2*i**3/3 + i**2 - 8*i. Determine k, given that y(k) = 0.
-1
Let x(s) be the third derivative of -1/336*s**8 + 0*s**3 + 1/120*s**6 - 1/60*s**5 + 0*s + 0*s**4 + 1/210*s**7 + 0 - 7*s**2. Determine d so that x(d) = 0.
-1, 0, 1
Let i(u) be the third derivative of u**7/525 - u**5/75 + u**3/15 - 4*u**2. Factor i(v).
2*(v - 1)**2*(v + 1)**2/5
Suppose -2*i - 2 + 7 = 3*g, 0 = -2*g + 3*i + 12. Suppose 0 = -3*o + 2*u - 7 + 22, 12 = g*o - u. Solve 4*v**3 + o*v**3 + 2*v**2 - 5*v**3 = 0.
-1, 0
Let c(w) = -2 + 15*w**2 - 14*w**2 + 7*w + 14. Let t be c(-5). Factor -4/11 - 2/11*m**t - 6/11*m.
-2*(m + 1)*(m + 2)/11
Let k(i) be the third derivative of i**8/756 - i**7/189 + i**6/180 + i**5/270 - i**4/108 - 27*i**2. Suppose k(p) = 0. Calculate p.
-1/2, 0, 1
Let t(i) be the second derivative of i**5/70 - i**4/42 - 15*i. Let t(g) = 0. Calculate g.
0, 1
Let z(t) be the first derivative of t**4/4 + 4*t**3/3 + t**2 - 3*t - 2. Let i be z(-3). Find w, given that 3*w + w**2 - 3*w - 3*w**4 + i*w + 2*w**5 = 0.
-1/2, 0, 1
Suppose -6*q - 17 = -29. Factor 0*b - 2/5*b**3 + 0 - 2/5*b**q.
-2*b**2*(b + 1)/5
Let p(i) be the second derivative of -i**4/6 - 4*i**3/3 - 4*i**2 - i. Factor p(j).
-2*(j + 2)**2
Factor -1/3*o**2 - 1/3*o + 0.
-o*(o + 1)/3
Let r(s) be the third derivative of -s**7/3360 - s**6/1440 + s**5/480 + s**4/96 + s**3/6 + s**2. Let u(p) be the first derivative of r(p). Solve u(o) = 0 for o.
-1, 1
Let h(f) be the second derivative of -f**6/40 + 3*f**5/40 - f**4/16 - 2*f. Factor h(w).
-3*w**2*(w - 1)**2/4
Let t(x) = x**2 - 3*x + 2. Let z be t(4). Find r, given that z*r**3 - 2*r + 3*r**2 - 4*r**3 + 0*r**3 - 3*r**3 = 0.
0, 1, 2
Factor 12*f**3 + 20*f**2 - 13*f + 7*f**4 + 8*f + 9*f + 11*f**3.
f*(f + 1)*(f + 2)*(7*f + 2)
Let b = 2/31 - -23/124. Let b*t**3 + 0*t**2 - 1/4*t + 0 = 0. What is t?
-1, 0, 1
Let w = 5 + -2. Solve -7*b**w + 6*b**2 - b - b + 0*b + 2*b**4 + b**3 = 0 for b.
0, 1
Let w be 3*(-2)/(-9) - 0. Suppose 2/3*v**4 + 2/3*v - w*v**3 + 0 - 2/3*v**2 = 0. What is v?
-1, 0, 1
Let z = 19 - 17. Let d be -5 + z - 15/(-2). Factor -3/2*w**2 - 3 - d*w.
-3*(w + 1)*(w + 2)/2
Let x(q) = -3*q**2 + 2*q + 1. Let o be x(-1). Let m = o + 5. Factor m + s**3 - 3*s - 3*s**2 + 2*s + 2*s**2.
(s - 1)**2*(s + 1)
Let d(l) = 2*l - 8. Let c be d(7). Let h be 2*3/12*c. Determine u, given that 0*u**3 - 2*u + 3*u**h - 2*u**2 + 3*u**2 = 0.
-1, 0, 2/3
Let x = 80 + -56. Suppose -x = 3*n - 6*n. Suppose n*c**4 + 9*c**2 + 2*c - 3*c**4 - 12*c**3 - 4*c = 0. What is c?
0, 2/5, 1
Let x(p) be the first derivative of -p**4/6 - 4*p**3/3 - 4*p**2 - 16*p/3 - 3. Determine v so that x(v) = 0.
-2
Suppose h + 4*h = 3*b - 9, -5*b + 15 = 4*h. Let -5*m**2 - 5*m + m**b + 8*m + 2*m**2 - 1 = 0. Calculate m.
1
Let t(p) be the first derivative of p**6/100 - 11*p**5/300 + p**4/30 - p**3 - 2. Let g(b) be the third derivative of t(b). Find v, given that g(v) = 0.
2/9, 1
Let x be 2*1*(-10)/4. Let q(l) = -3*l**2 - l - 4. Let t(y) = -4*y**2 - 2*y - 5. Let r(c) = x*q(c) + 4*t(c). Factor r(a).
-a*(a + 3)
Let d(u) be the second derivative of -u**6/10 - 9*u**5/20 + u**4/4 + 3*u**3/2 + 31*u. Determine f so that d(f) = 0.
-3, -1, 0, 1
Let y = 2 + 1. Factor -6*b**2 + 2*b - 3*b + 4*b**2 + y*b.
-2*b*(b - 1)
Factor 2/3*t**2 + 0 + 2/3*t.
2*t*(t + 1)/3
Factor -3/4*p**3 + 0 + 3/4*p**4 + 3/4*p**5 + 0*p - 3/4*p**2.
3*p**2*(p - 1)*(p + 1)**2/4
Suppose -40/3*n**2 + 4/3*n + 77/3*n**3 + 121/3*n**4 + 0 = 0. Calculate n.
-1, 0, 2/11
Let y(p) be the first derivative of -p**5/5 + 7*p**4/2 - 73*p**3/3 + 84*p**2 - 144*p + 24. Determine k so that y(k) = 0.
3, 4
Let n = 17 - 13. Let v(z) be the second derivative of 1/42*z**n + 0 - 1/7*z**2 + 1/7*z**3 - 3/70*z**5 + 2*z. Factor v(d).
-2*(d - 1)*(d + 1)*(3*d - 1)/7
Let s(g) be the second derivative of g**8/12600 + g**7/3150 - g**5/450 - g**4/180 + 7*g**3/6 - 4*g. Let q(i) be the second derivative of s(i). Factor q(n).
2*(n - 1)*(n + 1)**3/15
Let x = 1933/12 - 161. Let l(z) be the first derivative of 1/16*z**4 + 0*z + 2 - 1/4*z**2 + x*z**3. Factor l(c).
c*(c - 1)*(c + 2)/4
Let z = -1 + 5. Let k be (7/z)/(2/8). Find i such that -i + 7*i**3 + i**5 - 2*i**2 + 2*i**4 - k*i**3 = 0.
-1, 0, 1
Let a(k) be the first derivative of -k**6/180 - k**5/30 - k**4/12 - k**3/9 + 3*k**2/2 + 1. Let x(z) be the second derivative of a(z). Factor x(l).
-2*(l + 1)**3/3
Let g(w) be the second derivative of -w**5/30 - w**4/6 + w**3 + 3*w**2/2 + 6*w. Let c(q) be the first derivative of g(q). Suppose c(p) = 0. Calculate p.
-3, 1
Suppose 5*v = -5*u, 7*v + 8 = 3*v. Suppose 0 = u*i - 2*a - 6, -5*i + 4*a + 14 = -0*i. Suppose -2/9*r + 2/9*r**i + 0 = 0. What is r?
0, 1
Let w(b) = b**2 - 3*b - 1. Let d be w(4). Factor -105*g**d + 0 + 38*g**2 + 343/2*g**5 - 4*g + 49/2*g**4.
g*(g + 1)*(7*g - 2)**3/2
Let i = 4/9 - -1/18. Suppose -80*k = -77*k - 6. Let -i*n**k - n - 1/2 = 0. Calculate n.
-1
Suppose p + 5 = -4*q, 3*q - 3*p + 0*p = 15. Factor 4*n**2 + q*n**5 - 2 - 5*n**4 + 4*n**3 - 2*n + 3*n**4 - 2*n**5.
-2*(n - 1)**2*(n + 1)**3
Let k be (-2)/(-11) + (-2)/11. Let d be 6/(-21) + 28/49. Factor d*f**2 + k - 2/7*f.
2*f*(f - 1)/7
Suppose 0*i - 4/5 + 1/5*i**2 = 0. What is i?
-2, 2
Let k = -2/1953 - -691/39060. Let v(i) be the third derivative of 1/210*i**7 + 0*i**3 + k*i**6 + 2*i**2 + 1/60*i**5 + 0*i + 0 + 0*i**4. Let v(b) = 0. What is b?
-1, 0
Let y(m) be the third derivative of -1/120*m**4 - 1/1050*m**7 + 1/600*m**6 - m**2 + 0 + 1/300*m**5 + 0*m**3 + 0*m. Factor y(s).
-s*(s - 1)**2*(s + 1)/5
Suppose 3*k = -2*k + 15. Let g(b) be the second derivative of -1/15*b**k + 1/50*b**5 + 0 + b + 1/5*b**2 - 1/30*b**4. Let g(u) = 0. Calculate u.
-1, 1
Let m be 420/504 + 2/(-24). Factor m*d**2 + 3*d + 9/4.
3*(d + 1)*(d + 3)/4
Let z(v) = v**3 - 8*v**2 - v + 2. Let c be z(8). Let w be 0*(-1)/c*2. Factor -1/3*m**3 + 0 + w*m + 0*m**2 - 1/3*m**4.
-m**3*(m + 1)/3
Let j(b) = 2*b**2 - 6*b + 2. Let z(r) = -10*r**2 + 30*r - 9. Let h(u) = -11*j(u) - 2*z(u). Solve h(g) = 0 for g.
1, 2
Let u(m) be the third derivative of -m**8/840 - 2*m**7/525 + m**5/75 + m**4/60 - 7*m**2. Let u(k) = 0. What is k?
-1, 0, 1
Let o(w) be the third derivative of -w**7/70 - w**6/40 + w**5/20 + w**4/8 + 18*w**2. Factor o(x).
-3*x*(x - 1)*(x + 1)**2
Let j(m) be the second derivative of m**7/147 + m**6/35 - m**5/70 - m**4/6 + 4*m**2/7 - 16*m. Suppose j(n) = 0. Calculate n.
-2, -1, 1
Suppose -3*i = 2*g - 0*i - 4, 5*i = 0. Let u = -25 - -79/3. Factor 0 + 2/3*v**4 - u*v**3 - 2/3*v**g + 4/3*v.
2*v*(v - 2)*(v - 1)*(v + 1)/3
Determine u, given that 112*u - 7*u**3 - 64 - 16*u**2 - 2*u**3 - 3*u**3 = 0.
-4, 2/3, 2
Suppose 4*y - 186 - 38 = 0. Let f be (-2)/4*y/(-98). Factor 2/7*v + 0 + f*v**2.
2*v*(v + 1)/7
Let b(m) be the third derivative of -m**7/280 - m**6/60 - m**5/40 + m**4/4 - m**2. Let h(u) be the second derivative of b(u). Factor h(r).
-3*(r + 1)*(3*r + 1)
Let u(b) be the first derivative of -b**2 - 2 + 0*b**3 + 1/6*b**4 - 2*b. Let n(q) be the first derivative of u(q). Factor n(a).
2*(a - 1)*(a + 1)
Suppose 27 + 9 = -3*s. Let k be 9/(-21)*s/9. Solve -10/7*u + 6/7*u**2 - k = 0.
-1/3, 2
Suppose 4*h = -2*r + 2, -2*r - 2*r = -2*h + 16. Let p be (-2)/((-17)/2 - r). Factor p*g**3 + 2/11*g**4 + 0 + 2/11*g**2 + 0*g.
2*g**2*(g + 1)**2/11
Let g(m) be the third derivative of -2*m**2 + 0 - 1/1080*m**6 + 0*m + 1/3*m**3 + 1/72*m**4 + 0*m**5. Let h(i) be the first derivative of g(i). Factor h(a).
-(a - 1)*(a + 1)/3
What is m in 2/17*m**3 + 0 + 0*m**2 - 2/17*m = 0?
-1, 0, 1
Let u(i) be the second derivative of -i**7/5040 - i**4/2 - 2*i. Let a(y) be the third derivative of u(y). Factor a(w).
-w**2/2
Let o(q) be the second derivative of q**4/20 - 6*q**3/5 + 54*q**2/5 + 3*q. Factor o(f).
3*(f - 6)**2/5
Let k be 1 + (-21 - -22)*(-1)/5. Factor 6/5*y + k - 2*y**2.
-2*(y - 1)*(5*y + 2)/5
Let t(o) = -o**2 + 7*o - 6. Let h(a) = -a**2 + 6*a - 2. Let z be h(4). Let i be t(z). Factor -2/7*l + 2/7*l**2 + i.
2*l*(l - 1)/7
Suppose 3*i = -4*f - 15, -15 = -2*f + 4*i - i. Factor f*b - 1/4*b**2 + 1.
-(b - 2)*(b + 2)/4
Suppose 2/9*l**2 - 2/9 - 2/9*l**3 + 2/9*l = 0. Calculate l.
-1, 1
Factor 32/5 - 2/5*g**3 + 18/5*g**2 - 48/5*g.
-2*(g - 4)**2*(g - 1)/5
Solve -3/4*r**3 - 3/4*r**2 + 3/4*r + 3/4 = 0.
-1, 1
Suppose -9 = -3*j - 0*j. Let -40 + 3*q**2 + 40 - j*q - 6*q**2 = 0. Calculate q.
-1, 0
Let p(a) = 11*a**2 + 5*a. Let c(x) = 6*x**2 + 3*x. S