 - 10/7*k**2 + 0 - 8/7*k**3.
-2*k*(k + 1)*(4*k + 1)/7
Let s be 36/21*(-4 - (-15)/2). Let s*w - 6*w**3 + 9/2 - 9/2*w**2 = 0. Calculate w.
-1, -3/4, 1
Let t(k) be the third derivative of 13*k**2 + 0*k - 1/2*k**3 + 0 + 0*k**4 + 1/20*k**5. Factor t(g).
3*(g - 1)*(g + 1)
Suppose 38*i = 36*i - 2*y + 26, -3*i + 7 = -y. Suppose 0 + 0*l + 1/4*l**4 - 1/4*l**i - 1/4*l**2 + 1/4*l**3 = 0. Calculate l.
-1, 0, 1
Let a(z) be the first derivative of 1 - 15*z - 5/3*z**3 + 35/2*z**2 + 4*z**5 - 35/4*z**4. Factor a(x).
5*(x - 1)**2*(x + 1)*(4*x - 3)
Let x be -1 - (-9 - 9/(-3)). Suppose -z - 4*i = -4, x - 1 = z - 2*i. Suppose 0*l**z + 6*l**4 - 3*l**4 + l**2 + 2*l**3 + l**3 + l**5 = 0. Calculate l.
-1, 0
Let v(l) be the first derivative of 2*l**3/21 - 13*l**2/7 + 24*l/7 + 46. Factor v(n).
2*(n - 12)*(n - 1)/7
Let q(u) = 7*u**2 + 70*u + 159. Let g(d) = -6*d**2 - 69*d - 162. Let j(a) = -4*g(a) - 3*q(a). Factor j(x).
3*(x + 3)*(x + 19)
Let a(b) be the second derivative of 10/3*b**4 - 17/15*b**6 - 7*b + 0 + 0*b**2 + 8/3*b**3 - 5/21*b**7 - 3/5*b**5. Let a(c) = 0. What is c?
-2, -2/5, 0, 1
Suppose 3/2*q**2 + 1/4*q**3 + 5/4*q - 3 = 0. What is q?
-4, -3, 1
Factor 0 + 75/7*b - 1/7*b**3 - 10/7*b**2.
-b*(b - 5)*(b + 15)/7
Let w be ((-45)/30)/((-2)/4). Let n(q) be the second derivative of 2/5*q**2 + 1/25*q**5 - 5*q - 1/20*q**4 - 2/15*q**w - 1/150*q**6 + 0. What is f in n(f) = 0?
-1, 1, 2
Factor 0*f**2 - 12/7*f**3 + 2*f**5 + 0*f - 38/7*f**4 + 0.
2*f**3*(f - 3)*(7*f + 2)/7
Let v(h) be the first derivative of -h**4/4 - 77*h**3/12 + 61*h**2/8 + 5*h - 19. Find y, given that v(y) = 0.
-20, -1/4, 1
Let b(s) be the third derivative of -5/336*s**8 - 9*s**2 + 0*s**3 + 2*s**5 - 1/7*s**7 - 1/24*s**6 + 0 + 0*s - 10/3*s**4. What is l in b(l) = 0?
-4, 0, 1
Let p be (-1)/(-1)*(170 - 3). Factor 75 + 25*j + p + 19*j + 2*j**2.
2*(j + 11)**2
Let w(d) be the second derivative of 7*d**5/180 - 4*d**4/27 + 11*d**3/54 - d**2/9 - d + 5. Factor w(q).
(q - 1)**2*(7*q - 2)/9
Let f(n) be the first derivative of -2*n**3/27 + 32*n/9 - 59. Find s, given that f(s) = 0.
-4, 4
Let p = -46 - -46. Let g(l) be the second derivative of 2/15*l**3 - 1/50*l**5 + 4*l + p*l**2 + 0 - 1/30*l**4. Find s such that g(s) = 0.
-2, 0, 1
Let r(d) = d**3 + 3*d**2. Suppose 0 = -4*i - 1 - 7. Let j be r(i). Factor -p**3 - 1 + 0 + 3*p - 1 + 4*p**j - 12*p**2 + 8*p.
(p - 1)**2*(p + 2)*(4*p - 1)
Let h = 405 - 401. Let i(n) be the first derivative of 0*n**2 - 2/15*n**3 + 0*n**h + 2/25*n**5 + 0*n - 4. Factor i(r).
2*r**2*(r - 1)*(r + 1)/5
Let g(a) be the second derivative of a**4/30 - 206*a**3/15 + 10609*a**2/5 - 49*a. Let g(h) = 0. Calculate h.
103
Let a(n) be the first derivative of n**5/15 + 2*n**4/3 + 8*n**3/3 - 7*n**2/2 - 45. Let h(b) be the second derivative of a(b). Factor h(l).
4*(l + 2)**2
Let s(h) be the second derivative of -h**4/4 + 5*h**3 + 73*h. Factor s(d).
-3*d*(d - 10)
Let n(r) = 100*r - 20. Let m be n(13). Factor -73*f - 115*f + 28*f - 2*f**2 - m - 3*f**2.
-5*(f + 16)**2
Let i = -665 - -665. Let b(m) be the first derivative of -1/15*m**3 + i*m**2 + 2 + 0*m. Factor b(p).
-p**2/5
Suppose 2 = 3*q - 2*q. Suppose 84*t - 88*t + 7*t**2 + 2*t**5 + t**2 - 2*t**4 - 6*t**3 + q*t**2 = 0. Calculate t.
-2, 0, 1
Let r = 268/3 + -893/10. Let q(b) be the third derivative of 0*b**3 + 0*b + r*b**5 - b**2 - 1/6*b**4 + 0. Factor q(y).
2*y*(y - 2)
Suppose -t + t**2 - 1/4*t**3 + 0 = 0. Calculate t.
0, 2
Let t(r) be the first derivative of r**4/4 - 9*r**3/2 - 15*r**2 + 50*r - 17. Let z(k) be the first derivative of t(k). Solve z(l) = 0.
-1, 10
Let d = 4249 - 4247. Factor -25/3*z**3 + 56/3*z - 4 - 55/3*z**d.
-(z + 3)*(5*z - 2)**2/3
Factor -b**5 + 24*b**3 + 5*b**4 + b**2 - 23*b**3 - 6*b**4.
-b**2*(b - 1)*(b + 1)**2
Let r(m) be the third derivative of m**8/28 + 3*m**7/10 + 41*m**6/40 + 37*m**5/20 + 15*m**4/8 + m**3 - 137*m**2. Determine i, given that r(i) = 0.
-2, -1, -1/4
Let d = 95 - 92. What is n in 227*n**3 - 120*n**3 - 10*n**2 - 112*n**d = 0?
-2, 0
Suppose 93 = 4*z - z. Let f = 51 - z. Determine n so that 116*n**2 - f + 49*n**2 + 4 + 72*n**4 - 222*n**3 - n**2 - 8*n = 0.
-1/4, 2/3, 2
Suppose -2*r + 80 = 3*r. Suppose j + 3*c = -4*j - 6, 0 = 2*j + 2*c + 4. Factor -n**3 + j*n**3 - 11*n**3 - 4*n + r*n**2.
-4*n*(n - 1)*(3*n - 1)
Let 32*z - 64/5 + 5*z**4 - 8*z**3 - 84/5*z**2 = 0. Calculate z.
-2, 4/5, 2
Let d be 754/(-672) - (-128)/112. Let j(v) be the second derivative of -1/8*v**2 + 8*v + 0 - d*v**3 + 1/32*v**4. Solve j(m) = 0 for m.
-2/3, 1
Suppose 6*y - 2*p = 4*y + 4, -y + 5*p = -10. Let a(d) be the first derivative of -12*d**4 + y*d**2 + 0*d - 2*d**3 - 231/10*d**5 - 49/4*d**6 + 2. Solve a(g) = 0.
-1, -2/7, 0
Let w = 7808 + -23423/3. Determine g, given that -4/3*g + 0*g**2 + w*g**3 + 0 = 0.
-2, 0, 2
Suppose i = -5*p + 20, -p = -3*i + 4 - 8. Find h such that -2/3*h**2 + 0*h + i + 2/3*h**4 + 0*h**3 = 0.
-1, 0, 1
Suppose -6 = -3*n - 42. Let h(t) = 5*t**2 - 2*t + 1. Let x = 15 + -12. Let y(w) = w**2. Let v(j) = n*y(j) + x*h(j). Factor v(s).
3*(s - 1)**2
Let w(d) be the first derivative of 3*d**3 - 15*d**2/2 - 6*d - 24. Let w(g) = 0. What is g?
-1/3, 2
Solve 20*k**5 + 21/5*k + 4/5 + 63*k**4 - 79/5*k**2 - 361/5*k**3 = 0 for k.
-4, -1/5, 1/4, 1
Let y(d) be the second derivative of -d**5/50 - 7*d**4/30 - 2*d**3/3 + 299*d. Determine x, given that y(x) = 0.
-5, -2, 0
Let p(z) be the third derivative of z**10/30240 - z**9/15120 - 7*z**4/24 - 13*z**2. Let j(g) be the second derivative of p(g). Solve j(t) = 0 for t.
0, 1
Let h(l) = 2*l**2. Let u be h(-1). Suppose 4*r - 12 = 0, 2*v - 13 = -r - u*r. Factor 2 - 4 + 3*w**v - 1.
3*(w - 1)*(w + 1)
Let l(q) be the first derivative of q**6/6 - q**5 + q**4/4 + 17*q**3/3 - 11*q**2 + 8*q - 145. Find f, given that l(f) = 0.
-2, 1, 4
Let g(q) be the second derivative of -5*q**7/42 - 8*q**6 - 849*q**5/4 - 16625*q**4/6 - 18130*q**3 - 61740*q**2 - 12*q + 27. Factor g(i).
-5*(i + 3)**2*(i + 14)**3
Let m be 104/48 + 2*(3 - 4). Let y(a) be the third derivative of 0*a + 1/8*a**4 + 1/120*a**6 + 0 + m*a**3 - a**2 + 1/20*a**5. Factor y(l).
(l + 1)**3
Suppose 0 = 3*l - 6 - 9. Solve 2*p - 3*p**5 + 9*p**4 - 9*p**2 - 4*p + 3*p + l*p - 3*p**3 = 0.
-1, 0, 1, 2
Find r such that -39*r + 2*r**3 - r**2 - 384*r**4 + 37*r + 385*r**4 = 0.
-2, -1, 0, 1
Let q be (618/20)/(5/(-30)). Let k = -185 - q. Factor 1/5*r**3 + r + 4/5*r**2 + k.
(r + 1)**2*(r + 2)/5
Let p(l) be the second derivative of l**8/2240 - l**7/280 + l**6/120 - 11*l**4/12 + 2*l. Let i(w) be the third derivative of p(w). Factor i(h).
3*h*(h - 2)*(h - 1)
Let s(z) = -4*z - 16. Let w be 207/(-15) + (-2)/10. Let j be s(w). Factor j + 2*l**3 + 61*l + 4*l**2 + 14*l**2 - 7*l + 14.
2*(l + 3)**3
Suppose 8*i - 12*i = -9*v + 42, 4*v + 5*i = -22. Determine a, given that -12/5*a**v + 3*a + 3/5*a**3 - 6/5 = 0.
1, 2
Let d be -1*3 - 1*515/(-165). Let j(g) be the first derivative of 0*g + 2/55*g**5 - 4 + d*g**3 - 3/22*g**4 + 0*g**2. Factor j(p).
2*p**2*(p - 2)*(p - 1)/11
Let u = 2386803/7 + -340389. Let g = 584 - u. Factor 0 + 0*m + 2/7*m**5 - 4/7*m**2 + 10/7*m**3 - g*m**4.
2*m**2*(m - 2)*(m - 1)**2/7
Suppose 3 = -y, -23*i - 17 = -24*i + 5*y. Let c(p) be the third derivative of -9/7*p**3 + 0*p + 1/420*p**6 + 9/28*p**4 - 9*p**i - 3/70*p**5 + 0. Factor c(k).
2*(k - 3)**3/7
Let v(p) be the first derivative of 3*p**5/35 + 3*p**4/28 - p**3/7 - 3*p**2/14 - 6. Solve v(f) = 0.
-1, 0, 1
Let d = 2202/5 - 4399/10. Factor -d*o**3 - 1 + 1/2*o + o**2.
-(o - 2)*(o - 1)*(o + 1)/2
Let v = -1738 + 1742. Let k(b) be the first derivative of 1/4*b**3 + 8 + 0*b**2 - 9/16*b**v + 0*b + 0*b**5 + 1/2*b**6. Let k(a) = 0. What is a?
-1, 0, 1/2
Solve 3*j**3 + 5*j**2 - 3*j**4 - 2*j**3 + j**2 - 4*j**3 = 0.
-2, 0, 1
Let a(q) be the third derivative of q**4/12 - q**3 - 4*q**2. Let i be a(5). Factor -j**4 - 20*j**3 + 29*j**3 + 4*j**i + 3*j + 9*j**2.
3*j*(j + 1)**3
Let j(t) be the second derivative of -5*t**4/12 - 10*t**3/3 - 15*t**2/2 + 25*t + 1. Suppose j(c) = 0. What is c?
-3, -1
Let x be (-1 - (-6)/4)*4. Suppose -x*g + g = -13. Factor -2*t**3 + 7*t**4 + 2*t - g*t**2 + 0*t + 6*t**2.
t*(t - 1)*(t + 1)*(7*t - 2)
Let w be -24 - (0 + -2 - 2). Let o be 4/20 - 36/w. Factor -3 + 21*q**2 - 3*q**4 + 16*q**2 - 31*q**o.
-3*(q - 1)**2*(q + 1)**2
Let l(s) be the first derivative of s**3/12 - 4*s**2 - 33*s/4 - 135. Factor l(n).
(n - 33)*(n +