 t**4 + 7*t**3 + 3*t**2 - t - 4. Let i(a) = f*q(a) - 6*y(a). Factor i(c).
(c - 1)**2*(c + 1)*(c + 2)
Let o(n) be the third derivative of n**8/168 + 2*n**7/105 - n**6/80 - 7*n**5/120 - n**4/24 - 14*n**2. Suppose o(s) = 0. What is s?
-2, -1/2, 0, 1
Let p(q) be the second derivative of -q**6/60 + q**5/10 - q**4/12 - q**3/3 + 3*q**2/4 - 10*q. Factor p(i).
-(i - 3)*(i - 1)**2*(i + 1)/2
Let x be (-2*4/48)/2. Let u = x + 3/4. Factor -u*o**2 - 4/3 - 2*o.
-2*(o + 1)*(o + 2)/3
Let i(p) be the first derivative of -28*p**3/3 + 18*p**2 - 8*p - 12. Factor i(b).
-4*(b - 1)*(7*b - 2)
Suppose 5*y = -3*a + 9, -y = -4*a + 8 + 4. Determine n, given that 2/7*n - 2/7*n**3 + y + 2/7*n**2 - 2/7*n**4 = 0.
-1, 0, 1
Let u(f) be the third derivative of f**6/40 - f**4/8 + 11*f**2. Suppose u(n) = 0. Calculate n.
-1, 0, 1
Let k(i) = -i**3 - 28*i**2 - 51*i + 26. Let f be k(-26). Let o(l) be the second derivative of -1/4*l**4 + 0*l**2 - 3/20*l**5 + f + 0*l**3 - 3*l. Factor o(m).
-3*m**2*(m + 1)
Let n(l) be the second derivative of l**7/10080 + l**6/1440 + l**5/480 + l**4/12 + 3*l. Let y(t) be the third derivative of n(t). Factor y(j).
(j + 1)**2/4
Let x = -4 + 11/3. Let m = x + 2/3. Determine l so that -1/3*l**3 - m - l**2 - l = 0.
-1
Let k(f) = -f + 9. Let r be k(5). Let b(a) be the first derivative of -1/2*a**r + 1/10*a**5 - a**2 + a**3 - 3 + 1/2*a. Find m such that b(m) = 0.
1
Let d(m) = -m**2 + 6*m + 10. Let k be d(7). Factor 5*j**4 - 2*j**4 + 0*j**3 + k*j**3.
3*j**3*(j + 1)
Let r(d) be the first derivative of 3*d**5/10 + 11*d**4/8 + 11*d**3/6 + d**2/4 - d - 2. Suppose r(i) = 0. Calculate i.
-2, -1, 1/3
Let w(z) = -z**3 + 4*z**2 - 3*z + 3. Let k be w(3). Determine m so that 0*m**k + 0 + 1/3*m**4 + 0*m + 0*m**2 - 1/3*m**5 = 0.
0, 1
Suppose 13 + 7 = 5*i. Let d be (-171)/(-90) + (-6)/i. Suppose -3/5*x**4 + d*x + 0 + 3/5*x**2 - 1/5*x**5 - 1/5*x**3 = 0. Calculate x.
-2, -1, 0, 1
Factor 13*v**3 + 3*v**3 - 12*v**4 - v**3 - 3*v**2 - 3*v + 3*v**4.
-3*v*(v - 1)**2*(3*v + 1)
Let l be 5/(-20)*((-22)/7 - 2). Factor -1/7*v**5 - l*v**3 + 0 - v**2 - 2/7*v - 5/7*v**4.
-v*(v + 1)**3*(v + 2)/7
Let l(b) = -3*b**3 - 4*b**2 + 3*b + 4. Suppose 4*y + 40 = 9*y. Let c(t) = 1 - t**2 + y*t - 8*t. Let w(r) = c(r) - l(r). Solve w(s) = 0 for s.
-1, 1
Suppose 0 = 8*m - 23 - 1. Suppose -4*u + 2*u = -4*p + 2, 3*p - m*u - 3 = 0. Let p*i + 0 + 1/3*i**2 = 0. Calculate i.
0
Let z be 3*2/42 - 849/(-1260). Let y(v) be the third derivative of 0 - 7/6*v**4 + 2/3*v**3 - 2*v**2 + 0*v + z*v**5. Find g, given that y(g) = 0.
2/7
Let p(t) = -t - 7. Let o be p(-10). Solve 0 + 0*b + 0*b**2 + b**4 - 1/2*b**o - 1/2*b**5 = 0.
0, 1
Let w(c) be the first derivative of -3*c**4/8 + 13*c**3/6 - c**2 + 43. Factor w(q).
-q*(q - 4)*(3*q - 1)/2
Factor 2*p**4 + 5*p**3 + 8*p - 7 + 6*p**2 + 1 - 13*p**3 - 2.
2*(p - 2)**2*(p - 1)*(p + 1)
Let b be (174/10)/((-21)/(-30)). Factor -184/7*m**2 - 36/7 + 8*m**3 + b*m.
2*(2*m - 3)**2*(7*m - 2)/7
Let o be (110/(-25) - -4) + (-2)/(-5). What is u in 0 + o*u - 2/3*u**3 + 2/3*u**5 - 2/3*u**2 + 2/3*u**4 = 0?
-1, 0, 1
Let q(i) be the third derivative of -i**6/780 + i**4/52 + 2*i**3/39 - 7*i**2. Factor q(f).
-2*(f - 2)*(f + 1)**2/13
Let v = 164/185 - 18/37. Let -2/5*x**5 + 4/5*x**2 - 4/5*x**4 + v*x + 0*x**3 + 0 = 0. What is x?
-1, 0, 1
Let d(t) = -14*t**3 - 9*t**2 + 12*t + 11. Let x(a) = 1 - 3*a + 0*a**3 - a**2 - a**3 + 4*a + 0*a**3. Let q(s) = -2*d(s) + 22*x(s). Solve q(v) = 0.
-1/3, 0, 1
Suppose 4*v - 5*v**5 + 4*v**5 + 5*v**5 - 7*v**3 - v**3 = 0. What is v?
-1, 0, 1
Let g(d) be the third derivative of d**5/90 - d**4/18 + d**3/9 + 10*d**2. Factor g(p).
2*(p - 1)**2/3
Let -2/5*u**3 + 2/5*u - 2/5*u**4 + 2/5*u**2 + 0 = 0. Calculate u.
-1, 0, 1
Let q be (-1)/5*2*-1. Let h = -13/27 + 227/135. Factor -q*d**5 - 2/5*d**2 + 0*d - 6/5*d**3 - h*d**4 + 0.
-2*d**2*(d + 1)**3/5
Let j be (141/24 - 4)*4/10. Factor -3/4*s**4 + 0 + 3/4*s**2 + 3/4*s**3 + 0*s - j*s**5.
-3*s**2*(s - 1)*(s + 1)**2/4
Let y(s) = 3*s**2 - s. Let j be y(-2). Let m be ((-8)/6)/(j/(-3)). Factor -m*z**2 + 4/7*z - 2/7.
-2*(z - 1)**2/7
Let i(r) be the first derivative of r**3 - 6*r**2 + 12*r + 33. Find d such that i(d) = 0.
2
Let l = 5089643/180 - 28275. Let x = l + -2/45. Suppose -x*f**2 - 3/2*f - 3/4 = 0. Calculate f.
-1
Suppose 5*j - 5 - 5 = 0. Factor -1/5*y**j + 0*y + 1/5.
-(y - 1)*(y + 1)/5
Let d = 12 - 20. Let m = -8 - d. Determine v, given that 0 + m*v + 2/5*v**2 = 0.
0
Let x(w) be the first derivative of w**6/3 - 3*w**4/2 + 4*w**3/3 + 10. Factor x(h).
2*h**2*(h - 1)**2*(h + 2)
Let 0 + 4/7*n**4 + 2/7*n**2 + 1/7*n**5 + 5/7*n**3 + 0*n = 0. What is n?
-2, -1, 0
Let 12/19*m**2 + 0 - 14/19*m**3 + 0*m**4 + 2/19*m**5 + 0*m = 0. What is m?
-3, 0, 1, 2
Suppose -2*p = 4*x - x + 19, 2*p = -4*x - 22. Let a(k) = -k**2 - 3*k. Let i be a(x). Let i + 2/7*s + 2/7*s**3 + 4/7*s**2 = 0. Calculate s.
-1, 0
Let d(c) be the second derivative of 2/3*c**6 + 2*c + 4/21*c**7 + 0 + 1/40*c**5 - 19/12*c**4 - 1/2*c**2 - 17/12*c**3. Let d(r) = 0. Calculate r.
-2, -1, -1/4, 1
Let u be (-24)/(-13) + 62/403. Determine b so that 0 + 6*b - 30*b**u - 33*b**4 + 15/2*b**5 + 99/2*b**3 = 0.
0, 2/5, 1, 2
Let w(c) = -c**4 - 12*c**3 + 5*c**2 + 5. Let o(j) = -3*j**4 - 30*j**3 + 12*j**2 + 12. Let h(y) = -5*o(y) + 12*w(y). Suppose h(n) = 0. What is n?
-2, 0
Let i(k) = k**3 - 5*k**2 - 6*k + 2. Let a be i(6). Let x be ((-2 + 3)*4)/a. Let -2/5*d + 0*d**x + 2/5*d**3 + 0 = 0. Calculate d.
-1, 0, 1
Let y be (-1 + 1 + 1)*-2. Let l be y + -8*2/(-4). Let k(u) = u**3 + 2. Let o(d) = -2. Let x(p) = l*k(p) + 2*o(p). Factor x(r).
2*r**3
Let v(t) = 6*t**2 - 11*t + 16. Let x be (-148)/6 - 2/(-3). Let k = x + 35. Let n(z) = z**2 - 2*z + 3. Let p(m) = k*n(m) - 2*v(m). Factor p(y).
-(y - 1)*(y + 1)
Suppose -11*h = -7*h. Let x(y) be the first derivative of -1 + 1/4*y**4 + h*y**3 - 1/2*y**2 + 0*y. Let x(k) = 0. What is k?
-1, 0, 1
Suppose 236*y - 238*y = 0. Factor y + 1/5*a**2 - 1/5*a**4 + 1/5*a**3 - 1/5*a.
-a*(a - 1)**2*(a + 1)/5
Let v(u) be the second derivative of -13/10*u**5 - 13/4*u**3 + 2/15*u**6 + 9/8*u**2 - 7*u + 193/48*u**4 + 0. Suppose v(w) = 0. What is w?
1/4, 3
Let r be ((-3)/(-9))/(1/27). Let 4*d**3 + d**3 + 2*d**3 - 12 - d**3 + 27*d**2 - r*d**4 = 0. Calculate d.
-1, 2/3, 2
Let k(v) be the first derivative of -1/48*v**4 + 0*v**5 + 0*v**3 + 1/240*v**6 - 1 - 1/2*v**2 + 0*v. Let j(a) be the second derivative of k(a). Factor j(c).
c*(c - 1)*(c + 1)/2
Let z(t) be the second derivative of 2*t**6/15 + t**5/5 + 18*t. Find n such that z(n) = 0.
-1, 0
Let o be 8*-2*(-48)/288. Factor o*m + 10*m**2 - 8/3.
2*(3*m + 2)*(5*m - 2)/3
Let d = 2/97 + 172/1067. Determine c so that -2/11*c + 2/11*c**3 - d*c**2 + 2/11 = 0.
-1, 1
Factor -1381*s**2 + 2*s**4 + 1378*s**2 + s**4 - 3*s**3 + 3*s**5.
3*s**2*(s - 1)*(s + 1)**2
Let f(v) be the first derivative of -2*v**5/25 - 7*v**4/10 + 18*v**3/5 - 29*v**2/5 + 4*v - 17. Suppose f(p) = 0. What is p?
-10, 1
Let w(g) be the second derivative of -1/3*g**2 - 1/2*g**4 - 2/3*g**3 + 0 - g. Find r, given that w(r) = 0.
-1/3
Let o(v) be the second derivative of 6*v**6/35 + 57*v**5/140 + 2*v**4/7 + v**3/14 - v. Find a such that o(a) = 0.
-1, -1/3, -1/4, 0
Suppose 6*n + 10*n - 6*n = 0. Factor n*w - 2/5*w**3 + 4/5*w**2 + 0.
-2*w**2*(w - 2)/5
Let m be ((-18)/(-8))/((-2)/24). Let f = 83/3 + m. Solve 4/3*u + 2/3 + f*u**2 = 0.
-1
Factor -4/9 + 2/9*r**2 + 2/9*r.
2*(r - 1)*(r + 2)/9
Let y(z) be the first derivative of 2*z**5/25 + 3*z**4/10 + 2*z**3/5 + z**2/5 + 3. Solve y(o) = 0.
-1, 0
Let v(m) = m**3 - m**2 - 1. Let c(p) = 4*p**2 + p + 3. Let o(j) = -c(j) - 3*v(j). Let h be o(-1). Factor 0 - 2/5*r**2 - 4/5*r**h + 4/5*r + 2/5*r**4.
2*r*(r - 2)*(r - 1)*(r + 1)/5
Let z(w) be the third derivative of w**6/160 + 5*w**2. Find u, given that z(u) = 0.
0
Let s(v) be the first derivative of v**4/16 - v**3/4 - 8. Factor s(o).
o**2*(o - 3)/4
Let f be (-1)/(-2) + (-35)/(-10). Let y be (2 + 4)*2/f. Let -7*s + s**3 + s**4 - 5*s**y + 1 + 3*s + 6*s**2 = 0. What is s?
1
Let l(g) be the first derivative of -g**4/10 + 2*g**3/5 - 2*g**2/5 + 2. Find q such that l(q) = 0.
0, 1, 2
Factor 4/3 - 2*n + 2/3*n**2.
2*(n - 2)*(n - 1)/3
Let t = -609/2 - -305. Factor 1/4*q**2 + t + 3/4*q.
(q + 1)*(q + 2)/4
Let d(m) be the first derivative of -m**3/9 - m**2/18 - 9. What is f in d(f) = 0?
-1/3, 0
Let -6 - 267*p**4 + 63*p + 8