- 4. Let r(u) = -9*t(u) + 4*z(u). Factor r(d).
-d**3*(d + 1)
Let s = 20 + -12. Let u = -4 + s. Find z, given that 7*z**5 + 3*z**3 - 4*z**2 - 2*z**4 + 5*z**2 - 10*z**u + z**2 = 0.
-2/7, 0, 1
Let r(b) = -14*b**5 - 17*b**4 + 11*b**3 - 5*b**2 + 14*b + 11. Let s(v) = -5*v**5 - 6*v**4 + 4*v**3 - 2*v**2 + 5*v + 4. Let p(d) = 4*r(d) - 11*s(d). Factor p(x).
-x*(x - 1)*(x + 1)**3
Suppose 220 = 6*f + 202. What is l in 9/2*l**2 + f*l + 0 = 0?
-2/3, 0
Let f(l) = -l + 8. Let r be f(5). Suppose 18*z**3 - 370*z**2 - 240*z - 134*z**2 - 25*z**3 - 32 - 189*z**r = 0. Calculate z.
-2, -2/7
Let v(p) be the second derivative of -p**3/6 + 2*p**2 + 4*p. Let i be v(2). Determine t so that -2/9*t**i + 0 + 0*t + 2/9*t**3 = 0.
0, 1
Let b(a) be the second derivative of -a**5/110 + a**4/33 + 7*a**3/33 + 4*a**2/11 + 2*a. Factor b(v).
-2*(v - 4)*(v + 1)**2/11
Let r = -5 + 10. Factor -4*x**5 + 0*x**5 + 2*x**r.
-2*x**5
Let a(m) be the second derivative of -3*m**5/40 - 11*m**4/24 - 2*m**3/3 + m**2 + 9*m. Factor a(w).
-(w + 2)**2*(3*w - 1)/2
Let d = -1487342/1876461 + 2/423717. Let f = 2/31 - d. Solve 6/7*x**5 + 0*x + 0 - f*x**3 + 2/7*x**2 - 2/7*x**4 = 0 for x.
-1, 0, 1/3, 1
Let n = -3 + 5. Factor 3*m**3 - m**3 - 6*m**3 + 2*m**3 - 4*m**n.
-2*m**2*(m + 2)
Suppose 3*v + 12 - 18 = 0. Solve -7/2*n**3 + 7/2*n - 2*n**v - 1 + 3*n**4 = 0 for n.
-1, 1/2, 2/3, 1
Let i(m) = -3*m**3 - 6*m + 1. Let o(p) = -2*p**3 - 6*p. Let x(a) = -4*i(a) + 5*o(a). Factor x(r).
2*(r - 2)*(r + 1)**2
Let r = -40 + 40. Factor -2/7*u + 2/7*u**4 + 6/7*u**2 + r - 6/7*u**3.
2*u*(u - 1)**3/7
Let k(i) be the third derivative of -i**8/462 - 13*i**7/1155 - i**6/44 - 7*i**5/330 - i**4/132 + 5*i**2. Let k(o) = 0. Calculate o.
-1, -1/4, 0
Let f(w) be the second derivative of w**4/3 + 8*w**3/3 + 8*w**2 - 5*w. Factor f(v).
4*(v + 2)**2
Let j = -164 - -659/4. Let -3/4*p + 1/2 - j*p**2 + 1/2*p**3 = 0. What is p?
-1, 1/2, 2
Let b(p) be the second derivative of p**4/72 - p**3/9 + p**2/3 + 15*p. Solve b(r) = 0.
2
Determine y, given that -3*y - 6*y**3 + 5*y - 2*y**2 - 31*y**5 + 2*y**4 + 35*y**5 = 0.
-1, 0, 1/2, 1
Suppose 1/6 - 5/6*z**2 - 2/3*z = 0. What is z?
-1, 1/5
Let o be (1 + 2)/((-18)/(-12)). Suppose -5*m = o*n, -4*n - 30 = -5*m - 0*m. Find p, given that 5*p**2 - 6*p**2 + m*p**2 = 0.
0
Find d, given that -2*d**4 + 4*d**2 + 0*d + 0*d + 2*d**3 + 0*d = 0.
-1, 0, 2
Let o(v) be the first derivative of 3*v**4/16 + v**3/4 - 3*v**2/8 - 3*v/4 + 8. Factor o(q).
3*(q - 1)*(q + 1)**2/4
Let j be (-18)/(-2 + -4) - 28/10. Solve 0 + 0*g**3 + 0*g**2 + 0*g + j*g**4 = 0.
0
Let d = 16 - 206/13. Determine a, given that -8/13*a**3 + 2/13 - 8/13*a + d*a**4 + 12/13*a**2 = 0.
1
Let u(i) be the second derivative of 0 + 1/5*i**2 + 1/30*i**3 - 1/60*i**4 + i. Factor u(j).
-(j - 2)*(j + 1)/5
Let a(k) be the third derivative of -k**5/48 + 5*k**4/24 - 5*k**3/8 + 2*k**2 - 22*k. Determine c, given that a(c) = 0.
1, 3
Suppose 3*a + 1 = 4*p + 2, p + 7 = 3*a. Let j(x) be the first derivative of 2*x - x**a - 1 + 1/2*x**2. Factor j(o).
-(o - 1)*(3*o + 2)
Let q(n) = -3*n**4 - 3*n**3 - 9*n**2 - 9*n. Let o(v) = -3*v**4 - 4*v**3 - 9*v**2 - 8*v. Let p = -9 + 15. Let y(w) = p*o(w) - 5*q(w). Find l such that y(l) = 0.
-1, 0
Let v = -5 + 10. Factor -2*w + v*w - w**3 - 2*w.
-w*(w - 1)*(w + 1)
Let r(f) be the second derivative of 0 - 1/2*f**3 + 3*f**2 + 2*f - 1/4*f**4. Suppose r(i) = 0. Calculate i.
-2, 1
Let p = -8 - -11. Suppose -p*m = m - 12. Let 6*j**m + 11/2*j**2 + 0 + j = 0. What is j?
-2/3, -1/4, 0
Let i be ((-27)/(-3) + -3)*(-4)/(-84). Factor -2/7*k**2 + 6/7*k + i - 6/7*k**3.
-2*(k - 1)*(k + 1)*(3*k + 1)/7
Let y(m) be the second derivative of 3*m - 1/9*m**4 + 0*m**2 + 1/9*m**3 + 1/30*m**5 + 0. Factor y(q).
2*q*(q - 1)**2/3
Let s(t) be the second derivative of t**7/1260 - t**6/360 - t**4/6 - 3*t. Let z(w) be the third derivative of s(w). Solve z(a) = 0.
0, 1
Suppose 0 = 3*q - 0*d + d - 22, 2*q - 4*d = -4. Suppose -q = -2*t - t. Factor n**2 - 6*n**t - 3 - n + 3*n**3 + 8*n**2 - 2*n.
3*(n - 1)*(n + 1)**2
Factor -174*r**2 - 2*r**4 + 8*r - 2 + 11*r**3 + 162*r**2 - 3*r**3.
-2*(r - 1)**4
Let j(v) be the second derivative of v**8/3920 + v**7/1960 + 5*v**3/6 + 4*v. Let w(z) be the second derivative of j(z). Factor w(r).
3*r**3*(r + 1)/7
Let d(t) = -1. Let y(o) = o - 2. Let r(w) = 6*d(w) + y(w). Let j be r(10). Let -j*f**2 + 3 + 0 + 2 - 3 = 0. Calculate f.
-1, 1
Let u be 4*((-81)/48 - -2). Suppose 9 - 1 = 4*p. Factor 1/4 + u*l + 2*l**p + l**3.
(l + 1)*(2*l + 1)**2/4
Let p(f) = f**3 - 3*f**2 + 6*f - 4. Let n be p(2). Factor -2*q**3 + 0 + 2/3*q**n + 4/3*q**2 + 0*q.
2*q**2*(q - 2)*(q - 1)/3
Let i(d) be the first derivative of 5*d**6/6 - 3*d**5/5 - 17*d**4/4 + 19*d**3/3 - 4*d - 10. Factor i(v).
(v - 1)**3*(v + 2)*(5*v + 2)
Let n be 0 - -1 - (-6)/(-8). Let k = 21/4 + -5. Suppose 0*t**3 - n*t - 1/2*t**4 + k*t**5 + 0 + 1/2*t**2 = 0. What is t?
-1, 0, 1
Let i(b) = b**3 - 10*b**2 - 6*b - 14. Let h be i(11). Let c = h - 39. Let 26/9*o**c + 34/9*o**4 - 4/9*o + 0 - 16/3*o**3 - 8/9*o**5 = 0. Calculate o.
0, 1/4, 1, 2
Let b(q) = -8*q**4 + 15*q**2 + 7*q + 9. Let x(m) = 4*m**4 - 8*m**2 - 4*m - 4. Let f(l) = -4*b(l) - 9*x(l). What is z in f(z) = 0?
-1, 0, 2
Let o(q) be the second derivative of -q**4/20 + q**3/2 - 9*q**2/5 + 15*q. Let o(z) = 0. What is z?
2, 3
What is x in -12*x**3 + 75*x**2 - 138*x**2 + 91*x**2 - 16 = 0?
-2/3, 1, 2
Let m = -882988/22449 + -2/7483. Let b = m - -40. Factor -b*j**4 + 0*j - 4/3*j**3 + 0 - 2/3*j**2.
-2*j**2*(j + 1)**2/3
Let b = 10/19 - -46/57. Factor b*j**3 - 1/3 - 2*j**2 - 1/3*j**4 + 4/3*j.
-(j - 1)**4/3
Factor 2*i**3 - 4*i - 8*i**3 + 2*i**4 - 10*i**2 + 3*i**5 - i**5.
2*i*(i - 2)*(i + 1)**3
Let b(t) = -3*t**2 - 2*t + 5. Suppose 6*x = 2*x - 8. Let y(l) = l**2 + l - 2. Let f(m) = x*b(m) - 5*y(m). Determine n so that f(n) = 0.
0, 1
Let h = 1379/60 - 112/5. Let v = -1/4 + h. Factor -v*f - 1/6*f**2 + 0.
-f*(f + 2)/6
Let m(b) be the third derivative of b**9/2520 - b**8/2100 - b**7/700 + b**6/450 - 5*b**3/3 + 5*b**2. Let w(s) be the first derivative of m(s). Solve w(t) = 0.
-1, 0, 2/3, 1
Suppose 4*b - s = 7, 0 = s + 4*s - 25. Let z(m) be the first derivative of -245/6*m**4 - 28*m**3 + 16/3*m - b + 20/3*m**2 + 686/15*m**5. Solve z(y) = 0.
-2/7, 2/7, 1
Suppose z + 2 + 6 = 5*h, 0 = z + 3*h - 8. Suppose 0 = z*w - w - 4. Factor 2*j**4 - 2*j - 2*j**5 - w*j**2 + 2*j**3 + 2 + 3*j**3 - j**3.
-2*(j - 1)**3*(j + 1)**2
Factor 2/9*h**3 + 8 + 32/3*h + 26/9*h**2.
2*(h + 1)*(h + 6)**2/9
Suppose 15 - 36*d + 108/5*d**2 = 0. Calculate d.
5/6
Let n(p) be the first derivative of -p**2 - 1/3*p**3 + 1 + 3*p. Determine u, given that n(u) = 0.
-3, 1
Let d(h) be the first derivative of 2*h**5/5 - 4*h**3 - 8*h**2 - 6*h + 8. Factor d(z).
2*(z - 3)*(z + 1)**3
Let w(k) = 15*k - 9*k**2 - 13*k**2 + 24*k**2 + 9. Let p be w(-7). Suppose o**4 + 1/2*o**5 - 1/2*o**3 + 0 + 0*o - o**p = 0. What is o?
-2, -1, 0, 1
Let w = 70 - 70. Let a(u) be the third derivative of u**2 + 0*u**4 + 0*u**6 + w + 0*u**3 + 1/150*u**5 - 1/525*u**7 + 0*u. Let a(k) = 0. What is k?
-1, 0, 1
Let d(b) be the first derivative of 4 - 4*b - 3*b**2 - 2/3*b**3. Let d(k) = 0. What is k?
-2, -1
Let w(x) be the third derivative of -2*x**7/105 - x**6/15 - x**5/15 - 7*x**2. Factor w(q).
-4*q**2*(q + 1)**2
Factor 2/3*a**3 + 4/3*a**2 + 2/3*a + 0.
2*a*(a + 1)**2/3
Suppose 3*c + 2*c - 5*w - 25 = 0, c - 5*w - 13 = 0. Let k(o) be the second derivative of 3*o + 1/12*o**4 + 1/4*o**2 + 1/80*o**5 + 5/24*o**c + 0. Factor k(d).
(d + 1)**2*(d + 2)/4
Determine y, given that -7*y - 5*y**2 - 2*y - y = 0.
-2, 0
Let k(w) = w**3 - 3*w**2 + 3*w - 2. Let c be k(2). Factor 0 - 1/2*u**2 + c*u.
-u**2/2
Let d(j) be the second derivative of j**5/70 + 5*j**4/42 + j**3/3 + 3*j**2/7 - 5*j. Factor d(a).
2*(a + 1)**2*(a + 3)/7
Suppose a - 4 = -3*z + z, 3*z + 3*a - 9 = 0. Let r be 3 - z/(35/75). Determine c, given that 0*c**2 + 4/7 + 2/7*c**3 - r*c = 0.
-2, 1
Let s be 0 - 2 - (-987)/9. Let z = 109 - s. Solve z*c**2 - 16/3*c**3 - 2/3 + 8/3*c + 8/3*c**5 - 2/3*c**4 = 0.
-1, 1/4, 1
Let k be (-4)/(-18) + (-1)/18. Let q(v) be the first derivative of k*v**4 - 2/9*v**3 + 1 + 2/3*v - 1/3*v**2. Solve q(t) = 0 for t.
-1, 1
Suppose 10 = f + 8. Determine w so that -2*w**2 - 21 - 2*w + f*w**4 + 2*w**3 + 21 = 0.
-1, 0, 1
Let x(l) = l - 9. Let j be x(9). Let t(o) be the first derivative