 k(5). Suppose 0 = l*g + 16, -b - 3*b + 12 = g. Find n such that 5/2*n**3 - 1/2*n**b + 7/2*n - 1 - 9/2*n**2 = 0.
1, 2
Suppose -j - j = -4*t - 20, 26 = 3*j - 5*t. Let r(p) be the first derivative of 0*p**3 + 0*p**2 + 1/16*p**4 + 1/20*p**5 - j + 0*p. Let r(a) = 0. Calculate a.
-1, 0
Let h = 126 + -55. Let p = -211/3 + h. Factor 4/3*t**2 - p*t - 2/3*t**3 + 0.
-2*t*(t - 1)**2/3
Let r = -26 + 31. Let o(s) be the third derivative of -1/132*s**4 + 0*s + 0*s**3 + 4*s**2 + 1/330*s**r + 0. Let o(y) = 0. Calculate y.
0, 1
Let l = 12 + -8. Factor -2*q + l*q - 8*q**3 - 5*q**2 - q**2.
-2*q*(q + 1)*(4*q - 1)
Let f be (-1)/(-2) + 1 + 2/4. Suppose -3*n - 8 = -5*n. Factor -1/5*r**5 - r**n - f*r**3 - r - 1/5 - 2*r**2.
-(r + 1)**5/5
Let 8*g**2 + 7*g + 4*g - 5*g**2 - 5*g = 0. Calculate g.
-2, 0
Let s(b) be the second derivative of -8*b**6/15 + 11*b**5/5 - 3*b**4 + 2*b**3/3 + 2*b**2 - 4*b. Factor s(j).
-4*(j - 1)**3*(4*j + 1)
Suppose -i - 90 = i. Let h = i - -317/7. Factor h*c**4 - 2/7*c + 2/7*c**3 + 0 - 2/7*c**2.
2*c*(c - 1)*(c + 1)**2/7
Suppose -o + 2*i = -6, 0 = -0*o - o + 5*i + 9. Suppose 0*b**3 - 2/9*b**o + 0*b + 0 + 2/9*b**2 = 0. Calculate b.
-1, 0, 1
Suppose -13 = -4*k + 23. Find y such that -6*y**3 + 15*y**4 + 1 + 12*y - 12*y**4 - k*y**2 + 11 = 0.
-1, 2
Let q(t) = t**3 + 3*t**2 - 4*t + 2. Let d be q(-4). Let z be d/9 - 6/27. Find g, given that -2*g**2 + 4*g + z*g - 2*g - 4 + 4*g**2 = 0.
-2, 1
Let v(l) = -2*l**2 - 16*l - 54. Let n(w) = 4*w**2 + 31*w + 109. Let j(z) = -4*n(z) - 9*v(z). What is t in j(t) = 0?
-5
Find u such that 2*u**2 + 2*u + 6*u - 3*u - 3*u = 0.
-1, 0
Let b(j) be the second derivative of -j**6/45 + j**5/10 - j**4/6 + j**3/9 + 4*j. Let b(s) = 0. Calculate s.
0, 1
Factor 2/21*y**3 + 0*y + 2/21*y**2 + 0.
2*y**2*(y + 1)/21
Let p(h) be the second derivative of -h**6/75 + h**5/50 + h**4/30 - h**3/15 + 2*h. Suppose p(x) = 0. Calculate x.
-1, 0, 1
Let h = -2 + 4. Suppose 3*s - 20 = -4*o, -o = -h*o + 3*s + 20. Solve -o*l - 5*l**4 - 135*l**4 - 34*l**3 - 50*l**5 - 104*l**3 - 56*l**2 = 0.
-1, -2/5, 0
Let t(c) be the second derivative of -3*c**4/2 - 7*c**3/3 + 2*c**2 + 14*c. Determine q so that t(q) = 0.
-1, 2/9
Factor 5*m**2 - 4*m - 3*m - 2 - m**4 - 14*m**2 - 5*m**3.
-(m + 1)**3*(m + 2)
Let k(j) be the third derivative of j**8/560 - 4*j**7/525 + j**6/150 + j**5/50 - 7*j**4/120 + j**3/15 + 5*j**2. Let k(w) = 0. Calculate w.
-1, 2/3, 1
Let u(d) be the second derivative of -3*d**5/80 + d**3/8 + 7*d. Factor u(l).
-3*l*(l - 1)*(l + 1)/4
Let d(i) be the second derivative of i**6/1440 - i**5/240 - i**3/6 + 4*i. Let r(a) be the second derivative of d(a). Factor r(q).
q*(q - 2)/4
Suppose 2*z + 3*z + 85 = 0. Let h = z + 19. What is k in -1/5*k**4 + 0*k + 0 + 1/5*k**5 - 1/5*k**3 + 1/5*k**h = 0?
-1, 0, 1
Let o(t) be the third derivative of -t**7/1050 + t**6/150 - t**5/50 + t**4/30 - t**3/30 - 15*t**2. Suppose o(u) = 0. Calculate u.
1
Let g be 5/(-4 + 3)*-1. Let r(p) = 2*p**5 + p**4 + 6*p**3 + 2*p**2 - 5*p - 5. Let o(w) = -w**4 - w - 1. Let f(d) = g*o(d) - r(d). Find m such that f(m) = 0.
-1, 0
Let q be 4/(-10)*1635/(-218). Let -2/7*d**q - 6/7*d**2 - 2/7 - 6/7*d = 0. Calculate d.
-1
Let z(n) be the third derivative of -1/525*n**7 + 1/150*n**5 + 0 - 1/840*n**8 + 0*n + 1/300*n**6 + 0*n**4 - 2*n**2 + 0*n**3. Factor z(p).
-2*p**2*(p - 1)*(p + 1)**2/5
Find u, given that -21/4*u**5 - 3/4*u**3 + 57/4*u**4 - 69/4*u**2 + 6*u + 3 = 0.
-1, -2/7, 1, 2
Find x such that 6/7*x - 5/7 - 1/7*x**2 = 0.
1, 5
Let q = -28 + 28. Suppose 0 = -3*f - q*d - d + 1, 5*f - 30 = 4*d. Factor -2/5*p**f + 0*p**3 + 1/5 + 1/5*p**4 + 0*p.
(p - 1)**2*(p + 1)**2/5
Let s(d) be the first derivative of 5 + 3/10*d**2 - 1/15*d**3 - 2/5*d. Factor s(u).
-(u - 2)*(u - 1)/5
Let s be 38/285 + 236/30. Suppose 0 = -i - 6 + s. Suppose 0 - 1/3*u**i + 2/3*u = 0. What is u?
0, 2
Let p(t) be the second derivative of 0*t**3 + 0*t**2 + 2/21*t**7 - 3/20*t**5 - 1/12*t**4 - 4*t + 0*t**6 + 0. Factor p(c).
c**2*(c - 1)*(2*c + 1)**2
Let q(i) be the second derivative of 3*i**5/40 - 3*i**3/4 + 3*i**2/2 + 2*i. Factor q(a).
3*(a - 1)**2*(a + 2)/2
Suppose -13*t + 5 = -21. Solve 3*o**4 + 57/7*o**3 - 6/7 + 45/7*o**t + 3/7*o = 0.
-1, 2/7
Let h be 1 - 2/(-2 - -6). Factor -h*q + 1/2*q**2 + 0.
q*(q - 1)/2
Factor 0*m**2 - 2/3*m + 2/3*m**3 + 0.
2*m*(m - 1)*(m + 1)/3
Factor -6*j**4 + 3*j**5 + 9*j**4 - 6*j**4.
3*j**4*(j - 1)
Let g = -7 + 11. Suppose -3*t = -5*r + 4, 3 = 2*t + g*r - 9. Suppose -2/3*p**t + 0 - 2/3*p = 0. What is p?
-1, 0
Let i = 47 + -45. Let p be 15/140 + i/14. Factor 1/2*y + 0 + p*y**2.
y*(y + 2)/4
Let r(s) = 2*s**2 + 16*s + 6. Let v(i) = -i - 1. Let x(a) = r(a) + 12*v(a). Factor x(z).
2*(z - 1)*(z + 3)
Let w(h) be the second derivative of -h**4/12 - 7*h**3/6 - h**2/2 + 4*h. Let a(o) = -o**2 - 8*o - 1. Let f(q) = -5*a(q) + 6*w(q). What is l in f(l) = 0?
-1
Let y(q) be the second derivative of -q**6/135 + q**5/15 - 2*q**4/9 + 10*q**3/27 - q**2/3 - 11*q. Suppose y(i) = 0. Calculate i.
1, 3
Let a(n) be the second derivative of n**4/54 + 4*n**3/27 + 4*n**2/9 + 4*n. Factor a(g).
2*(g + 2)**2/9
Let j(l) be the first derivative of l**6/12 - l**5/5 + l**3/3 - l**2/4 + 15. Factor j(m).
m*(m - 1)**3*(m + 1)/2
Factor 4*y**4 + 8*y**3 + 0*y**2 - 8*y - y**4 - 8 - y**4 + 6*y**2.
2*(y - 1)*(y + 1)*(y + 2)**2
Suppose -4*g + 3*u + 1 = 0, -u - 1 = -3*g + 6. Let r(b) be the first derivative of 0*b**2 + 1/18*b**3 + 1 - 1/24*b**g + 0*b. Factor r(x).
-x**2*(x - 1)/6
Let k(f) be the first derivative of -2/35*f**5 - 8/7*f - 26/21*f**3 - 3/7*f**4 - 12/7*f**2 - 2. Suppose k(y) = 0. What is y?
-2, -1
Let a(b) = -4*b**3 + 15*b**2 + 16*b - 20. Let z(w) = 3*w**3 - 15*w**2 - 15*w + 21. Let c(x) = -6*a(x) - 7*z(x). Determine l so that c(l) = 0.
-3, 1
Let s(i) be the first derivative of -2*i**3/15 - 1. Factor s(t).
-2*t**2/5
Determine t so that 0*t**3 + 0*t + 0 + 2/7*t**2 - 2/7*t**4 = 0.
-1, 0, 1
Let m(i) = -i + 1. Let b be m(-2). Let g(n) be the third derivative of -1/120*n**4 + 0*n**b + n**2 - 1/300*n**5 + 0*n + 0. Let g(p) = 0. What is p?
-1, 0
Let i(b) be the third derivative of 0*b**4 + 1/180*b**6 - 1/135*b**5 + 0*b**3 + 0*b + 4*b**2 - 1/945*b**7 + 0. Solve i(k) = 0.
0, 1, 2
Suppose 3*p = 2*t - 13, t + 3*p - 1 - 1 = 0. Let u be t/((-5)/2) + 2. Factor 0*s**3 - 1/2*s**4 - 1/2*s**5 + u + 0*s + 0*s**2.
-s**4*(s + 1)/2
Let p(r) be the third derivative of r**8/5040 + r**7/5040 - r**5/20 - 3*r**2. Let i(c) be the third derivative of p(c). Factor i(f).
f*(4*f + 1)
Suppose 678*o - 681*o = -6. Factor -3/2*y**5 + 1/2*y - 1/2 + 3*y**o - 7*y**3 + 11/2*y**4.
-(y - 1)**4*(3*y + 1)/2
Let q = 19 + -16. Let m(o) be the first derivative of -2 - 2/3*o + 7/3*o**q - 1/6*o**2. Find z such that m(z) = 0.
-2/7, 1/3
Let u = 857/5 - 171. Factor 1/5*l - u - 1/5*l**3 + 2/5*l**2.
-(l - 2)*(l - 1)*(l + 1)/5
Let k = -42 - -59. Let k*j - 2*j**3 + j**4 - 17*j = 0. What is j?
0, 2
Let h(u) be the second derivative of -2*u - 1/2*u**4 + 0*u**2 - 1/10*u**5 + 0 - 2/3*u**3. Find q, given that h(q) = 0.
-2, -1, 0
Let b = 101/210 - -2/105. Determine f so that f + b*f**2 + 1/2 = 0.
-1
Let n be (-4)/14 - (-18)/14. Let c be n/(-2)*9/(-18). Factor 1/4*r**4 - 1/4*r**2 - c*r**3 + 1/4*r + 0.
r*(r - 1)**2*(r + 1)/4
Factor 0 + 3/4*w**3 + 9/4*w**2 + 3/2*w.
3*w*(w + 1)*(w + 2)/4
Suppose -4*n**3 - 22*n**2 + 12*n - 22*n**2 + 36*n**2 = 0. Calculate n.
-3, 0, 1
Let i(a) be the first derivative of -3*a**4/22 - 10*a**3/33 + 2*a**2/11 - 17. Let i(o) = 0. Calculate o.
-2, 0, 1/3
Suppose q - 5*w - 18 = 0, -5*q + 9 = -4*w - 18. Let h(l) be the first derivative of -l - l**q - 3/2*l**2 - 1/4*l**4 + 2. Factor h(y).
-(y + 1)**3
Let t = -75/4 - -19. Factor -t + 0*m + 1/4*m**2.
(m - 1)*(m + 1)/4
Let a(h) be the first derivative of h**6/300 + 4*h**5/225 - h**4/60 + h**2/2 - 7. Let w(n) be the second derivative of a(n). What is o in w(o) = 0?
-3, 0, 1/3
Let l(u) = -2*u - 9. Let m be l(-6). Let w = 7 + -5. Factor 8/7*f + 0*f**w - 6/7*f**m + 0 + 2/7*f**4.
2*f*(f - 2)**2*(f + 1)/7
Let c(m) = m**2 - 6*m + 5. Let n(d) be the first derivative of d**3/3 - 3*d**2 + 6*d + 6. Let i(v) = -3*c(v) + 4*n(v). Let i(y) = 0. What is y?
3
Let n = 86/3 + -24. Let m be (-4)/(-14) - 38/(-63). Suppose -2*c**3 - n*c**2 - 32/9*c - m = 0. Calculate c.
-1, -2/3
Let c(j) be the second derivative of -2*j**5/5 + 7*j**4/3 - 16*j**3/3 + 6*j**2 - 10*j