/2*p**3 + 0.
-p**2*(3*p - 1)/2
Let u(w) be the second derivative of -w**6/15 - w**5/10 - 11*w. Solve u(y) = 0.
-1, 0
Let z = 38 + -27. Let b = z + -9. Solve 0*h + 1/3*h**4 + 1/3*h**5 - 1/3*h**b - 1/3*h**3 + 0 = 0.
-1, 0, 1
Suppose -16/9*x - 14/9*x**2 - 2/9*x**3 + 32/9 = 0. Calculate x.
-4, 1
Factor -t**3 + 0*t**5 - 10*t**2 + 2*t**5 - 5*t**3 + 2*t**4 + 9*t - 13*t.
2*t*(t - 2)*(t + 1)**3
Let 1/6*o**3 - 1/6*o**2 + 0 + 0*o = 0. Calculate o.
0, 1
Let o(n) be the first derivative of n**5/45 + n**4/18 + n**3/27 + 1. Solve o(i) = 0.
-1, 0
Let w be 1 - 24/(3 - 6). Let n be ((-6)/w - -1) + 0. What is a in -2/3 - a - n*a**2 = 0?
-2, -1
Let y(p) = p**2 + 5*p + 2. Let m be y(-5). Suppose -m*k = -3*k. Determine f so that k*f**2 + 0*f**2 + f**2 = 0.
0
Suppose 3*k = -3*t + 6, -3*t = t - 3*k + 6. Let s be -1 + (t - -1) + 0. Factor -3/2*z**2 - z - 1/2*z**3 + s.
-z*(z + 1)*(z + 2)/2
Let c(s) be the first derivative of -2*s**4/9 - 10*s**3/27 - s**2/9 + 5. Determine x, given that c(x) = 0.
-1, -1/4, 0
Factor 1/2*s - 1/8*s**2 - 3/8.
-(s - 3)*(s - 1)/8
Suppose -2*n = -5*q, 3*n = q - 5*q + 23. Let z(w) be the second derivative of 0*w**q - 1/6*w**3 + 0 + 1/12*w**4 - 2*w. Solve z(k) = 0 for k.
0, 1
Suppose -40*w + 54 = -66. Solve 0 - 1/3*m**5 + m**w - 2/3*m - 1/3*m**4 + 1/3*m**2 = 0 for m.
-2, -1, 0, 1
Let b(m) = m**3 - 3*m**2 - 3*m - 1. Let i be b(4). Suppose -5*u = -i*u. Factor 2/11*n**2 + u + 2/11*n**3 + 0*n.
2*n**2*(n + 1)/11
Let r(t) be the third derivative of -t**8/504 - t**7/90 - t**6/40 - t**5/36 - t**4/72 - 2*t**2. Factor r(k).
-k*(k + 1)**3*(2*k + 1)/3
Let c(h) = 7*h**3 - 19*h**2 + 13*h + 27. Let g(d) = -13*d**3 + 37*d**2 - 25*d - 54. Let n(v) = -7*c(v) - 4*g(v). Factor n(l).
3*(l - 3)**2*(l + 1)
Let d(y) be the first derivative of 4/9*y**3 - 3/2*y**4 + 8/15*y**5 + 0*y + 0*y**2 - 4. What is f in d(f) = 0?
0, 1/4, 2
Let w(j) be the third derivative of 0*j + 1/30*j**5 + 1/336*j**8 + 1/60*j**6 + 2*j**2 + 1/6*j**3 - 1/8*j**4 + 0 - 1/70*j**7. Factor w(y).
(y - 1)**4*(y + 1)
Let a(p) be the second derivative of -p**5/35 + p**4/21 + 4*p**3/21 - 8*p. Factor a(m).
-4*m*(m - 2)*(m + 1)/7
Let p(o) be the first derivative of o**6/15 + o**5/5 - o**4/6 - 2*o**3/3 - 3*o + 2. Let x(l) be the first derivative of p(l). Let x(q) = 0. Calculate q.
-2, -1, 0, 1
Let f(b) be the second derivative of b**4/18 - 2*b**3/9 - 3*b. What is w in f(w) = 0?
0, 2
Factor 5*r**3 - 6*r**2 - 9*r - 7*r**3 + 5*r.
-2*r*(r + 1)*(r + 2)
Factor -12*z**3 + 4*z**3 + 8 - 8*z**2 + 4*z**3 + 4*z.
-4*(z - 1)*(z + 1)*(z + 2)
Let b = 47 + -297/7. Find z such that 18/7*z**4 - 6*z**3 + 0 + b*z**2 - 8/7*z = 0.
0, 2/3, 1
Let j = -1 - -3. Suppose -l - 5 = -j*l. Factor 1 - 2 + l*m**2 - m**2 + m - 4*m.
(m - 1)*(4*m + 1)
Suppose 2*h - 8 = 4*t - 2*h, -3*h - 8 = 4*t. Let j = t - -6. Factor g**4 - 2*g**j + g**3 - 8*g**2 + 8*g**2.
-g**3*(g - 1)
Let n = 2 - 4. Let f(o) = o - o**2 + 9*o + 0*o**2. Let r(y) = 2*y. Let c(u) = n*f(u) + 11*r(u). Factor c(p).
2*p*(p + 1)
Let k = 348 - 346. Suppose 2/11*c**k + 6/11*c + 4/11 = 0. Calculate c.
-2, -1
Let t(d) be the first derivative of 2*d**5/45 + 7*d**4/18 + 8*d**3/9 - 7. Determine m so that t(m) = 0.
-4, -3, 0
Determine z, given that 4/5*z + 14/5*z**2 + 2*z**3 + 0 = 0.
-1, -2/5, 0
Let t(r) be the second derivative of 3*r**5/20 - 3*r**3/2 + 3*r**2 - 42*r. Factor t(u).
3*(u - 1)**2*(u + 2)
Let b(o) be the second derivative of -1/105*o**7 - 1/75*o**6 + 2/15*o**3 + 3/50*o**5 + 1/6*o**4 - o + 0 + 0*o**2. Suppose b(x) = 0. Calculate x.
-1, 0, 2
Factor 3/4*h**3 - 3/2*h**2 + 3/4*h + 0.
3*h*(h - 1)**2/4
Let g(k) be the first derivative of 2*k**3/3 - 2*k**2 + 2*k + 13. Let l be g(2). Factor 4/5*d - 2/5*d**l + 0.
-2*d*(d - 2)/5
Let y(d) = -3*d**2 + d + 1. Let a be y(-1). Let j be 1/(-2)*2 - a. Factor w - 2*w**2 + 6*w - 4*w + j + 3*w**2.
(w + 1)*(w + 2)
Factor 0 + 1/4*a + 1/4*a**2.
a*(a + 1)/4
Solve 4*y**3 + 11*y**2 + 16*y**2 - 21*y**2 = 0 for y.
-3/2, 0
Let -72*t**2 + 33*t**2 - 2*t**4 - 8*t**3 + 31*t**2 = 0. Calculate t.
-2, 0
Factor 0 + 4/9*j**3 + 196/9*j + 56/9*j**2.
4*j*(j + 7)**2/9
Let y be 0/((-3 - -2)/(-4 + 3)). Factor y + 0*x - 1/2*x**3 - x**2.
-x**2*(x + 2)/2
Let w(z) be the second derivative of 343*z**6/30 - 637*z**5/20 + 63*z**4/2 - 46*z**3/3 + 4*z**2 + 4*z. Find g such that w(g) = 0.
2/7, 1
Let x = -37 - -75/2. Let -1/2*i**4 + 1/2*i - 1/2*i**3 + x*i**2 + 0 = 0. Calculate i.
-1, 0, 