(c - 2)**2*(c + 1)*(c + 2)
Let a(y) be the third derivative of y**6/24 - 7*y**5/6 - 5*y**4/24 + 35*y**3/3 + 270*y**2. Factor a(r).
5*(r - 14)*(r - 1)*(r + 1)
Let y = 18 + -15. Suppose -9 = -y*h + 9. Suppose -4 - 3 + 16*n**3 - 1 - 4*n**2 + h*n**4 - 4*n**5 - 6*n**2 - 24*n = 0. Calculate n.
-1, -1/2, 2
Let o(l) = l**3 + l**2 + 1. Let n(b) = 16*b**3 + 264*b**2 + 5292*b + 37056. Let p(y) = -n(y) + 12*o(y). Factor p(w).
-4*(w + 21)**3
Factor -141*y - 6*y**3 + 6*y**2 - 14*y**2 + 149*y + 2*y**5 + 4*y**4.
2*y*(y - 1)**2*(y + 2)**2
Let y(i) be the first derivative of -1/12*i**3 + 5 + 1/16*i**4 + 1/20*i**5 - 1/24*i**6 + 0*i + 0*i**2. Solve y(a) = 0.
-1, 0, 1
Let w(u) be the first derivative of 4*u**3/15 + 904*u**2/5 + 204304*u/5 - 275. Factor w(i).
4*(i + 226)**2/5
Let i(s) = -6*s - 1. Let r be i(-2). Solve -25*z**2 - 5*z + z + 15 + 25*z**3 - r + 0*z = 0 for z.
-2/5, 2/5, 1
Solve 5*x**5 + 4083*x**4 - 33*x**2 + 75*x**3 - 12*x**2 - 4118*x**4 = 0.
0, 1, 3
Let h(w) be the first derivative of 4/3*w**3 + 0*w + 2*w**2 - 17. Factor h(q).
4*q*(q + 1)
Let v(d) = -2*d**3 + d**2 + d + 2. Let w be v(0). Let s(l) be the third derivative of -5*l**w + 0*l**4 + 0*l**3 + 0*l + 1/120*l**6 + 0 - 1/60*l**5. Factor s(x).
x**2*(x - 1)
Let z(b) be the second derivative of -5/12*b**5 - 2*b - 5/2*b**2 + 5/4*b**4 + 0 - 3/2*b**3. Let f(r) be the first derivative of z(r). Factor f(y).
-(5*y - 3)**2
Let o(h) be the third derivative of h**7/504 + h**6/144 + 2*h**4/3 + 13*h**2. Let r(n) be the second derivative of o(n). Factor r(t).
5*t*(t + 1)
Let k(m) = 323*m + 649. Let f be k(-2). Suppose 8/3*w - 8/3*w**2 + 2/3*w**f + 0 = 0. What is w?
0, 2
Suppose 22 = 5*j + 4*n, 0 = j - 2*j + 5*n - 13. Factor 14*o**5 + o**j - 3*o**4 + 0 - 16*o**5 + 0.
-o**2*(o + 1)**2*(2*o - 1)
Let j(k) be the first derivative of k**4/9 + 20*k**3/27 + 4*k**2/3 + 15. Let j(v) = 0. Calculate v.
-3, -2, 0
Let r = 547 + -366. Determine y so that -4*y**3 - 20*y + 35*y**2 + 24*y**3 - 50 + 13*y**2 - 179*y**4 + r*y**4 = 0.
-5, -1, 1
Let r(w) be the first derivative of -49*w**4/16 - 371*w**3/12 - 25*w**2 - 7*w + 47. Find k such that r(k) = 0.
-7, -2/7
Suppose 0 = -3*l - 4*d + 35, -d = -40*l + 37*l + 10. Suppose 0 + 2/5*p**3 - 1/5*p**l + 0*p**2 - 1/5*p + 0*p**4 = 0. What is p?
-1, 0, 1
Suppose 4*f = 2*q - 8, -140 = -5*q + 3*f - 120. What is n in -15*n**4 + 0 - 18*n**3 - q*n**2 + 0*n + 25/2*n**5 = 0?
-2/5, 0, 2
Suppose 0 = 6*y - 11 - 19. Factor 3*d**4 - 6*d + 4*d**3 - 34 + 3*d**y - d**5 - 9*d**4 + 36 + 4*d**2.
2*(d - 1)**4*(d + 1)
Determine f so that -139*f + 3*f**5 + 6*f**2 - 4*f**4 + f**3 - 14*f**3 + 159*f + 8 = 0.
-1, -2/3, 2
Factor 17/3*z - 1/9*z**2 + 106/9.
-(z - 53)*(z + 2)/9
Let n be (5/36)/((-940)/(-1504)). Find k such that -2/3*k + 4/9 + n*k**2 = 0.
1, 2
Let r(x) be the first derivative of 3*x**4/4 + 4*x**3/5 - 3*x**2/10 + 600. What is w in r(w) = 0?
-1, 0, 1/5
Let w be 7650/(-272) + 28 - 2/(-4). Suppose -w*p**2 - 9/8*p + 0 = 0. Calculate p.
-3, 0
Let l(z) be the first derivative of -1/7*z**4 - 4/7*z**3 - 4/7*z + 20 - 6/7*z**2. Factor l(n).
-4*(n + 1)**3/7
Determine o so that -38/3*o**3 + 8/3 - 2/3*o**5 + 14/3*o**4 + 50/3*o**2 - 32/3*o = 0.
1, 2
Suppose 243*s - 93*s = 47*s. Factor -3/5*o**2 - 24/5*o + s.
-3*o*(o + 8)/5
Suppose 2 - f**3 + 25/3*f**2 + 2/3*f**5 - 7/3*f**4 - 23/3*f = 0. What is f?
-2, 1/2, 1, 3
Let o(c) = -c**2 + c. Let y(t) = -44*t**2 + 27*t**2 - 59*t - 2*t + 18. Let p(d) = -4*o(d) - y(d). Determine w so that p(w) = 0.
-3, 2/7
Factor -4/3*y + 0 - 10/3*y**2 + 2/3*y**5 - 2*y**3 + 2/3*y**4.
2*y*(y - 2)*(y + 1)**3/3
Factor 36105*v**2 - 40 - 36135*v**2 + 5*v**3 + 0*v**3 - 75*v.
5*(v - 8)*(v + 1)**2
Let o(g) be the first derivative of 4*g**3/3 - 38*g**2 - 80*g + 41. Find r such that o(r) = 0.
-1, 20
Let q(d) be the second derivative of 0 - 3/55*d**5 - 6/11*d**2 - 4/11*d**4 + 1/77*d**7 - 8*d + 2/55*d**6 - 7/11*d**3. Find i such that q(i) = 0.
-1, 2
Let s(v) be the first derivative of -v**3 + 28 + 5*v + 3*v - 22 - 5*v. Factor s(c).
-3*(c - 1)*(c + 1)
Let p be 0*(-14 + 18)*1/(-4). Let m(g) be the second derivative of -10*g + p - 5/24*g**3 - 1/16*g**4 - 1/4*g**2 + 1/80*g**5 + 1/120*g**6. Factor m(i).
(i - 2)*(i + 1)**3/4
Let s be (-103)/(-22) - (-58)/(-319). Solve -3/2*k**2 + s + 3*k = 0.
-1, 3
Let 0*f**4 + 0 - 2/3*f**5 + 0*f**2 + 0*f + 2/3*f**3 = 0. What is f?
-1, 0, 1
Let d(i) = 93*i**3 + 345*i**2 - 126*i - 216. Let p(h) = 19*h**3 + 69*h**2 - 25*h - 43. Let x(t) = 5*d(t) - 24*p(t). Determine b, given that x(b) = 0.
-8, -2/3, 1
Let v = -312 - -318. Let x(z) be the second derivative of 0*z**3 - 5*z + 1/30*z**v + 1/10*z**5 + 0*z**2 + 0*z**4 + 0. Suppose x(h) = 0. Calculate h.
-2, 0
Let i(q) = q**3 - 20*q**2 + 34*q + 41. Let g be i(18). Factor 56/5*k**3 + 36/5*k - 24/5*k**4 + 4/5*k**g - 8/5 - 64/5*k**2.
4*(k - 2)*(k - 1)**4/5
Solve 0*l - 21/4*l**3 + 0 - 11/2*l**2 + 1/4*l**4 = 0 for l.
-1, 0, 22
Let u(o) = 2*o**3 - 45*o**2 + 69*o - 126. Let m be u(21). Factor m + 0*p**2 + 1/3*p**4 + 2/3*p**3 + 0*p.
p**3*(p + 2)/3
Let d(f) be the first derivative of f**6/720 - f**5/30 + f**4/3 - 7*f**3/3 - 8. Let k(o) be the third derivative of d(o). Factor k(h).
(h - 4)**2/2
Suppose -12*y + 29 = 5. Let 10 + 23*f**2 - 66*f**y + 3*f**3 - 5*f + 28*f**2 + 5*f**4 + 2*f**3 = 0. Calculate f.
-2, -1, 1
Let v(t) be the third derivative of -t**6/64 + 21*t**5/160 - t**4/16 + 8*t**2. Factor v(n).
-3*n*(n - 4)*(5*n - 1)/8
Let y be 76/35 - (53/106)/((-10)/8). Let -2/7*p**4 - 10/7*p**3 - 2*p - 4/7 - y*p**2 = 0. What is p?
-2, -1
Let n(v) be the second derivative of -9/14*v**2 - 4*v + 0 + 1/7*v**3 + 1/28*v**4. Solve n(x) = 0.
-3, 1
Suppose 3*r = 5*r - 32. Solve 9*f**2 + 60*f**3 + 8*f + 5*f**5 + 27*f**2 + 7*f**5 + 60*f**4 - r*f**4 = 0.
-1, -2/3, 0
Let w(r) = -r**4 + 6*r**3 + 144*r**2 + 234*r + 109. Let s(m) = 5*m**3 + 145*m**2 + 235*m + 110. Let b(x) = 4*s(x) - 5*w(x). Factor b(a).
5*(a - 7)*(a + 1)**2*(a + 3)
Let w(z) be the first derivative of -28 - 14/11*z - 8/33*z**3 + 29/11*z**2. Factor w(h).
-2*(h - 7)*(4*h - 1)/11
Let s = 739/168 + -61/14. Let v(f) be the second derivative of -1/8*f**2 - 1/168*f**7 - 1/120*f**6 - 13*f + s*f**4 - 1/24*f**3 + 0 + 1/40*f**5. Factor v(b).
-(b - 1)**2*(b + 1)**3/4
Let m(x) be the first derivative of -75*x**4/4 + 215*x**3/3 - 60*x**2 - 20*x - 392. Factor m(p).
-5*(p - 2)*(p - 1)*(15*p + 2)
Let t(b) = 2*b**2. Let j(i) = 2*i**2 + 10*i. Let n(h) = -j(h) + 2*t(h). Find d, given that n(d) = 0.
0, 5
Factor 0 + 0*h + 1/5*h**3 - 3*h**2.
h**2*(h - 15)/5
Let r be (-3)/2*324/(-243). Let -2/5*a + 0 + 2/5*a**r + 2/5*a**3 - 2/5*a**4 = 0. What is a?
-1, 0, 1
Factor -536*x + 5*x**2 - 828*x + 146205 - 346*x.
5*(x - 171)**2
Let q(g) = 11*g**2 + 22*g + 2. Let r be q(-2). Let j(h) be the first derivative of -2/7*h + 7 + 0*h**4 + 4/21*h**3 + 0*h**r - 2/35*h**5. Factor j(b).
-2*(b - 1)**2*(b + 1)**2/7
Let s(j) be the first derivative of j**5/15 - 4*j**4/3 + 32*j**3/3 - 2*j**2 + 6. Let y(i) be the second derivative of s(i). Factor y(r).
4*(r - 4)**2
Suppose 14/5*l**2 - 2/5*l**3 - 32/5 - 16/5*l = 0. What is l?
-1, 4
Find c, given that 0*c + 35/4*c**3 + 0 + 15/4*c**5 - 5/2*c**2 - 10*c**4 = 0.
0, 2/3, 1
Let j(v) be the first derivative of 2*v**5/25 - 21*v**4/10 + 6*v**3 + 689*v**2/5 + 2028*v/5 + 966. Solve j(w) = 0.
-3, -2, 13
Suppose 25*n - 13*n = 19*n - 14. Factor 3*w - 9/2 - 1/2*w**n.
-(w - 3)**2/2
Let r(z) be the second derivative of -z**5/5 - z**4/3 + 20*z**3 + 7*z - 71. Factor r(y).
-4*y*(y - 5)*(y + 6)
Suppose -2*k + 21 = -3*g, 0*g - 26 = -2*k + 4*g. Suppose k*n - 4 = 2. Factor 0*q**2 - 3*q**n - q + 7*q.
-3*q*(q - 2)
Let q(r) = r**2 + 130*r + 1448. Let g(m) = 4*m**2 + 649*m + 7238. Let z(w) = -2*g(w) + 11*q(w). Let z(l) = 0. What is l?
-22
Let c(z) be the third derivative of -4*z**7/2205 + 131*z**6/1260 + 103*z**5/210 + 209*z**4/252 + 5*z**3/9 + 151*z**2. Find h such that c(h) = 0.
-1, -1/4, 35
Let f(t) = 3*t + t**2 - 2*t - 21*t**3 + 2*t**2 - 18*t**2 - 11*t**4 + 6. Let j(x) = -x**4 - x**3 + x + 1. Let g(z) = f(z) - 6*j(z). Factor g(v).
-5*v*(v + 1)**3
Let q(c) be the first derivative of -c**6/150 - c**5/100 + c**4/30 + 9*c - 5. Let n(y) be the first derivative of q(y). Find r, given that n(r) = 0.
-2, 0, 1
Let y(w) be the first derivative of 2*w**2 + 4/9*w**3 + 1/30*w**5 - 8 + 0*w + 1/360*w**6 + 1/6*w**4. Let z(f) be the second