Let y(v) = -3*v**4 + 3*v**3 - 106*v**2 - 48*v + 7. Let p(u) = u**4 + 53*u**2 + 24*u - 3. Let x(b) = -21*p(b) - 9*y(b). Factor x(q).
3*q*(q - 8)*(q + 3)*(2*q + 1)
What is j in -1904*j**2 + 54*j**2 - 528*j - 15*j**4 + 3068*j + 445*j**3 - 1000 = 0?
2/3, 2, 25
Let d = 869481 - 3477923/4. Factor -13/4*t**2 + 1/2*t**3 + 0 + 5/2*t + d*t**4.
t*(t - 2)*(t - 1)*(t + 5)/4
Let o(i) be the second derivative of -i**6/120 - i**5/2 - 28*i**4/3 - 64*i**3 + 1571*i. Let o(z) = 0. Calculate z.
-24, -8, 0
Find s, given that -120 + 5*s**3 + 1/5*s**4 + 194/5*s**2 + 76*s = 0.
-10, -6, 1
Let s = -3/1531361881 - -200397078477431/3067317847643. Let y = s + 2/6009. Let 796/3*r**2 - y*r**4 + 280/3*r**3 + 368/3*r + 16 = 0. What is r?
-1, -2/7, 3
Let n be 1698/(-600) - -3 - ((-196)/(-50) - 4). Let g(x) be the first derivative of -n*x**4 - 8/3*x + 13 + x**2 + 11/9*x**3. Factor g(y).
-(y - 4)*(y + 1)*(3*y - 2)/3
Let b(x) be the third derivative of x**7/840 - x**6/90 - x**5/120 + x**4/6 + 136*x**3/3 - 130*x**2. Let u(q) be the first derivative of b(q). Factor u(k).
(k - 4)*(k - 1)*(k + 1)
Factor -66*a + 1557/8 + 3/8*a**2.
3*(a - 173)*(a - 3)/8
Let f(r) be the first derivative of 1200*r**5 - 2175*r**4 + 1035*r**3 - 1701*r**2/8 + 81*r/4 + 1379. Factor f(k).
3*(k - 1)*(20*k - 3)**3/4
Let f(b) be the third derivative of 47 + b**2 + 1/15*b**5 + 0*b + 50/3*b**3 - 5/3*b**4. Find p such that f(p) = 0.
5
Let r(k) = 25*k**3 + 580*k**2 + 120*k + 115. Let x be r(-23). Factor 0 + 0*o**2 + 1/5*o**5 + 0*o + x*o**3 + 1/5*o**4.
o**4*(o + 1)/5
Suppose 228*q - 14 = 242*q. Let f(h) = 3*h**2 - h - 1. Let w(z) = -100*z**2 + 65*z. Let k(t) = q*w(t) - 30*f(t). Determine p, given that k(p) = 0.
3/2, 2
Let a(m) be the second derivative of -m**6/90 + 29*m**5/30 - 224*m**4/9 + 784*m**3/9 + 287*m - 2. Suppose a(l) = 0. What is l?
0, 2, 28
Let f(o) be the second derivative of o**4/78 - 2*o**3/39 - 15*o**2 + 96*o - 10. Find i, given that f(i) = 0.
-13, 15
Suppose -a + 2*t - 7543 = -7555, a - 4*t = 24. Factor a - 10/7*z**2 + 4/7*z + 8/7*z**3 - 2/7*z**4.
-2*z*(z - 2)*(z - 1)**2/7
Let r(a) be the first derivative of 4*a**3/9 + 374*a**2/3 + 1480*a/3 + 1055. Factor r(z).
4*(z + 2)*(z + 185)/3
Suppose -6 = -3*f + 9. Suppose -3*p + 4*q - 11 = 0, f*q - 22 = -0*p + p. Factor -p*v**3 - 5*v**3 - 24*v + 16 + 6*v**3 + 12*v**2.
-2*(v - 2)**3
Let q(s) be the first derivative of s**6/2 - 12*s**5/5 - 249*s**4/4 - 150*s**3 - 108*s**2 - 8432. Let q(w) = 0. Calculate w.
-6, -1, 0, 12
Let j(l) be the second derivative of 30*l - 113/30*l**6 - 53/12*l**4 + 2/3*l**7 + 71/10*l**5 + 2*l**2 - 4/3*l**3 - 2. Suppose j(g) = 0. Calculate g.
-1/4, 2/7, 1, 2
Let d(r) be the first derivative of 1/6*r**6 + 25/4*r**4 + 38/3*r**3 + 14*r**2 - 62 + 8/5*r**5 + 8*r. Solve d(a) = 0.
-2, -1
Let t(b) be the second derivative of b**4/60 - 17*b**3/30 - 6*b. Find u, given that t(u) = 0.
0, 17
Suppose -46840 = -20*a - 20*a. Let b = -1171 + a. Factor b + 0*n + 1/6*n**3 - 1/6*n**2.
n**2*(n - 1)/6
Factor 136*t**2 - 160 - 4*t**5 - 13*t**3 + 96*t**3 - 7*t**3 - 48*t.
-4*(t - 5)*(t - 1)*(t + 2)**3
Let i = 60075 - 60070. What is a in 2/9*a**4 - 2/9*a**2 - 2/9*a**i + 0 + 0*a + 2/9*a**3 = 0?
-1, 0, 1
Factor -188 - 2/7*q**2 + 662/7*q.
-2*(q - 329)*(q - 2)/7
Let s(x) be the third derivative of x**7/560 - 3*x**5/80 + x**4/8 + 11*x**3/3 - 73*x**2. Let t(u) be the first derivative of s(u). Factor t(b).
3*(b - 1)**2*(b + 2)/2
Let c = 68 + -24. What is s in -40*s - c*s**2 - 7 - 5 - 36*s**2 + 68*s**2 = 0?
-3, -1/3
Let z(h) be the first derivative of 0*h**2 + 1/8*h**4 - 3/20*h**5 + 1/2*h**3 + 16 - 52*h - 1/20*h**6. Let d(x) be the first derivative of z(x). Factor d(y).
-3*y*(y - 1)*(y + 1)*(y + 2)/2
Suppose k**5 - 4 + 936*k - 104 + 2130*k**3 + 318*k**4 + 40*k**5 - 1035*k**4 - 2505*k**2 + 43*k**5 = 0. Calculate k.
1/4, 2/7, 2, 3
Let 19*r**4 + 42*r**2 + 8*r**5 - r**5 - 120*r**3 - 1296 - 182*r**2 + 432*r - 8*r**5 + 356*r**2 = 0. What is r?
-2, 3, 6
Let u(y) be the first derivative of y**4/16 + 13*y**3/12 + 5*y**2 - 5453. Let u(n) = 0. Calculate n.
-8, -5, 0
Let y be 3 - 0/4 - -20. Let n(h) = 2*h - 44. Let m be n(y). Find j, given that 24 - 65*j + 78*j**m + 47*j + 27*j**3 - 21*j**4 - 90*j = 0.
-2, 2/7, 1, 2
Factor -3/7*v**3 + 45/7*v**2 + 162/7*v + 0.
-3*v*(v - 18)*(v + 3)/7
Let 141/2*i - 9/2 - 475/2*i**2 - 625/2*i**3 = 0. Calculate i.
-1, 3/25
Let h be ((-3)/(-45) - 0)/(-11 + 935/30 - 20). Solve 0*i - 1/10*i**5 + 11/10*i**3 + 0 - 3/5*i**2 - h*i**4 = 0 for i.
-6, 0, 1
Suppose -5*k = -5*g - 15, 7 = -4*g + 3*k - 9. Let x be (-4)/(-22) - g/154*-4. Solve 2/5*s - 2*s**2 + 2*s**4 + 6/5*s**3 + x - 8/5*s**5 = 0 for s.
-1, 0, 1/4, 1
Let b(t) be the second derivative of -t**4/30 - 196*t**3/5 - 86436*t**2/5 + 3697*t. Suppose b(v) = 0. What is v?
-294
Suppose i + 0*i = -i. Suppose 1565 = 482*f + 119. Find s, given that -3/5*s**4 + s**f - 12/5*s + 16/5*s**2 + i = 0.
-2, 0, 2/3, 3
Factor 1097*a**4 + 1090*a**4 - 4372*a**4 + 283*a + 97*a**3 - 285*a**2 - 94 + 1095*a**4 + 1089*a**4.
-(a - 94)*(a - 1)**3
Factor 3*u**3 + 7 - 5*u**4 + 34*u - 17 + 15*u**2 - 39*u - u**3 + 3*u**3.
-5*(u - 2)*(u - 1)*(u + 1)**2
Let p(a) be the third derivative of 5*a**8/2688 + 8*a**7/105 - 187*a**6/960 + 9*a**5/80 + a**2 - 22*a. Suppose p(s) = 0. Calculate s.
-27, 0, 2/5, 1
Let u(s) be the third derivative of s**7/2520 + 7*s**6/720 + s**5/20 - 65*s**4/24 - 67*s**2. Let r(d) be the second derivative of u(d). Factor r(t).
(t + 1)*(t + 6)
Let i(u) = -22*u**2 + 76*u - 27. Let x(j) = 1. Let s(z) = -2*i(z) + 6*x(z). Suppose s(v) = 0. What is v?
5/11, 3
Let u be 348/60 + 1/(10/(-8)). Let h be (2 + -1)*(8 - u). Suppose 4*s**4 + 52*s + h*s**4 + 47*s**3 - 8 - 39*s**2 - 16*s**4 - 43*s**2 = 0. What is s?
2/9, 1, 2
Let k(m) be the first derivative of m**5/30 - m**4/9 - 7*m**3/9 - 4*m**2/3 - 48*m + 84. Let b(n) be the first derivative of k(n). Factor b(a).
2*(a - 4)*(a + 1)**2/3
Let c be -6*(143/22)/(-13). Let y(q) be the third derivative of 0*q + 1/78*q**5 - 12*q**2 + 0 - 1/780*q**6 - 7/156*q**4 + 1/13*q**c. Factor y(o).
-2*(o - 3)*(o - 1)**2/13
Suppose 8*z = 26 - 2. Let 4*i**2 - 10*i**3 + z*i**4 + 10*i**5 - 4*i**4 - 3*i**4 = 0. Calculate i.
-1, 0, 2/5, 1
Suppose 0 = -0*m - m - 1. Let t be (1 - 3) + (3 - m). Find w such that -3*w**2 - t*w**3 - 3*w**3 + 5*w - w**3 - 2*w = 0.
-1, 0, 1/2
Let g(j) be the third derivative of j**2 + 0*j**4 - 13/42*j**7 + 1/3*j**5 - 4 + 0*j**3 + 0*j - 25/336*j**8 - 1/6*j**6. Suppose g(a) = 0. What is a?
-2, -1, 0, 2/5
Suppose -28*u + 32 = -12*u. Find t such that -22*t + 2304 - 71*t + 11*t**u - 29*t + 26*t - 10*t**2 = 0.
48
Let p = 437 + -435. Suppose 3*a = -3*j + 3, a = 5*j - 0*j + 13. Factor -9*s**4 - 9*s**3 - a*s**p - 7*s + 0*s + 7*s - 3*s**5.
-3*s**2*(s + 1)**3
Let p(f) be the first derivative of -110889*f**4/2 - 74814*f**3 - 1336*f**2 - 8*f + 2179. Factor p(m).
-2*(m + 1)*(333*m + 2)**2
Factor -166*q + 271 + 3*q**2 - 33 + 76 + 526 + 64*q.
3*(q - 20)*(q - 14)
Factor 3 + 1011*w**3 - 95*w**2 - 919*w**3 - 3 + 7*w**2 - 4*w**4.
-4*w**2*(w - 22)*(w - 1)
Let h(g) = 11*g - 2. Let c be h(2). Let q be (16/c)/((-4)/(-10)). What is i in -2 + 26*i**q + 2 + 20*i - 30*i**2 - 16 = 0?
1, 4
Let b = 3218 + -3218. Let i(r) be the third derivative of 1/330*r**6 + 1/330*r**5 + 22*r**2 + b*r**3 + 0 + 1/1155*r**7 + 0*r + 0*r**4. Solve i(g) = 0.
-1, 0
Let q be -2 - ((-87)/27 + 1). Let y = 3/31924 + 510775/95772. Factor -q*n**3 + 2*n**2 - y*n + 32/9.
-2*(n - 4)**2*(n - 1)/9
Let k be (5/((-1725)/184))/((-4)/3). Factor 0 - 1/5*c**2 + k*c.
-c*(c - 2)/5
Let t(p) be the second derivative of -3*p**5/20 + 17*p**4 - 67*p**3/2 - 124*p - 9. Factor t(j).
-3*j*(j - 67)*(j - 1)
Let i(d) = -13*d**4 - 334*d**3 - 29238*d**2 - 57448*d - 28543. Let p(o) = 2*o**4 - o**3 - 2*o - 3. Let z(v) = -i(v) - 6*p(v). Factor z(b).
(b + 1)**2*(b + 169)**2
Suppose -1/7*t**3 - 4/7*t**2 + 36/7 + 9/7*t = 0. What is t?
-4, -3, 3
Suppose 8*t**2 + 616 + 60*t + 0*t - 4081 - 3*t**2 = 0. Calculate t.
-33, 21
Suppose 0 = -15*r - 11078 - 8482. Let m = r + 6526/5. Factor -1/5*v - 1/5*v**2 + m.
-(v - 2)*(v + 3)/5
Let p(l) = 3*l**3 + 3*l**2 + l - 3. Let j be (10/15)/(6/9). Let i be p(j). Factor 0*c**3 + c**2 - 5*c + 9*c - i - c**3 + 0*c**2.
-(c - 2)*(c - 1)*(c + 2)
Let i(t) be the third derivative of -t**7/210 + t**6/90 + t**5/15 + 23*t**3/6 - 6*t**2 + 2*t. Let k(n) b