 1)/5
Let i(z) = -49*z**2 - 2450*z + 2. Let b be i(-50). Factor -3/7*j**4 + 4/7*j + 0 - 11/7*j**3 - 8/7*j**b.
-j*(j + 2)**2*(3*j - 1)/7
Suppose -7*g + 17 + 25 = 0. Factor -3*p**2 - 3*p + p + g*p**3 - p.
3*p*(p - 1)*(2*p + 1)
Let o be (-540)/240 - 1*(-1)/4. Let w be (25 - 24)*(-6)/o. What is l in 1/2*l**2 - 1/4*l - 1/4*l**w + 0 = 0?
0, 1
Factor -2/3 + 3*k - 4/3*k**2.
-(k - 2)*(4*k - 1)/3
Suppose -2*c = -9*c - 42. Let w be (-5 - -5)*(-3)/(3 + c). Find u, given that w*u + 1/3*u**3 + 0*u**2 + 0 - 1/3*u**5 + 0*u**4 = 0.
-1, 0, 1
Let w be -13 - 18/(5292/(-3850)). Find k, given that 2/21*k**2 - 2/21*k - w*k**4 + 0 + 2/21*k**3 = 0.
-1, 0, 1
Let u be (10/(-90))/((-8)/12). Let l(c) be the first derivative of 0*c + u*c**6 - 2/5*c**5 + 0*c**3 + 6 + 1/4*c**4 + 0*c**2. Factor l(n).
n**3*(n - 1)**2
Suppose -s - 157 = 5*j - 172, -5*s - j = -3. Factor s - 2/11*l - 4/11*l**2 + 2/11*l**5 + 4/11*l**4 + 0*l**3.
2*l*(l - 1)*(l + 1)**3/11
Suppose -2*n + 24*a - 25*a = -9, -5*n + 18 = a. Determine r, given that 9/4 + 3/4*r**n - 3/4*r - 9/4*r**2 = 0.
-1, 1, 3
Let z(t) be the third derivative of -3/56*t**4 + 1/140*t**5 + 14*t**2 + 0 + 1/7*t**3 + 0*t. Factor z(v).
3*(v - 2)*(v - 1)/7
Find r, given that -26/3*r**2 + 44/3*r**3 - 10/3*r**4 + 8 - 56/3*r = 0.
-1, 2/5, 2, 3
Let f(o) = 6*o**4 - 45*o**3 + 222*o**2 - 498*o + 432. Let l(d) = -5*d**4 + 44*d**3 - 221*d**2 + 500*d - 432. Let i(y) = 2*f(y) + 3*l(y). Factor i(q).
-3*(q - 4)**2*(q - 3)**2
Suppose 4*u - 3*l + 11 = 3*u, -3*u = 2*l. Let n be (-15)/(-8) + u - 3/(-24). Suppose n*d - 2/5*d**2 + 2/5 = 0. Calculate d.
-1, 1
Let a(l) be the second derivative of l**4/42 - 116*l**3/21 + 3364*l**2/7 - l - 109. Factor a(m).
2*(m - 58)**2/7
Suppose c = 3 - 0. Find r, given that -25*r + 6*r**2 - 7*r**3 - 30 + 12*r**c + 4*r**2 = 0.
-3, -1, 2
Let t(a) be the first derivative of -2*a**5/15 + a**4/3 + 2*a**3/3 + 120. Factor t(u).
-2*u**2*(u - 3)*(u + 1)/3
Let d be (6 + -20 + 12)/(0 - 2/4). Let -234/7*c**2 - 150/7*c**d + 320/7*c**3 + 72/7*c - 8/7 = 0. What is c?
1/3, 2/5, 1
Let q(d) be the third derivative of d**7/210 + 31*d**6/120 - 13*d**5/12 + 11*d**4/8 + 5*d**2 - 85*d. Determine v, given that q(v) = 0.
-33, 0, 1
Let y(x) = -5*x**4 - 78*x**3 + 212*x**2 - 222*x + 69. Let o(s) = -9*s**4 - 154*s**3 + 425*s**2 - 443*s + 139. Let d(i) = -4*o(i) + 7*y(i). Solve d(p) = 0.
-73, 1
Let m(b) = -25*b - 272. Let n be m(-11). Let j(p) be the second derivative of 3*p**2 - 2*p + 0 + 2/3*p**n + 1/18*p**4. Factor j(r).
2*(r + 3)**2/3
Suppose -n - 2*n = -6, 0 = 5*s - 4*n - 2. Let v be 3 - 0/(0 + s). Factor -35*a - 8*a**3 - 25*a**2 - 92 + v*a**3 + 77.
-5*(a + 1)**2*(a + 3)
Let l = 54 + -22. Let w = l + -53/2. Find d, given that 9/2*d**3 + w*d**2 + 0 + d = 0.
-1, -2/9, 0
Suppose -4*w + 0*w + 12 = 0. Let z = -49 + 51. Suppose -2 + m**z - 6*m - 3*m**w - 8*m**2 + m**3 + m**2 = 0. Calculate m.
-1
Let w(i) be the third derivative of -i**5/15 + 5*i**4/6 - 4*i**2 - 30. Factor w(r).
-4*r*(r - 5)
Let a(q) be the third derivative of q**5/80 + 11*q**4/32 + 9*q**3/4 + 2*q**2 + 11*q. Factor a(g).
3*(g + 2)*(g + 9)/4
Let p(q) = -q**2 + 80*q - 442. Let s be p(6). Factor 2 - 4/3*i - 2/3*i**s.
-2*(i - 1)*(i + 3)/3
Let z(d) be the first derivative of 10/7*d - 6 - 1/2*d**2 + 1/21*d**3. Factor z(f).
(f - 5)*(f - 2)/7
Let a(b) be the second derivative of -b**7/210 - b**6/150 + 3*b**5/100 + b**4/12 + b**3/15 - 9*b + 3. Solve a(l) = 0.
-1, 0, 2
Let y = 10/19 - 1/38. Suppose -33 = -23*r + 9*r - 5. Determine p so that -1 - y*p**r - 3/2*p = 0.
-2, -1
Suppose 2*b + 0 + 21 = c, 3*c = -2*b + 103. Let 17*u + 44 - 117 - 71 - 4*u**2 + c*u = 0. What is u?
6
Let b(w) be the second derivative of w**5/20 - 7*w**4/4 + 150*w. Suppose b(o) = 0. What is o?
0, 21
Suppose p = -3*r - 208, -2*r - p = 167 - 27. Let m = 206/3 + r. Solve -1/3*f**2 + m - 1/3*f = 0.
-2, 1
Let f(t) be the first derivative of -t**5/6 + 25*t**4/24 + 5*t**3/2 - 13*t**2/2 + 9. Let h(n) be the second derivative of f(n). Factor h(k).
-5*(k - 3)*(2*k + 1)
Let l(z) = 18*z**3 - 78*z**2 + 110*z - 52. Let a = -32 - -31. Let k(i) = -1. Let n(y) = a*l(y) + 2*k(y). Solve n(h) = 0.
1, 5/3
Factor -3/2*r**4 + 1/2 - 1/2*r**5 - r**3 + r**2 + 3/2*r.
-(r - 1)*(r + 1)**4/2
Let v(r) = -12*r**5 - 199*r**4 - 14711*r**3 - 342989*r**2 + 11*r. Let c(j) = -j**5 + j**4 - j**3 + j**2 + j. Let o(g) = 22*c(g) - 2*v(g). Factor o(u).
2*u**2*(u + 70)**3
Let l = -571 - -575. Let 8/5*o - o**l - 4*o**2 + 33/10*o**3 + 1/10*o**5 + 0 = 0. What is o?
0, 1, 4
Let v(x) be the second derivative of -x**4/36 - 25*x**3/18 - 4*x**2 + 6*x - 2. Factor v(s).
-(s + 1)*(s + 24)/3
Factor -14*h**2 - 27*h + 8*h**2 - 25*h**2 + 3*h**3 + 4*h**2 + 3*h**4.
3*h*(h - 3)*(h + 1)*(h + 3)
Let y(o) = -2*o**2 + 22*o + 12. Suppose 5*c - 13 = 4*h, -h + 4 - 1 = 0. Let p = 76 - 88. Let u(s) = -s**2 + 9*s + 5. Let t(f) = c*y(f) + p*u(f). Factor t(r).
2*r*(r + 1)
Let z(w) be the third derivative of 1/210*w**5 + 0*w + 0 + 0*w**3 - 1/21*w**4 + 6*w**2. Factor z(d).
2*d*(d - 4)/7
Solve -2030*j**2 + 144 - 152*j + 728*j**2 + 70*j**3 + 50*j**2 = 0 for j.
-2/5, 2/7, 18
Let u(q) be the second derivative of -q**7/8820 + q**6/840 - q**5/210 + 43*q**4/12 - 20*q. Let y(i) be the third derivative of u(i). Factor y(a).
-2*(a - 2)*(a - 1)/7
Factor 46*y**3 + 6*y**4 + y**5 + 5*y**4 + 17*y**4 + 7*y**3 + 26*y**2.
y**2*(y + 1)**2*(y + 26)
Let n be ((-36)/(-24))/(1/2)*1. Suppose 2 = n*w + 5*k + 5, 3*w + 3*k = 3. Find q, given that 0*q + 0 - 1/2*q**3 - 1/4*q**w + 0*q**2 = 0.
-2, 0
Let w be (14/((-280)/15))/((-3)/8). Factor 1/4*m**3 + 1/4*m**w + 0*m + 0.
m**2*(m + 1)/4
Suppose f + u - 6 = 0, -202*f - u + 8 = -200*f. Factor 12/5*k + 3/5*k**f + 0.
3*k*(k + 4)/5
Let x = -5 - -9. Suppose 10 - 30*u**x - 20*u**4 + 50*u**3 - 21*u - 6*u + 15*u**5 + 2*u = 0. What is u?
-2/3, 1
Let r(b) be the first derivative of b**6/6 + b**5/2 - 5*b**4/4 - 20*b**3/3 - 10*b**2 + 6*b - 34. Let m(x) be the first derivative of r(x). Factor m(z).
5*(z - 2)*(z + 1)**2*(z + 2)
Let i be (3 - -26) + (-1 - 1). Let b = -25 + i. Solve -1/3*h**b + 2/3 + 1/3*h = 0.
-1, 2
Let q(g) be the second derivative of -g**6/100 + g**5/5 - 33*g**4/20 + 36*g**3/5 + 20*g**2 - 2*g + 4. Let f(p) be the first derivative of q(p). Factor f(r).
-6*(r - 4)*(r - 3)**2/5
Let f(l) = -l**4 + 4*l**3 - 1. Let z(s) = 3*s**4 - 8*s**3 - s**2 + 2. Let r(a) = 10*f(a) + 5*z(a). Factor r(o).
5*o**2*(o - 1)*(o + 1)
Let o(n) be the first derivative of 0*n**2 + 0*n - 2/9*n**3 + 7 + 1/4*n**4 + 1/3*n**5. Factor o(k).
k**2*(k + 1)*(5*k - 2)/3
Factor -13*s**2 + 36 + 7*s**2 - s + 8*s**2 - 12*s - s**2.
(s - 9)*(s - 4)
What is q in 0*q + 0 + 3/2*q**3 - 105/2*q**2 = 0?
0, 35
Let v(x) = -8*x**3 + 33*x**2 + 78*x + 43. Let w(i) = 95*i**3 - 395*i**2 - 935*i - 515. Let d(z) = -35*v(z) - 3*w(z). Let d(k) = 0. Calculate k.
-1, 8
Let k(o) = -16*o**2 - 35*o + 13. Let y(b) = 9*b**2 + 18*b - 6. Let n(z) = -6*k(z) - 11*y(z). Suppose n(v) = 0. Calculate v.
2
Let o(p) = -p**4 + 15*p**3 + 8*p**2 + 4*p - 4. Let l(b) = -b**4 - b**2 + b - 1. Let g(j) = -4*l(j) + o(j). Suppose g(c) = 0. What is c?
-4, -1, 0
Let y(l) = -l**3 - 6*l**2 - 6*l + 1. Let u be y(-5). Let f be (-3)/4 - (-5 - (2 - u)). Factor -f*j**2 - 1/2*j + 0.
-j*(j + 2)/4
Let u = -214 + 214. Let a(b) be the second derivative of 0*b**3 + 1/18*b**4 + 7*b + 0 - 1/45*b**6 + u*b**2 + 0*b**5. Suppose a(v) = 0. Calculate v.
-1, 0, 1
Suppose -74*f + 82 = -216 + 76. Determine n so that 0*n + 45/2*n**3 - f*n**2 - 189/4*n**4 + 0 + 147/8*n**5 = 0.
0, 2/7, 2
Let f be ((-6)/(-7))/((-3315)/(-210) + -16) + 4. Factor 2/3*s**4 + 0*s + f + 0*s**2 + 2/3*s**3.
2*s**3*(s + 1)/3
Let k(n) = -28*n**3 + 476*n**2 - 9557*n - 33271. Let w(d) = 15*d**3 - 237*d**2 + 4779*d + 16635. Let b(t) = 6*k(t) + 11*w(t). Determine q so that b(q) = 0.
-3, 43
Let h(i) be the third derivative of 0*i - 1/60*i**5 - 1/12*i**4 + 0*i**3 + 1/30*i**6 + 2*i**2 - 8 + 1/70*i**7. Solve h(a) = 0.
-1, 0, 2/3
Let j = 4/63 - 11/210. Let t(q) be the third derivative of 1/9*q**4 + 0*q - 8*q**2 + j*q**5 + 0 + 4/9*q**3. Let t(p) = 0. What is p?
-2
Let z(h) be the third derivative of -1/168*h**4 - 1/140*h**5 + 0*h + 0 + 1/21*h**3 + 15*h**2 + 1/1470*h**7 + 1/840*h**6. Determine j so that z(j) = 0.
-2, -1, 1
Let o = 3636/11 + -330. Let w = o - 13/44. Factor 0 + 3/4*s**3 + 1/4*s + w*s**4 + 3/4*s**2.
s*(s + 1)**3/4
Let i(n)