Suppose 0 = -6*y - 231 + 231. Let f(i) be the third derivative of i**3 + 3/8*i**4 + 1/20*i**5 + 0 - 3*i**2 + y*i. Factor f(c).
3*(c + 1)*(c + 2)
Let g = 154228/518655 + 19/2435. Let b = 2/71 + g. Factor -1/3 + b*n**2 + 2/3*n**3 - 2/3*n.
(n - 1)*(n + 1)*(2*n + 1)/3
Let r = -113 - -1245/11. Let x be 4/(-26) - 5060/(-3146). Solve -r*y**2 - 32/11 - x*y = 0 for y.
-4
Suppose -20*a + 58 = -59 + 37. Factor 5/2*v**a + 13/2*v**3 - 1/2*v + 9/2*v**2 - 1.
(v + 1)**3*(5*v - 2)/2
Let t be (-4648)/5760 + 8/10. Let q = 193/144 + t. Factor q*v + 2/3 + 2/3*v**2.
2*(v + 1)**2/3
Let j = 71 - 81. Let h be (8/(-126))/(j/30). Determine z so that 0 + 2/7*z**2 + 2/21*z**3 + h*z = 0.
-2, -1, 0
Determine c so that -9/4*c**2 - 2*c**3 + 9/2*c - 1/4*c**4 + 0 = 0.
-6, -3, 0, 1
Let c = -146/3 - -1046/21. Let v be (-11 + 1)*45/3150*-4. Let -c*d**3 + 2*d**2 + v*d + 0 = 0. Calculate d.
-1/4, 0, 2
Let k(x) be the first derivative of -x**5/20 + x**3/6 - 4*x + 4. Let b(c) be the first derivative of k(c). Factor b(a).
-a*(a - 1)*(a + 1)
Suppose 6*x = x + 10. Suppose -x*g + 5*g - 12 = 0. Let -4 + 4 - 2 - g*r - 2*r**2 = 0. Calculate r.
-1
Solve 164*r**3 - 170*r**2 - 192*r + 78*r**3 - 22 + 198*r**4 + 224*r**5 + 12*r**4 - 18 - 274*r**5 = 0.
-1, -2/5, 1, 5
Let a be (-3 - -9)/3 - -3. Solve 1/9 + 7/9*q + 14/9*q**2 - 5/3*q**4 - q**a + 2/9*q**3 = 0.
-1, -1/3, 1
Let q = -111 + 107. Let f be 3/q*(4 + (-65)/15). Factor f*k**2 + 1/8*k**3 + 0 + 1/8*k.
k*(k + 1)**2/8
Let z be 1*(-4)/5*-10. Suppose p = a - 3*p - z, -5*a - 5*p + 15 = 0. Factor 0*n**4 + n**2 + 2*n**3 + 5*n**4 - a*n**4.
n**2*(n + 1)**2
Solve 30/7 - 27/7*i**3 + 75/7*i**2 + 3/7*i**4 - 81/7*i = 0.
1, 2, 5
Let o(l) = 11*l**2 + 60*l - 71. Let r(k) = -3*k**2 - 20*k + 23. Let t(v) = -4*o(v) - 13*r(v). Factor t(w).
-5*(w - 3)*(w - 1)
Factor 0 + 0*z + 7/5*z**4 + 0*z**2 + 1/5*z**5 + 2*z**3.
z**3*(z + 2)*(z + 5)/5
Factor -1/4*g**3 + 1/2*g**2 - 1/2 + 1/4*g.
-(g - 2)*(g - 1)*(g + 1)/4
Let x = -345/29 - -4543/377. Factor -2/13*g**2 + 2/13*g + x*g**4 - 2/13*g**3 + 0.
2*g*(g - 1)**2*(g + 1)/13
Let z(v) = -65*v**3 - 485*v**2 - 440*v + 45. Let w(k) = -3*k**3 - 22*k**2 - 20*k + 2. Let n(d) = 45*w(d) - 2*z(d). Determine j, given that n(j) = 0.
-2, 0
Let b(n) be the second derivative of 3*n**7/7 + 106*n**6/15 - 141*n**5/10 + 13*n**4/3 - 130*n. Let b(k) = 0. What is k?
-13, 0, 2/9, 1
Let h(b) be the second derivative of 0 + 5*b**4 + 20*b + 1/4*b**5 + 0*b**2 + 30*b**3. Factor h(n).
5*n*(n + 6)**2
Let g(f) = -2*f**3 - f**2. Let p(m) = -18*m**3 - 48*m**2 - 34*m - 6. Let o(t) = 2*g(t) + p(t). Solve o(r) = 0.
-1, -3/11
Suppose -4*p - 4 = -4*v - 52, 4*p - 4 = 0. Let w = v - -16. Solve -2*g**2 - g - 8 - w*g + 4 = 0.
-2, -1
Let b be (6/9)/((-4)/(-42)). Suppose 4*i + 141 = 3*k + 52, -k = 4*i - 3. Find t such that b*t**3 - t**4 - k*t - 2*t**4 - 13*t - 12 - 39*t**2 - 25*t**3 = 0.
-2, -1
Find n such that -2/7*n**4 + 0 + 8/7*n**3 + 4/7*n - 10/7*n**2 = 0.
0, 1, 2
Suppose 0 = 6*b - 2*b + 4. Let h be 3/(6/4) - b. Factor -5*r - 10*r**4 - 5*r**4 - 52*r**h + 15*r**2 + 57*r**3.
-5*r*(r - 1)*(r + 1)*(3*r - 1)
Let h(j) be the third derivative of -j**7/840 + j**6/90 - j**5/30 - 13*j**3/2 - 31*j**2. Let n(f) be the first derivative of h(f). Factor n(b).
-b*(b - 2)**2
Let -57/8 - 3/8*i**2 - 15/2*i = 0. What is i?
-19, -1
What is n in 249/4*n**2 - 1/4*n**3 - 20667/4*n + 571787/4 = 0?
83
Let y(z) be the second derivative of 3/20*z**5 - 10*z + 0 + z**3 + 3/4*z**4 + 0*z**2. Factor y(s).
3*s*(s + 1)*(s + 2)
Suppose -5*l + 4*m = -0*l - 112, -4*l + 83 = -m. Factor -l*w**2 - 74*w**4 - 40*w**3 + 2*w**5 - 7*w**5 + 49*w**4.
-5*w**2*(w + 1)*(w + 2)**2
What is o in 0*o - o**2 + 1/3*o**4 + 2/3*o**3 + 0 = 0?
-3, 0, 1
Let d(x) = -x - 3. Let i be d(-5). Suppose -16*z + i*z = -28. Suppose 6/5*y - 3/5*y**z - 3/5 = 0. What is y?
1
Let j(q) = 2*q - 7. Let y be j(5). Factor -1 - 39*r**2 - 7*r - 5*r + 3*r**y + 25 + 12*r**4 + 3*r**5 + 9*r**2.
3*(r - 1)**2*(r + 2)**3
Let s = 16 - 4. What is x in -8 - 9*x**2 - 4*x + 7*x**2 + s*x = 0?
2
Let p(s) = -s**2 - 5*s - 1. Let y be p(-3). Factor -6*a**2 + y + 13*a**2 + 4*a - 8*a**2.
-(a - 5)*(a + 1)
Let a(t) be the third derivative of 2*t**2 + 0 + 1/48*t**5 + 0*t + 1/6*t**3 + 1/6*t**4 - 5/96*t**6. Factor a(d).
-(d - 1)*(5*d + 2)**2/4
Let y be (3/(-367))/((-3)/(-2)). Let o = 2212/1835 + y. Factor -12/5 - o*c**2 + 22/5*c.
-2*(c - 3)*(3*c - 2)/5
Let t(f) be the third derivative of -f**6/24 + 7*f**5/12 - 5*f**2 + 3*f. Factor t(z).
-5*z**2*(z - 7)
Determine u, given that -14/9*u**4 + 4/9*u**2 - 1/3*u**3 + 0 + 1/9*u - 8/9*u**5 = 0.
-1, -1/4, 0, 1/2
Let u be (-6)/63*((-210)/12)/5. Determine p so that 1/3*p**3 - 2/3*p**2 + u*p**4 + 0*p + 0 = 0.
-2, 0, 1
Let k be 9400/1040 + (-6)/156. Find c such that 13/2*c + 1 + k*c**2 = 0.
-1/2, -2/9
Let l(z) = -z**3 + z**2 - 13 + 3 + 11. Let v(c) = 3*c**3 - c**3 + 3 - 4. Let x(h) = l(h) + v(h). Suppose x(k) = 0. Calculate k.
-1, 0
Let i(h) be the second derivative of 19*h + 0 - 5/2*h**3 + 3/2*h**6 - 31/12*h**4 - h**2 + 3/20*h**5. Factor i(p).
(p - 1)*(3*p + 1)**2*(5*p + 2)
Let -64*p**3 + 85*p**2 + 11*p**3 + 204*p - 79*p**2 + 2*p**3 - 24 = 0. What is p?
-2, 2/17, 2
Factor 2/13*k**2 + 72/13 - 24/13*k.
2*(k - 6)**2/13
Suppose 0 = 3*u - 4*k - 16 - 7, 4*u - 28 = 4*k. Suppose 2*x = 5*h + 26, h + 1 = -u*x - 3*h. What is c in 51*c**2 - 141*c**x - 36*c + 3 + 93*c**2 - 51*c**3 = 0?
1/4
Suppose -4*a = 2*x - 10 - 10, a = 2*x. Let n(j) be the second derivative of -1/18*j**a + 4*j + 0 - 2/3*j**3 - 3*j**2. Factor n(h).
-2*(h + 3)**2/3
Let k(q) be the first derivative of -q**7/63 + 2*q**6/45 - q**4/9 + q**3/9 + 15*q + 7. Let j(p) be the first derivative of k(p). Determine v so that j(v) = 0.
-1, 0, 1
Let n = 3375874/78145 + -2/15629. Determine p so that 1/5*p**3 + 108/5*p - 18/5*p**2 - n = 0.
6
Let v be -4 + (-70)/(-17) + 3890/170 + -5. Factor v + 1/2*w**2 - 6*w.
(w - 6)**2/2
Let z(x) be the third derivative of 0 + 0*x + 1/120*x**5 + 2/3*x**3 - 3/16*x**4 - 8*x**2. Solve z(q) = 0.
1, 8
Let c(j) be the first derivative of 5/12*j**3 + 1/2*j**2 + 4*j + 1/8*j**4 - 3. Let z(w) be the first derivative of c(w). Factor z(y).
(y + 1)*(3*y + 2)/2
Let z(y) be the first derivative of -y**6/10 + 9*y**5/20 - 21*y + 22. Let s(m) be the first derivative of z(m). Suppose s(q) = 0. Calculate q.
0, 3
Suppose 3 + 91 = k - 5*y, 3*k - 2*y = 321. Suppose 2*h - 113 = -k. Factor -8/7*b**h - 10/7*b**4 + 0 + 0*b - 2/7*b**5 - 16/7*b**3.
-2*b**2*(b + 1)*(b + 2)**2/7
Let a(p) be the first derivative of -p**3/3 + 247*p**2 - 61009*p - 961. Factor a(f).
-(f - 247)**2
Suppose 0 + 51/5*g**4 - 12/5*g + 24*g**2 - 159/5*g**3 = 0. What is g?
0, 2/17, 1, 2
Find c, given that -4353*c**3 + 2103*c**3 - 60*c**4 - 4*c**5 + 1998*c**3 - 196*c**2 = 0.
-7, -1, 0
Let x(u) be the first derivative of -u**7/210 - u**6/30 - u**5/12 - u**4/12 + 11*u**2/2 + 43. Let k(v) be the second derivative of x(v). Factor k(h).
-h*(h + 1)**2*(h + 2)
Let o(w) be the second derivative of w**5/50 + 119*w**4/30 + 47*w**3/3 + 117*w**2/5 - 858*w. Solve o(z) = 0 for z.
-117, -1
Let t = 1871/3790 - -12/1895. Solve t*s + 3/2*s**2 - 1 - 1/2*s**4 - 1/2*s**3 = 0 for s.
-2, -1, 1
Let c be 108/(-16) + (-9)/(-12). Let z be 12/(-48)*8/c. Factor z - 1/3*i**2 + 0*i.
-(i - 1)*(i + 1)/3
Factor -176*l + 635*l**2 - 316*l**2 - 317*l**2 + 174.
2*(l - 87)*(l - 1)
Let n = -94 + 94. Let j(c) be the third derivative of 1/30*c**6 + n*c**4 + 0*c**5 + 0*c - 2*c**2 - 2/105*c**7 + 0*c**3 + 0. What is s in j(s) = 0?
0, 1
Determine z, given that -40474*z**2 - 118006*z**2 - 440*z**4 - 429555*z - 439040 - 13460*z**3 - 5*z**5 - 56525*z = 0.
-28, -2
Suppose -18732*f = -18723*f. Factor 2/9*y + 4/9*y**2 + f.
2*y*(2*y + 1)/9
Let f(d) = -d - 7. Let l be f(-9). Factor -5 + n**l + 2*n**2 - 6 + 2 - 6*n.
3*(n - 3)*(n + 1)
Let d = 4543769/6888 - -49/984. Let c = d + -654. Let 20/7*n**3 + 20/7*n**5 - 8/7 - 50/7*n**2 + 58/7*n**4 - c*n = 0. What is n?
-2, -1, -1/2, -2/5, 1
Suppose 3*j + 0*a = -5*a - 1, -4*a = -2*j + 14. Let n be (-4)/18*j + 1. Factor n*m + 1/2*m**2 + 0.
m*(3*m + 2)/6
Let a(r) = 7*r**2 - 46*r + 52. Let m(z) = -z**2 - z + 8. Let t(k) = 5*a(k) + 30*m(k). Factor t(c).
5*(c - 50)*(c - 2)
Let n = 17 - 9. Let w be (-6)/4*n/(-6). Suppose -19*g**2 + 44*g**2 - 23*g**w = 0. Calculate g.
0
Find x such that 8213*x - x**2 - 92 + 3*x**2 - 8123*x = 0.
-46, 1
Let v