ive of y**8/2240 - y**7/1260 + y**4/8 + y**2. Let s(x) be the second derivative of l(x). Suppose s(d) = 0. What is d?
0, 2/3
Let s(d) = -d**2 - 13*d - 27. Let o be s(-10). Suppose 2/7*z - 4/7*z**2 + 0 + 2/7*z**o = 0. Calculate z.
0, 1
Let w(a) be the first derivative of -a**5/30 - a**4/24 + a**3/6 + a**2/12 - a/3 + 3. Factor w(z).
-(z - 1)**2*(z + 1)*(z + 2)/6
Let u(j) be the third derivative of 0*j**4 + 0*j**6 + 1/630*j**7 + 0*j + 0 + 0*j**3 - 1/180*j**5 - j**2. Find y, given that u(y) = 0.
-1, 0, 1
Suppose 0 + 6/7*t + 3/7*t**3 + 9/7*t**2 = 0. Calculate t.
-2, -1, 0
Suppose 0 = o + a - 7, 4*o + 20 = -5*a + 53. Factor -4*l**2 + 2*l**3 - 2*l - 8*l + 2*l**3 + o*l.
4*l*(l - 2)*(l + 1)
Determine o so that -4/15 - 6/5*o + 0*o**3 - 22/15*o**2 + 8/15*o**4 = 0.
-1, -1/2, 2
Let h be 5 - 2/((-10)/(-15)). Factor 1/5*n**3 - 8/5 + 12/5*n - 6/5*n**h.
(n - 2)**3/5
Let s(w) = -w**2 - 10*w - 5. Let v be (0 + (-18)/4)*2. Let x be s(v). Let -i + x - 2*i**2 + 0 - 3 = 0. What is i?
-1, 1/2
Let f(i) be the first derivative of -5*i**4/6 - 14*i**3/9 - 2*i**2/3 - 4. Factor f(m).
-2*m*(m + 1)*(5*m + 2)/3
Let 0*x**3 + 0 - 2/3*x + x**2 - 1/3*x**4 = 0. What is x?
-2, 0, 1
Let p(k) be the third derivative of k**8/1848 + k**7/231 + 3*k**6/220 + 7*k**5/330 + k**4/66 + 7*k**2 + 3*k. Solve p(q) = 0 for q.
-2, -1, 0
Let a(x) be the first derivative of 0*x - 6 + 0*x**2 - 2/5*x**5 + 0*x**3 + 2/3*x**6 - 1/2*x**4. What is t in a(t) = 0?
-1/2, 0, 1
Let u be (16/10)/((-4)/(-10)). Let d(p) = -p**2 + 5*p - 4. Let j be d(u). Find n such that 6/5*n**2 - 6/5*n**3 + j + 2/5*n**4 - 2/5*n = 0.
0, 1
Let s(c) be the third derivative of c**5/270 + 5*c**4/108 + 4*c**3/27 - 48*c**2. Find y, given that s(y) = 0.
-4, -1
Let v(n) be the first derivative of n**8/168 - n**6/30 + n**4/12 + 2*n**2 + 2. Let b(j) be the second derivative of v(j). Let b(d) = 0. Calculate d.
-1, 0, 1
Let p(k) be the third derivative of -5*k**8/336 + k**7/42 + 5*k**6/24 - 5*k**5/12 - 5*k**4/6 + 10*k**3/3 - 18*k**2. Find a, given that p(a) = 0.
-2, -1, 1, 2
Let z be 2/((12/(-9))/(-4)). Let m(n) be the first derivative of 3/2*n**4 + 0*n + 2 + 1/3*n**z + 6/5*n**5 + 0*n**2 + 2/3*n**3. Factor m(i).
2*i**2*(i + 1)**3
Find y such that y + 4 + 6*y - 4*y**2 + 5*y - 4*y - 8*y**3 = 0.
-1, -1/2, 1
Let j = -2/89 - -184/267. Solve 1/3 + 1/3*n**2 + j*n = 0.
-1
Let v(x) be the second derivative of x**4 - 2*x**3/3 - 4*x**2 + 3*x. Suppose v(t) = 0. Calculate t.
-2/3, 1
Let p(n) be the third derivative of 2*n**7/315 + n**6/30 + n**5/15 + n**4/18 + 19*n**2. Factor p(b).
4*b*(b + 1)**3/3
Let 30*s**5 - 39*s**2 + 0*s**5 + 90*s**3 + 6*s - 86*s**4 - s**4 = 0. What is s?
0, 2/5, 1/2, 1
Let a(r) be the third derivative of -r**8/1176 - r**7/735 + r**6/210 - r**2. Determine c, given that a(c) = 0.
-2, 0, 1
Let o(v) be the third derivative of 2*v**7/105 + v**6/15 + v**5/15 - v**2. Solve o(i) = 0 for i.
-1, 0
Let f(y) be the first derivative of y**3/3 - y**2/2 + y - 2. Let n(s) = s**2 + 11*s + 1. Let c(o) = 3*f(o) + n(o). Factor c(j).
4*(j + 1)**2
Let w be (-2)/(-9) + 50/18. What is f in -4*f**3 + 2*f**4 + 0*f**3 + 0*f**w + 2*f**2 = 0?
0, 1
Let b = -31 + 15. Let d = -13 - b. Factor 1/4*g**2 - 1/4*g**d - 1/4 + 1/4*g.
-(g - 1)**2*(g + 1)/4
Suppose 5*x - 30 = -0*x. Let y = 6 - x. Factor y + 0*l + 0*l**3 + 0*l**2 + 2/5*l**4.
2*l**4/5
Find t, given that -2/5*t**2 + 21/5*t + 11/5 = 0.
-1/2, 11
Let c(w) be the third derivative of -2/27*w**3 + 0*w - 2*w**2 + 0 + 7/108*w**4 - 1/54*w**5. Suppose c(a) = 0. What is a?
2/5, 1
Let j(c) = -7*c - 21. Let s be j(-3). Factor -2/5*x**2 - 2/5*x + s.
-2*x*(x + 1)/5
Let a(m) = m**3 - 3*m**2 + m - 3. Let n be a(3). Suppose n = 2*u - u. Factor u - 1/4*i**2 + 1/4*i.
-i*(i - 1)/4
Factor 6*o - 2*o**2 - o**2 + 2*o**2 - 3 - 2*o**2.
-3*(o - 1)**2
Let l = -57 - -61. Factor -4/7*q**2 + 2/7 - 24/7*q**3 + 18/7*q**l + 8/7*q.
2*(q - 1)**2*(3*q + 1)**2/7
Let k(s) be the first derivative of s**6/10 + 6*s**5/5 + 9*s**4/2 - 81*s**2/2 + s - 4. Let y(c) be the first derivative of k(c). Find b, given that y(b) = 0.
-3, 1
Let n = 21 - 17. Let v(k) be the first derivative of 1/14*k**n - 1/7*k**2 - 4/21*k**3 + 3 + 4/7*k. Factor v(b).
2*(b - 2)*(b - 1)*(b + 1)/7
Suppose 3*r = t + 6*r - 14, 0 = t + 4*r - 15. Factor -t*s**3 - 4 + 3 - 3*s + 10*s**3 - 3*s**2.
-(s + 1)**3
Let r(f) be the second derivative of 1/14*f**5 - 2/21*f**3 + 4*f + 0 + 1/14*f**4 + 0*f**2. Factor r(x).
2*x*(x + 1)*(5*x - 2)/7
Factor 5*d**3 + 33*d**2 - 5*d**5 - 18*d**2 + 25*d**4 - 40*d**3.
-5*d**2*(d - 3)*(d - 1)**2
Let u = -18 - -20. Let m = -772/5 + 155. Factor -3/5*p**u + 3/5*p**3 - m*p + 3/5.
3*(p - 1)**2*(p + 1)/5
Let m(r) be the second derivative of -r**5/70 + 5*r**4/42 - 8*r**3/21 + 4*r**2/7 - 19*r. Factor m(o).
-2*(o - 2)**2*(o - 1)/7
Let x(f) be the second derivative of f**6/30 + f**5/5 + f**4/4 - 2*f**3/3 - 2*f**2 - 9*f. Factor x(y).
(y - 1)*(y + 1)*(y + 2)**2
Let u(a) be the first derivative of -a**6/360 - a**5/90 - a**4/72 - a**2/2 + 2. Let r(p) be the second derivative of u(p). Solve r(l) = 0 for l.
-1, 0
Let r be (-3 - -5)*(-6)/(-4). Determine t, given that -3/2*t**2 - t + 0 + 0*t**r + 1/2*t**4 = 0.
-1, 0, 2
Let p(s) be the third derivative of s**5/120 - s**4/16 + s**3/6 - 19*s**2. What is m in p(m) = 0?
1, 2
Let u(v) be the third derivative of v**7/280 - v**6/96 + v**5/240 + v**4/96 + v**2. Suppose u(g) = 0. What is g?
-1/3, 0, 1
Let a(s) be the third derivative of s**6/240 - s**5/60 - s**4/48 + s**3/6 + 8*s**2. Factor a(n).
(n - 2)*(n - 1)*(n + 1)/2
Suppose 4*j + 4*n = -j + 11, -4*j + 14 = -2*n. Let t(l) be the first derivative of -j + 4*l**2 + 2/3*l**3 + 8*l. Factor t(k).
2*(k + 2)**2
Factor 0*m**2 + 0 - 2/11*m**3 + 2/11*m.
-2*m*(m - 1)*(m + 1)/11
Let l(c) = 9*c**2 + 10*c - 35. Let f(s) = 23 + 7*s - 6*s**2 + 0*s - 14*s. Let k(v) = -8*f(v) - 5*l(v). Factor k(g).
3*(g - 1)*(g + 3)
Suppose -w + 7 = 4*p, -4*p - p = -4*w - 14. Let z(o) be the second derivative of 0*o**3 + 1/135*o**6 + 0*o**p + 1/54*o**4 + 2*o + 1/45*o**5 + 0. Factor z(d).
2*d**2*(d + 1)**2/9
Suppose 3*x + 3 = 2*t - 5*t, 4*x = t + 11. Let f(r) = 8*r + 6. Let a(u) = u**2 - 17*u - 13. Let z(l) = x*a(l) + 5*f(l). Determine b so that z(b) = 0.
-2, -1
Factor 24/5*z**2 - 6/5*z + 0 - 36/5*z**3 - 6/5*z**5 + 24/5*z**4.
-6*z*(z - 1)**4/5
Let b(t) be the second derivative of t**6/240 - t**5/60 - t**4/48 + t**3/6 - 3*t**2/2 - t. Let k(j) be the first derivative of b(j). Factor k(p).
(p - 2)*(p - 1)*(p + 1)/2
Let n(w) be the third derivative of -1/380*w**6 + 7*w**2 + 1/57*w**4 + 0*w - 1/1995*w**7 + 0 + 0*w**3 + 0*w**5. Factor n(s).
-2*s*(s - 1)*(s + 2)**2/19
Let h be (-1 - 0) + 2 - (-4 + 2). Let d(n) be the third derivative of 1/180*n**6 + 0*n + 0 - 1/36*n**4 + 1/90*n**5 + 0*n**h - n**2 - 1/315*n**7. Solve d(i) = 0.
-1, 0, 1
Let c(v) be the second derivative of -1/75*v**6 + 1/25*v**5 + v + 0*v**2 + 0 + 0*v**3 - 1/30*v**4. Factor c(p).
-2*p**2*(p - 1)**2/5
Let q(p) = p**2 - 19*p + 20. Let d be q(18). Let a(t) be the first derivative of -1/4*t**4 - 1 - 1/6*t**3 - 1/10*t**5 + 0*t + 0*t**d. Let a(c) = 0. What is c?
-1, 0
Let t(s) be the first derivative of s**7/42 + s**6/10 + s**5/20 - s**4/4 - s**3/3 + 2*s + 5. Let g(a) be the first derivative of t(a). Factor g(y).
y*(y - 1)*(y + 1)**2*(y + 2)
Let j = -10 - -16. Suppose -4 = -5*b - 3*i, 4*i + 12 = b + b. Factor -z**3 + 4*z**b + z + 1 + z**2 - j*z**2.
-(z - 1)*(z + 1)**2
Suppose 0*z + 16 = 3*o + 5*z, 5*z = -4*o + 13. Let a be 2/o + 252/135. Factor 6/5*i + 2/5 + 2/5*i**3 + a*i**2.
2*(i + 1)**3/5
Determine u so that 10/9*u - 4/9 - 4/9*u**2 - 2/9*u**5 + 8/9*u**4 - 8/9*u**3 = 0.
-1, 1, 2
Let o(v) be the second derivative of -4*v - 1/4*v**3 + 0 - 1/8*v**4 + 3/2*v**2. Determine s, given that o(s) = 0.
-2, 1
Let 0*k**4 + 0*k**2 + 0*k + 0 - 2/7*k**3 + 2/7*k**5 = 0. Calculate k.
-1, 0, 1
Let s be (0 + 1)*(-21)/(-63). Factor -2/3*l + s + 1/3*l**2.
(l - 1)**2/3
Solve 0*a + 1/2*a**5 + 0*a**3 + 0 + 0*a**2 - 1/2*a**4 = 0.
0, 1
Let x(g) = 5*g**3 + 2*g**2 + 6*g + 6. Let z(i) = i**3 + i + 1. Let y(r) = x(r) - 6*z(r). Factor y(n).
-n**2*(n - 2)
Suppose 4*w - 9 = w. Factor v**3 - 2*v**2 + v - 3*v**3 + w*v**3 + 0*v**2.
v*(v - 1)**2
Let c(v) be the second derivative of -v**6/180 + v**5/30 - 5*v**4/72 + v**3/18 - 37*v. Solve c(a) = 0 for a.
0, 1, 2
Find r such that 10 - 32/3*r + 2/3*r**2 = 0