9/4. Solve 0 - r*k**2 + 3/2*k = 0.
0, 2
Suppose j**3 + 6*j**5 - 3*j**5 + 6*j**4 + 2*j**3 = 0. Calculate j.
-1, 0
Let o = 2/459 + 1822/3213. Find q such that o*q**2 + 0 - 4/7*q = 0.
0, 1
Let t be (-2)/3 - (-4)/6. Let o(r) be the second derivative of -r - 1/10*r**3 - 1/10*r**2 + t - 1/20*r**4 - 1/100*r**5. Determine p so that o(p) = 0.
-1
Suppose -5*k = k - 36. Let a(x) be the second derivative of 5/3*x**3 + 2/15*x**k + 7/10*x**5 + x**2 + 0 + 2*x + 3/2*x**4. Factor a(p).
2*(p + 1)**3*(2*p + 1)
Factor 0 + 2/9*r**4 + 2/9*r**3 - 2/9*r - 2/9*r**2.
2*r*(r - 1)*(r + 1)**2/9
Let u(m) be the third derivative of -m**6/840 - m**5/84 + m**4/28 - 11*m**2. Find b such that u(b) = 0.
-6, 0, 1
Let h(r) = 9*r - 144. Let o be h(22). What is d in 24*d - 154/3*d**2 - 8/3 + o*d**4 - 24*d**3 = 0?
-1, 2/9, 1
What is l in 34*l**3 - 23*l**3 - 14*l**3 - 3*l**4 - l**2 - l**5 = 0?
-1, 0
Let y(g) be the second derivative of g**8/3360 - g**7/630 + g**6/360 + g**4/6 + 7*g. Let j(v) be the third derivative of y(v). Factor j(m).
2*m*(m - 1)**2
Suppose -5*k + v = -4*k - 5, -v = -5*k + 29. Let 2*g - k*g**3 + 3*g**3 + g = 0. What is g?
-1, 0, 1
Let n(i) = -2*i**2 - 14*i + 12. Let u(f) = f. Let v(x) = -n(x) - 4*u(x). Suppose v(l) = 0. What is l?
-6, 1
Let r(l) be the first derivative of 3 - 1/4*l**4 - 1/3*l**3 + 1/4*l**5 - 4*l + 0*l**2. Let n(g) be the first derivative of r(g). Factor n(i).
i*(i - 1)*(5*i + 2)
Let m = 739/15 + -233/5. Factor -2/3*n**2 - 8/3 - m*n.
-2*(n + 2)**2/3
Let c = 13 - 7. Factor -5*y - c*y**4 - 2*y**3 + 8*y**2 + 7*y - 2*y**4.
-2*y*(y - 1)*(y + 1)*(4*y + 1)
Factor 24*b - 87*b**2 + 97*b**2 + 5 - 32*b**3 + 9*b**4 - 9*b**3 - 7*b**3.
(b - 5)*(b - 1)*(3*b + 1)**2
Let g(z) be the first derivative of 4 - 1/15*z**3 + 1/60*z**4 + 1/10*z**2 - 4*z. Let o(b) be the first derivative of g(b). Determine y so that o(y) = 0.
1
Suppose -21*k**3 + 3/2*k**2 - 9/2*k**4 + 90*k + 54 = 0. What is k?
-3, -2/3, 2
Let j = 2 + 0. Suppose -5 = -4*a + 3. Factor -j + 5*k**3 + 3 + a*k - 7*k**3 - k**4.
-(k - 1)*(k + 1)**3
Let v(i) = -i**2 + i - 1. Let s(g) = -3*g**2 + 4*g + 1. Let j(u) = s(u) - 2*v(u). Factor j(p).
-(p - 3)*(p + 1)
Let g(s) = 8*s**2 - 7*s - 1. Let i(a) = -a**2 + a. Let j(l) = -3*g(l) - 21*i(l). Factor j(w).
-3*(w - 1)*(w + 1)
Let i(c) = -4*c + 0*c**3 + 12*c**4 - 8*c - 2*c**5 + 2*c**3. Let j(q) = q**4 - q. Let h be 0 + -1 + (8 - 8). Let w(s) = h*i(s) + 12*j(s). Factor w(a).
2*a**3*(a - 1)*(a + 1)
Let l(p) be the second derivative of -p**7/70 - 2*p**6/25 + 9*p**5/100 + 9*p**4/10 + 2*p. Factor l(r).
-3*r**2*(r - 2)*(r + 3)**2/5
Suppose 5 - 19 = -d. Let v(m) = m**2 + 2*m - 1. Let h(j) = 3*j**2 + 7*j - 3. Let l(k) = d*v(k) - 4*h(k). Let l(a) = 0. Calculate a.
-1, 1
Let u(d) be the second derivative of -d**5/30 + d**4/36 + d**2/2 - d. Let f(v) be the first derivative of u(v). Solve f(l) = 0.
0, 1/3
What is x in 0 + 2/5*x**5 + 4/5*x - 6/5*x**3 + 2/5*x**4 - 2/5*x**2 = 0?
-2, -1, 0, 1
Suppose -5*m + 2*m = -2*x + 10, 5*m - 2*x + 10 = 0. Let b(d) be the third derivative of -1/9*d**4 + 2*d**2 + 0 - 1/90*d**5 - 4/9*d**3 + m*d. Solve b(c) = 0.
-2
Let h = 4402863/6709259 - -7/104289. Let c = h + 2/193. Factor -2/3*i**3 - c*i**4 + 2/3*i**2 + 0*i + 2/3*i**5 + 0.
2*i**2*(i - 1)**2*(i + 1)/3
Solve 2*l**2 + 393*l - 219*l + 20 - 196*l = 0.
1, 10
Let b(j) be the first derivative of j**6/540 - j**5/270 + j**2 + 1. Let c(m) be the second derivative of b(m). Determine t so that c(t) = 0.
0, 1
Let a(f) = -7*f**2 - 5*f - 2. Let k(c) = -13*c**2 - 11*c - 5. Let h(b) = 7*a(b) - 4*k(b). Factor h(l).
3*(l + 1)*(l + 2)
Let h = 19 - 23. Let m be 99/(-154) - 6/h. Factor -m*a**2 + 2/7*a**3 + 4/7*a + 0.
2*a*(a - 2)*(a - 1)/7
Solve -14/13*t**3 + 6/13*t**2 + 0*t + 0 = 0 for t.
0, 3/7
Let w(m) be the second derivative of -15/7*m**3 - 27/14*m**2 - 6*m + 0 - 25/28*m**4. Factor w(c).
-3*(5*c + 3)**2/7
Let l(i) be the third derivative of -i**8/1680 + i**7/1050 + i**6/200 - i**5/300 - i**4/60 + 15*i**2. Suppose l(j) = 0. Calculate j.
-1, 0, 1, 2
Let c(v) = 2*v**2 - 11*v + 37. Let k(y) = 6*y - 18 + y - 2*y - y**2 - 1. Let p(i) = 3*c(i) + 5*k(i). Factor p(z).
(z - 4)**2
Suppose 3*o - 2*n = 9, -2*o + 0*n - n = -13. Suppose 4*q + 4*j = 0, o*q - j = -0*q. Determine y so that y**3 - 2/3*y**4 + q*y + 0 - 1/3*y**2 = 0.
0, 1/2, 1
Find n, given that -12 + 16*n**3 + 15*n**4 + 16*n + 44*n**2 - 27*n**4 + 13*n**2 - n**2 = 0.
-1, 1/3, 3
Suppose 5*m + 2*m = 14. Find p, given that 1/2*p**5 + 0*p + 0 - 1/2*p**3 - 1/2*p**4 + 1/2*p**m = 0.
-1, 0, 1
Let l be (-1 + 1)*(-4)/8. Suppose -r + 2*r - 1 = l. Factor -2 + 4*v - r - v**2 - 1.
-(v - 2)**2
Suppose 6 = 2*j - 0. Factor 3*i**2 + 3*i**2 + 9*i + 3*i**j + 3 + 0 + 3*i**2.
3*(i + 1)**3
Let m(o) be the second derivative of 0 + 1/60*o**4 - 1/30*o**3 + 2*o - 1/10*o**2 + 1/100*o**5. Determine w, given that m(w) = 0.
-1, 1
Factor -34 + 3*n**2 + 20 + 8 + 3*n.
3*(n - 1)*(n + 2)
Factor 2/3*h**3 + 4/3*h**2 + 2/3*h + 0.
2*h*(h + 1)**2/3
Let g = 91/2 - 44. Let y(l) be the first derivative of 3 + 0*l - g*l**2 + l**3. Factor y(k).
3*k*(k - 1)
Let o(b) be the third derivative of 5*b**2 - 1/12*b**4 - 1/30*b**5 + 0*b + 0*b**3 + 0. Factor o(n).
-2*n*(n + 1)
Suppose 0 = a + 3*c, -5*c = -2*c + 3. Let z = 5 + -1. Let 5*g**4 - 2*g**4 - a*g**4 - g**z = 0. Calculate g.
0
Let z(o) be the first derivative of o**3/3 + o**2/2 - 9*o + 3. Let c be z(3). Factor 3/2 + 3*a**3 + 3/2*a**2 + 3/4*a**5 - 15/4*a - c*a**4.
3*(a - 2)*(a - 1)**3*(a + 1)/4
Suppose -4*d = -4 + 12. Let z be d + 0 + 4 + 0. Factor -2*f**3 + 3*f**3 - 3*f**4 + z*f**4.
-f**3*(f - 1)
Let u be -3*(4 + -5) - 4. Let v be 10/54*-3 - u. Factor 0*s + v*s**2 - 2/9*s**4 + 2/9*s**3 + 0.
-2*s**2*(s - 2)*(s + 1)/9
Let v = 2969/4 - 742. Let n be (-22)/(-10) - 4/20. Suppose 3/2*h**2 + n*h**3 - v + 3/4*h**4 + 0*h = 0. Calculate h.
-1, 1/3
Let y(m) be the first derivative of 0*m**4 - 1/80*m**5 - m + 1/24*m**3 + 0*m**2 + 2. Let w(c) be the first derivative of y(c). Find a, given that w(a) = 0.
-1, 0, 1
Let j(n) be the second derivative of n**4/3 + 10*n**3/3 - 12*n. Factor j(d).
4*d*(d + 5)
Let g(z) be the second derivative of -z**4/2 - 4*z**3/3 - z**2 - 7*z. Factor g(b).
-2*(b + 1)*(3*b + 1)
Suppose -4*a - 1 = -9. Let q be (a/(-18))/(2/(-12)). Suppose -1/3*s**4 + 1/3 + q*s + 0*s**2 - 2/3*s**3 = 0. Calculate s.
-1, 1
Let i(p) be the first derivative of 0*p**5 + 0*p - 1/4*p**4 + 0*p**3 + 3 + 1/6*p**6 + 0*p**2. Factor i(k).
k**3*(k - 1)*(k + 1)
Let y = -31 + 125/4. Factor -1/2 - 1/4*c + y*c**2.
(c - 2)*(c + 1)/4
Let l(g) = -2*g**3 - 2*g**2. Let w be -3 - 3*(-28)/6. Let x(q) = 9*q**3 + 9*q**2. Let s(t) = w*l(t) + 2*x(t). Factor s(u).
-4*u**2*(u + 1)
Factor 0*a**3 - 2/11*a**4 + 0 + 2/11*a**2 + 0*a.
-2*a**2*(a - 1)*(a + 1)/11
Suppose 126/11*v**2 - 81/11*v**3 + 8/11 + 68/11*v = 0. What is v?
-2/9, 2
Suppose -i = -4, i + 11 + 9 = 2*k. Suppose -2*v + k = v. Solve 3*z**4 - z**v + z - 2*z**2 - 3*z + 2*z**3 = 0.
-1, 0, 1
Let u(a) = -a. Let c be u(-8). Suppose -2 = -5*k + c. Determine q so that -2/9*q + 2/3*q**k + 0 = 0.
0, 1/3
Suppose -3*g - 2*g = -10. Factor 0*k**g - 2/9*k**4 + 2/9 - 4/9*k + 4/9*k**3.
-2*(k - 1)**3*(k + 1)/9
Let a(z) be the third derivative of 0 + 1/84*z**4 + 2/21*z**3 - 1/210*z**5 + 3*z**2 + 0*z. Factor a(l).
-2*(l - 2)*(l + 1)/7
Let g(m) be the second derivative of m**8/5880 - m**7/2940 + 2*m**3/3 - 4*m. Let t(l) be the second derivative of g(l). Solve t(k) = 0.
0, 1
Suppose 13 = 6*x + 13. Let r(v) be the third derivative of -3*v**2 + 0 + 0*v**3 + 0*v - 1/120*v**6 + x*v**4 - 1/210*v**7 + 0*v**5. Factor r(d).
-d**3*(d + 1)
Suppose -8*o = -3*o - 20. Let g be 60/18 - (o + -1). Suppose -g*a**2 - 2/3*a - 1/3 = 0. What is a?
-1
Factor -5*c**2 - 240 + 0*c**2 + 240 - 5*c.
-5*c*(c + 1)
Let y(p) be the third derivative of p**5/15 - p**4/4 - 2*p**3/3 - 7*p**2. Find t such that y(t) = 0.
-1/2, 2
Suppose -1 - 5 = -j. Suppose 5*g - c - 11 = 0, 5 = -5*g - c + j*c. Let 1 + 2*r + r**2 - g*r - r = 0. Calculate r.
1
Suppose 60 = 25*t - 15. Find q, given that -2/9*q**4 + 2/9*q**2 + 0*q**t + 0*q + 0 = 0.
-1, 0, 1
Let y(b) be the third derivative of 0*b**3 + 0*b + 0 + 4*b**2 - 1/60*b**6 - 1/30*b**5 + 1/6*b**4. Solve y(u) = 0 for u.
-2, 0, 1
Let n(i) = -5*i**4 - 5*i**3 + 4*i**2 + 4. Suppose p = 4 + 3. Let j(a) = 9*a**4 + 9*a**3 - 7*a**2 - 7. Let b(s) = p*n(s) + 4*j(s). Let b(g) = 0. 