 the second derivative of 2*u**7/21 + 8*u**6/15 + 6*u**5/5 + 4*u**4/3 + 2*u**3/3 + 8*u. Determine k, given that p(k) = 0.
-1, 0
Let w = 69 + -67. Factor l**w - l + 1/3 - 1/3*l**3.
-(l - 1)**3/3
Let g(q) be the first derivative of 1/4*q**2 + 5/12*q**3 - 1/4*q**5 - 9/16*q**4 + 2 + 0*q + 7/24*q**6. Suppose g(r) = 0. What is r?
-1, -2/7, 0, 1
Let i(m) be the first derivative of 1/16*m**4 + 1/4*m**2 + 0*m + 7 - 1/4*m**3. What is w in i(w) = 0?
0, 1, 2
Let h(l) be the first derivative of -1/3*l**3 - 2 + 0*l**2 + 1/540*l**6 + 1/90*l**5 + 1/36*l**4 + 0*l. Let t(d) be the third derivative of h(d). Solve t(r) = 0.
-1
Let p be (-91)/(-105) - 1/3*2. Determine t so that p*t + 0 + 1/5*t**2 = 0.
-1, 0
Suppose -238*w + w**2 - 14 + 132*w + 119*w + 0 = 0. Calculate w.
-14, 1
Let g(c) = 2*c**2 + 2*c**2 + 1 + 7*c**3 + 4 - 8*c. Let q(w) = 3*w**3 + 2*w**2 - 4*w + 3. Let j(r) = 3*g(r) - 5*q(r). What is m in j(m) = 0?
-1, 0, 2/3
Let b(h) be the second derivative of h**4/12 + 5*h**3/2 - 8*h**2 + 3*h. Let f be b(-16). Factor 1/2*a**2 + a + f.
a*(a + 2)/2
Factor -2/5*n**5 - 4/5*n**2 - 2/5*n + 4/5*n**3 + 2/5*n**4 + 2/5.
-2*(n - 1)**3*(n + 1)**2/5
Let q(d) = -7*d**3 - 12*d**2 + 19*d. Let l(v) = -8*v**3 - 12*v**2 + 20*v. Let i(r) = -3*l(r) + 4*q(r). Factor i(c).
-4*c*(c - 1)*(c + 4)
Let l(k) be the second derivative of 0*k**3 - 1/30*k**4 + 1/150*k**6 - 1/100*k**5 + 0*k**2 + 7*k + 0. Solve l(v) = 0 for v.
-1, 0, 2
Let j be 6/15 + 216/10. Let t be 6 - ((-7 - 0) + 10). Solve 8*a**2 + 14/3*a**5 + j*a**4 - 16/3*a + 0 + 92/3*a**t = 0 for a.
-2, -1, 0, 2/7
Find j such that 2/7*j**2 + 0 + 10/7*j = 0.
-5, 0
Let b = 461/180 - 38/15. Let g(s) be the third derivative of 0 + 1/120*s**6 + b*s**4 - s**2 + 0*s + 7/180*s**5 + 0*s**3. Let g(x) = 0. What is x?
-2, -1/3, 0
Let q = 26/63 + 2/63. Let 0*j + 0 - 2/9*j**5 + 0*j**2 - q*j**4 - 2/9*j**3 = 0. What is j?
-1, 0
Let i(z) be the second derivative of z**4/54 + z**3/9 - 13*z. Solve i(w) = 0.
-3, 0
Let t(a) be the first derivative of 2*a**5/15 - 2*a**4/3 - 10*a**3/9 - 18. Factor t(s).
2*s**2*(s - 5)*(s + 1)/3
Let s(i) be the first derivative of -i**9/504 - i**8/120 - i**7/84 - i**6/180 - 2*i**3 + 5. Let g(d) be the third derivative of s(d). Factor g(w).
-2*w**2*(w + 1)**2*(3*w + 1)
Let j(a) be the third derivative of -a**7/3780 - a**6/360 - a**5/90 - a**4/8 - 2*a**2. Let d(z) be the second derivative of j(z). Factor d(q).
-2*(q + 1)*(q + 2)/3
Suppose 0*t - 10 = -5*l + 2*t, -4*l - 5*t = 25. Let y(v) be the first derivative of -3*v**3 - 3*v**2 + 1 - 3/4*v**4 + l*v. Find r, given that y(r) = 0.
-2, -1, 0
Let v(r) be the third derivative of -r**7/840 + r**6/360 - r**3/3 + 3*r**2. Let m(u) be the first derivative of v(u). Determine c so that m(c) = 0.
0, 1
Let q = 165/4 + -41. Determine i so that 0*i + 0 - 1/4*i**2 + q*i**3 = 0.
0, 1
Let y be 2/(-6) - (-13 - -12). Find a such that 2/3*a**2 + y*a**3 - 2/3*a - 2/3 = 0.
-1, 1
Let s(i) = 4*i**5 - 4*i**4 + 6*i**3 + 6*i**2 - 6*i + 2. Let m(f) = f**5 + f**4 + f**3 + f**2. Let d(x) = 2*m(x) - s(x). Suppose d(b) = 0. What is b?
-1, 1
Let t = 28 - 26. Factor 2*n**3 - 3 - 5*n**3 + 3 - 3*n**t.
-3*n**2*(n + 1)
Suppose -3*h = -3*o - 12, 6 = -0*h + 5*h + 2*o. Let v(r) be the second derivative of 0 - 1/60*r**4 - 1/30*r**3 + 0*r**h + r. Suppose v(u) = 0. What is u?
-1, 0
Let b(r) be the third derivative of -r**5/15 + 2*r**3/3 + 9*r**2. Let b(v) = 0. Calculate v.
-1, 1
Let 32/7 + 0*h**2 + 8/7*h**3 - 2/7*h**4 - 32/7*h = 0. What is h?
-2, 2
Let i be (4 - (-25)/(-6))/(-2). Let y(o) be the second derivative of 0 + i*o**4 - 3*o + 0*o**2 + 0*o**3. Solve y(f) = 0 for f.
0
Let g(h) = h**2 + 11*h - 6. Let f(t) = -5*t**2 - 65*t + 35. Let r(s) = -6*f(s) - 35*g(s). Solve r(a) = 0.
0, 1
Let i = -21 - -31. Suppose i*o**3 - 2*o**4 - o**4 - 7*o**3 = 0. Calculate o.
0, 1
Let x = 13 - 11. Factor -5*t**2 - 3*t**x + 2*t + 6*t**2.
-2*t*(t - 1)
Let f(o) = -2*o**2 - 2*o + 3. Let j be f(0). Suppose i - 5 = -j. Solve -2/5*w + 2/5*w**i + 0 = 0.
0, 1
Let g(q) be the second derivative of -q**4/3 - 2*q**3/3 + 4*q**2 + 6*q. Suppose g(a) = 0. What is a?
-2, 1
Let x be -2*1/2*-9. Factor -4*m - 7*m + 17*m - x - m**2.
-(m - 3)**2
Factor 2/15*d**2 + 24/5 + 8/5*d.
2*(d + 6)**2/15
Let a be 1/(2 - 6/4). Factor -k**2 - 2*k**2 - 3 - 5*k**a - 7*k + 4*k**2.
-(k + 1)*(4*k + 3)
Let f(o) = -o**2 + 4*o - 2. Let d be f(2). Factor 3*a**d + 2*a**2 - 7*a**2 + 2*a**3 - 4*a + 2*a + 2.
2*(a - 1)**2*(a + 1)
Let g(z) be the first derivative of 8/15*z**3 + 3/5*z**2 - 2/5*z - 1. Suppose g(s) = 0. Calculate s.
-1, 1/4
Determine j so that -1/3*j**3 + 1/3*j + 1/3 - 1/3*j**2 = 0.
-1, 1
Let u be (0 - (-3)/(-18))*(-3)/4. Let h(f) be the third derivative of 0 + u*f**4 + 2*f**2 + 1/10*f**5 + 0*f**3 + 1/40*f**6 + 0*f. Let h(c) = 0. Calculate c.
-1, 0
Suppose -6/5*m + 8/5*m**3 - 2/5*m**5 + 0*m**4 - 4/5*m**2 + 4/5 = 0. What is m?
-2, -1, 1
Let r(s) = s**2 - 7*s + 1. Let w(i) = -4*i**2 + 34*i - 4. Let f(k) = 14*r(k) + 3*w(k). Let f(y) = 0. What is y?
-1
Suppose 11*m + 4 + 4*m**3 + m**2 - 2*m**2 - 15*m - 2*m**2 - m**4 = 0. What is m?
-1, 1, 2
Let s = 9 + -6. Let f(p) = p**2 - p + 2. Let d be f(1). Factor 0 - 1/3*l**s - 1/3*l**d + 0*l.
-l**2*(l + 1)/3
Let i(g) be the first derivative of 5*g**6/6 + 5*g**5 - 5*g**4/4 - 25*g**3/3 + 56. Factor i(v).
5*v**2*(v - 1)*(v + 1)*(v + 5)
Let l(b) = 9*b**3 - 79*b**2 - 18*b + 2. Let o be l(9). Factor -16/3*i**3 + 0*i**o - 4/3 + 4*i.
-4*(i + 1)*(2*i - 1)**2/3
Let j(u) be the third derivative of 0 + 1/40*u**6 - u**2 - 1/8*u**4 - 1/10*u**5 + u**3 + 0*u. What is g in j(g) = 0?
-1, 1, 2
Let q(a) be the second derivative of a**4/54 + 5*a**3/27 + 2*a**2/3 - 2*a. What is h in q(h) = 0?
-3, -2
Suppose -5*m + 25 = -3*s, 20 = 5*m - s - s. Let y = 5 - m. Find z, given that -2*z + 5*z**y - 3*z**3 + 3*z**3 - 3*z**3 = 0.
-1, 0, 1
Factor -50/9 - 2/9*s**2 - 20/9*s.
-2*(s + 5)**2/9
Suppose -l + 5*y = -22, 3*y + 26 = 4*l + 6. Suppose -l*o + 14 = 6. Factor 0*h**3 - h**2 - h**2 - o*h**3.
-2*h**2*(2*h + 1)
Let s(n) be the first derivative of 1/7*n**4 + 4/21*n**3 - 6/35*n**5 + 2/7*n + 1/21*n**6 + 1 - 3/7*n**2. Solve s(i) = 0 for i.
-1, 1
Let m(v) = 4*v - 13. Let p be m(6). Let g = 13 - p. Factor 0*r + 1/2*r**3 + 3/2*r**2 - g.
(r - 1)*(r + 2)**2/2
Let i(y) be the first derivative of -5*y**5/12 + 95*y**4/48 - 16*y**3/9 + y**2/2 + 10. Find t, given that i(t) = 0.
0, 2/5, 3
Let d(u) be the third derivative of 0*u - 1/175*u**7 - 2*u**2 + 1/20*u**4 + 0 - 1/840*u**8 + 1/75*u**5 - 1/150*u**6 + 1/15*u**3. Let d(k) = 0. Calculate k.
-1, 1
Let u be 3*2/(-3) - -2. Suppose -5*q + u*q = 0. Factor -2/9*d + q + 2/9*d**2.
2*d*(d - 1)/9
Let f(n) be the third derivative of 2/105*n**7 + 0*n + 0 - 1/9*n**4 - 13/180*n**6 - 1/504*n**8 + 8*n**2 + 2/15*n**5 + 0*n**3. Factor f(r).
-2*r*(r - 2)**2*(r - 1)**2/3
Let f(l) be the third derivative of l**4/24 + 2*l**3/3 + 10*l**2. Let n be f(-2). Determine u so that -1/3 + u**n + 2/3*u = 0.
-1, 1/3
Let b = -1231/9 + 137. Determine i, given that 0 - 2/3*i**2 - 4/9*i - b*i**3 = 0.
-2, -1, 0
Let m(g) be the second derivative of 3*g**6/10 + 3*g**5/4 + g**4/4 - g**3/2 + g. Factor m(w).
3*w*(w + 1)**2*(3*w - 1)
Suppose f + 4*f - 20 = 0. Suppose 32*z**2 - 18*z**3 + 3*z**f + 0*z**4 - 5*z**2 = 0. Calculate z.
0, 3
Let c(h) be the second derivative of h**5/30 - h**4/18 - 2*h**3/9 + 8*h + 5. Factor c(v).
2*v*(v - 2)*(v + 1)/3
Let w = -4 + 18. Suppose -4*l - w = -11*l. Suppose 5/2*j**3 + 27/2*j**2 - 10*j + 15/2*j**5 - 31/2*j**4 + l = 0. Calculate j.
-1, 2/5, 2/3, 1
Let u = 288/185 - 28/37. Factor -4/5*r + 27/5*r**2 + 7/5*r**4 - u - 26/5*r**3.
(r - 2)*(r - 1)**2*(7*r + 2)/5
Suppose 0 = 3*q + 2*q - 2*i - 7, -2*q = 2*i - 14. Let f(r) be the first derivative of 1/3*r**2 + 0*r + 1/9*r**q - 3. Factor f(c).
c*(c + 2)/3
Let f(l) be the third derivative of -l**6/30 - l**5/8 - l**4/8 + 5*l**3/6 + 6*l**2. Let q(u) be the first derivative of f(u). Let q(i) = 0. What is i?
-1, -1/4
Let f(g) = -g**2 + 7*g - 4. Let t = 4 + 2. Let x be f(t). Factor 2*d + 4*d - 4*d - 2 - 4*d**3 + 4*d**2 - 2*d**4 + x*d**5.
2*(d - 1)**3*(d + 1)**2
Let x(r) be the third derivative of -1/15*r**5 + 1/10*r**6 - 1/3*r**4 + 0 + 0*r**3 - 6*r**2 + 0*r. Factor x(q).
4*q*(q - 1)*(3*q + 2)
Solve -8/11*t**3 + 0 + 6/11*t**2 + 2/11*t**4 + 0*t = 0.
0, 1, 3
Let f be (11 - 9)*(3 - (-14)/(-5)). Let 4/5*r - 2/5 -