ulate m.
-2/195, 1
Let y(q) = -q**2 + 10*q + 4. Let w be y(0). Solve 1/5*f**3 - 1/5*f - 1/5*f**2 + 0 + 1/5*f**w = 0.
-1, 0, 1
Let x(q) = -q**3 + 8*q**2 + 2*q - 12. Let l be x(8). Determine s, given that -6*s**2 + 0*s - s**l - 3*s**5 + s + 2*s + 7*s**4 = 0.
-1, 0, 1
Let b(g) be the first derivative of g**6/39 - 4*g**5/65 - 90. Factor b(i).
2*i**4*(i - 2)/13
Let u be (2/5)/(-4 + (-205)/(-50)). Suppose 0 = -k - u + 7. Determine q so that 9/2*q**k - 3/2*q**2 - 3/2*q**5 + 3/2*q**4 - 3*q + 0 = 0.
-1, 0, 1, 2
Let r(y) be the first derivative of y**6/6 - 2*y**5/5 - 54. What is o in r(o) = 0?
0, 2
Let j(i) be the second derivative of 0 - 2/5*i**6 + 33*i + 15/4*i**4 + 6*i**2 - 10*i**3 + 3/4*i**5. What is s in j(s) = 0?
-2, 1/4, 1, 2
Let f(s) be the first derivative of s**4/24 + 10*s - 6. Let i(j) be the first derivative of f(j). Find a such that i(a) = 0.
0
Solve 4/3*k**3 + 1/3*k**4 + 20/3*k - 7/3 - 6*k**2 = 0 for k.
-7, 1
Let g(u) = -u**3 + 3*u**2 + 2*u - 2. Suppose -5 = 2*l - 11. Let k be g(l). Factor 6*r**2 + 6*r - 3*r - 3 - 3*r**3 + 1 - k.
-3*(r - 2)*(r - 1)*(r + 1)
Suppose -j = -13 + 8, 0 = f - 4*j + 20. Solve 5/3*m**3 + 0*m - 2/3*m**2 + f + 7/3*m**4 = 0.
-1, 0, 2/7
Let w(j) be the second derivative of 5*j - 1/72*j**4 + 1/9*j**3 - 1/2*j**2 + 1/360*j**6 - 1/90*j**5 + 0. Let l(p) be the first derivative of w(p). Factor l(f).
(f - 2)*(f - 1)*(f + 1)/3
Suppose 12*f + 51*f + 9 - 8*f**3 + 7 + 33*f**2 - 9*f + 3*f**3 = 0. What is f?
-1, -2/5, 8
Let i(a) be the second derivative of -a**7/98 + 3*a**6/70 - 3*a**5/140 - 3*a**4/28 + a**3/7 + 2*a - 20. Find f, given that i(f) = 0.
-1, 0, 1, 2
Let j be 0 - 0/(0 - 3). Let k be j/1 - (-6 + 3). Factor 6*n**3 + 9*n**3 + 7*n**2 - n**2 - k*n**5 - 6*n**3.
-3*n**2*(n - 2)*(n + 1)**2
Determine f so that 0*f**3 - 12 - 28*f**2 - 8*f - 2*f**3 + 40 + 10*f = 0.
-14, -1, 1
Let k(g) be the first derivative of 20*g + 5/4*g**4 + 45/2*g**2 + 16 + 10*g**3. Factor k(j).
5*(j + 1)**2*(j + 4)
Suppose 21 = 3*b + 7*h - 11*h, 2*b + 4*h + 6 = 0. Determine i, given that 3*i + 3/5*i**b - 12/5*i**2 - 6/5 = 0.
1, 2
Suppose n + 21 = -y + 8, 5*n = -5. Let d be 5 - ((-5)/3)/(10/y). Suppose -8/11*p**2 + 2/11*p**d - 2/11*p + 0 + 8/11*p**4 = 0. What is p?
-1, -1/4, 0, 1
Let d = 1478 + -1474. Let w(x) be the second derivative of -7*x + 2*x**3 + 0 + 2/15*x**6 - 3/5*x**5 + 1/3*x**4 - d*x**2. Factor w(y).
4*(y - 2)*(y - 1)**2*(y + 1)
Let p = -110 + 100. Let f(h) = 4*h**2 + 12*h - 10. Let z(w) = 1. Let r(u) = p*z(u) - f(u). Factor r(d).
-4*d*(d + 3)
Let f(o) be the third derivative of o**5/90 + o**4/36 - 2*o**3/9 + 71*o**2. Factor f(i).
2*(i - 1)*(i + 2)/3
Let d = 10 - 10. Suppose 2*i + 3*c - 9 = 0, 3*i - 5*c + 0 + 15 = d. Let -r**2 + 6 + 4*r - 9 + i = 0. What is r?
1, 3
Suppose -7*j = -8*j + 58. Factor 24*y + 8*y + 5*y**4 + j*y - 16*y**2 + 121*y**2 + 40*y**3.
5*y*(y + 2)*(y + 3)**2
Let s(h) be the second derivative of 1/2*h**2 - 1/12*h**4 + 0 - 2*h + 0*h**3. Determine w, given that s(w) = 0.
-1, 1
Suppose -88*a + 71*a = 0. Let k(z) be the second derivative of -7/120*z**6 - 9/80*z**5 - 1/84*z**7 + 0*z**2 - 1/24*z**3 + a - 5/48*z**4 + 6*z. Factor k(s).
-s*(s + 1)**3*(2*s + 1)/4
Factor 3654*h + 3654*h + 3*h**2 - 18 - 7311*h.
3*(h - 3)*(h + 2)
Find c such that 22*c**3 - 94*c**3 - 28*c**4 + 12 - 8139*c - 48*c**2 + 8147*c = 0.
-1, 3/7
Let l be -2 + (1 - -2) + -9 + 106/13. Solve l*i**2 + 6/13*i + 0 = 0 for i.
-3, 0
Let l(x) = 17*x**2 - 28*x + 9. Let t(k) = -2*k**2 + 1. Let z(i) = l(i) + 3*t(i). Find a such that z(a) = 0.
6/11, 2
Let r(j) = -3*j**5 + 36*j**4 + 42*j**3 - 36*j**2 - 21*j + 18. Let k(l) = 2*l**4 + l**3 - l**2. Let a(q) = 18*k(q) - r(q). Solve a(u) = 0 for u.
-3, -1, 1, 2
Let q = -110 + 110. Let b(n) be the second derivative of 2*n - 1/3*n**2 + 0 + q*n**3 + 1/18*n**4. Factor b(k).
2*(k - 1)*(k + 1)/3
What is w in -10/9*w**2 - 2/3 + 2/9*w**3 + 14/9*w = 0?
1, 3
Determine u, given that 36*u + 5*u**2 - 23*u - 203*u + 61 - 61 = 0.
0, 38
Let g(k) = -k**4 - 45*k**3 + 176*k**2 + 117*k - 103. Let w(p) = p**4 + 2*p**3 + p**2 + p + 1. Let t(i) = g(i) + 3*w(i). Factor t(v).
(v - 10)**2*(v + 1)*(2*v - 1)
Let b(t) be the first derivative of 11 - 5/2*t**6 - 15/2*t**2 + 20/3*t**3 - 2*t**5 + 15/2*t**4 - 10*t. Determine n so that b(n) = 0.
-1, -2/3, 1
Suppose y = -2*y - 6. Let w = 2 - y. Factor -2*n**3 + 2*n - 5*n + n**5 + w*n.
n*(n - 1)**2*(n + 1)**2
Let m = -111 - -114. Let c(r) = -4*r + 12. Let s be c(m). Factor 0*x**2 + s*x - 1/3*x**3 + 0 - 2/3*x**4 - 1/3*x**5.
-x**3*(x + 1)**2/3
Let h(m) = m**2 + 4*m - 10. Let t be h(-6). Let x(j) be the first derivative of 5 + j**t + 3*j**4 + 0*j - 11/3*j**3. Find d, given that x(d) = 0.
0, 1/4, 2/3
Let j = -5 + -14. Let v = j + 21. Factor 8/11*r**2 + v*r - 6/11.
2*(r + 3)*(4*r - 1)/11
Let g(v) be the second derivative of -v**6/15 - v**5/5 - v**4/6 + 3*v + 62. Factor g(b).
-2*b**2*(b + 1)**2
Suppose 245 = 2*h + 2*j + 129, -5*h + 5*j = -220. What is r in 45/2*r**3 + 0*r + 63/2*r**5 + h*r**4 + 0 + 3*r**2 = 0?
-1, -1/3, -2/7, 0
Let i(c) be the second derivative of -c**6/150 - 4*c**5/25 + c**4/60 + 8*c**3/15 + 69*c + 1. Factor i(x).
-x*(x - 1)*(x + 1)*(x + 16)/5
Determine a, given that -1225/4 + 35/2*a - 1/4*a**2 = 0.
35
Suppose 0*v - 20 = -2*r - 4*v, 0 = -3*v + 9. Suppose 1 = -q + r. Factor 4*l - l**4 + 2*l**2 + 12 - 12 - 4*l**q - l**4.
-2*l*(l - 1)*(l + 1)*(l + 2)
Let r be 7/(-1) + ((-4)/10)/(224/(-5320)). Determine h, given that -r*h**2 - 5/2*h + 0 = 0.
-1, 0
Let x(a) be the first derivative of -a**4 - 232*a**3 - 20184*a**2 - 780448*a + 185. Factor x(r).
-4*(r + 58)**3
Factor 49836*m**2 + 227925*m**2 - 31358*m**2 + 18598*m**2 + 118644*m**2 + 5540*m + 20.
5*(277*m + 2)**2
Let h be 1/15*((-2 - (-2 - -3)) + 9). Factor -6/5*f**2 + 6/5*f + 2/5*f**3 - h.
2*(f - 1)**3/5
Suppose -2*x**2 + 1/10*x**3 + 0 + 15/2*x = 0. What is x?
0, 5, 15
Let g be 7/3 + (-6)/(-9). Suppose -3 = 17*h - 18*h. Solve h*t**3 + g*t**4 - 5*t**3 - 4*t**3 + 3*t**2 = 0 for t.
0, 1
Let o(c) be the third derivative of -c**6/80 - c**5/40 + 3*c**4/8 - 35*c**2 - 2*c. Determine y so that o(y) = 0.
-3, 0, 2
Let o(c) be the first derivative of -3/10*c**5 + 2*c**3 - 3/8*c**4 + 3*c**2 + 4 + 0*c. Factor o(q).
-3*q*(q - 2)*(q + 1)*(q + 2)/2
Find r such that 2 - 12/7*r - 2/7*r**2 = 0.
-7, 1
Let h = 71 - 51. Let -4 - 15*a + 0 - h*a**2 + 9 = 0. What is a?
-1, 1/4
Let b(x) be the first derivative of -x**4/24 - 7*x**3/18 - 5*x**2/4 - 3*x/2 - 3. Find a such that b(a) = 0.
-3, -1
Let x = -4106 + 4108. Let 20/3*f + 2/3*f**x + 50/3 = 0. What is f?
-5
Determine j, given that 1/5*j**3 - 9*j**2 + 483/5*j + 529/5 = 0.
-1, 23
Suppose 5*g - 2*a - 3*a = 40, 4*g - 12 = -a. Let -114*u**2 - 11*u**3 - 14*u**g + 4 - 7*u**3 + 124*u**2 + 18*u = 0. Calculate u.
-1, -2/7, 1
Let c be -2 + 44/(-4)*2. Let x = c + 33. What is m in 16 - 44*m**2 + 37*m**4 - 8*m**5 - x*m**4 - 4*m**5 + 12*m**3 = 0?
-1, -2/3, 1, 2
Let v(o) be the first derivative of -o**6/9 + 6*o**5/5 - 13*o**4/6 - 2*o**3 + 14*o**2/3 - 118. Let v(l) = 0. What is l?
-1, 0, 1, 2, 7
Let x be 3/((4 + -1)/6). Factor j - 3*j**2 + x*j - j.
-3*j*(j - 2)
Let o(h) be the first derivative of -8*h + 3/100*h**5 + 3/10*h**3 - 1/5*h**4 + 1 + 0*h**2. Let v(i) be the first derivative of o(i). Factor v(u).
3*u*(u - 3)*(u - 1)/5
Let w(i) be the second derivative of -i**7/14 + 7*i**6/10 - 9*i**5/20 - 23*i**4/4 + 16*i**3 - 18*i**2 + i - 54. Find b such that w(b) = 0.
-2, 1, 6
Let v(o) = -o - 7. Let f be v(-11). Determine q, given that 7*q**f - 3*q**4 - 5*q**3 + q**3 = 0.
0, 1
Let w(t) be the second derivative of -t**7/168 - t**6/30 + t**5/10 + 7*t**4/24 - 7*t**3/24 - 5*t**2/4 + 119*t. Solve w(z) = 0.
-5, -1, 1, 2
Let f(r) = 2*r**3 + 4*r**2 - 6*r. Let u be (18*-1)/((-6)/8). Let v be (-16)/(-2)*(-18)/u. Let y(z) = z**2 - z. Let o(p) = v*y(p) + f(p). Factor o(a).
2*a**2*(a - 1)
Let 1/2*p**5 - 2*p**3 + 3/2*p + 5/3*p**4 + 2/3 - 7/3*p**2 = 0. Calculate p.
-4, -1, -1/3, 1
Let p(z) be the third derivative of z**9/13608 - z**8/7560 + z**3/2 + 8*z**2. Let r(u) be the first derivative of p(u). Suppose r(g) = 0. Calculate g.
0, 1
Let i = 26 + -16. Suppose 4*f - i = -r + 3*f, -2*r - 5*f + 5 = 0. Factor 2*x**3 + 26*x - r*x - 13*x.
2*x*(x - 1)*(x + 1)
Let l be ((-4)/11)/(242/(-1331)). Factor -1/2*q**l + 7/2 - 3*q.
-(q - 1)*(q + 7)/2
Let z(l) = l**4 + 5*l**3 + l**2 - 1. Let n(