(k + 1)*(k + 6)
Let b = -56 + 61. Suppose r + 6*k - 2*k = 16, -3*r = b*k - 27. Let -8/7*l**5 + 4/7*l**2 + 12/7*l**3 - 4/7*l**r + 0 - 4/7*l = 0. What is l?
-1, 0, 1/2, 1
Let q(f) be the second derivative of -7/12*f**4 - 1/42*f**7 + 0 - 1/3*f**3 - 5*f - 9/20*f**5 + 0*f**2 - 1/6*f**6. Factor q(h).
-h*(h + 1)**3*(h + 2)
Let s(o) be the first derivative of -3*o**4/4 - o**3 + 15*o**2 - 24*o - 182. Determine q so that s(q) = 0.
-4, 1, 2
Let n = -4/285 + 598/1995. Solve -2/7*u**2 + 4/7 - n*u = 0.
-2, 1
Let s = -9499/20 - -475. Let r(a) be the third derivative of 0 + s*a**5 + 6*a**2 + 1/4*a**4 + 0*a + 1/2*a**3. Determine l, given that r(l) = 0.
-1
Let n(q) = -2*q**3 + 1. Let b(a) = -5*a**3 - 4*a**2 + 2. Let m(w) = -b(w) + 2*n(w). Determine p, given that m(p) = 0.
-4, 0
Let n = 3867 + -3867. Find k such that n*k - 1/10*k**2 + 2/5 = 0.
-2, 2
Suppose 0 = -6*u + 4*u + 6*u. Let x(r) be the third derivative of u*r**3 + 0 + 0*r + 1/20*r**5 + 1/2*r**4 - 3*r**2. Suppose x(d) = 0. Calculate d.
-4, 0
Let v(o) = -67*o**2 - 77*o - 31. Let p(g) = -66*g**2 - 78*g - 29. Let d(j) = 3*p(j) - 2*v(j). Solve d(u) = 0.
-5/8
Let m(l) be the third derivative of l**8/168 + 47*l**7/735 - 226*l**5/105 - 136*l**4/21 + 64*l**3/7 + 186*l**2. Suppose m(d) = 0. Calculate d.
-4, -2, 2/7, 3
Let x(b) be the second derivative of -b**4/30 - 8*b**3/15 + 4*b**2 + 81*b. Factor x(w).
-2*(w - 2)*(w + 10)/5
Suppose 4*f + 52 - 64 = 0. Let b(j) be the second derivative of j**2 - 4/3*j**f + 0 + 1/2*j**4 - j. Let b(z) = 0. Calculate z.
1/3, 1
Let i be (-4)/(-24) + (-89)/(-6). Suppose 3*l - 4*p - 9 = 43, 0 = p - 2. Let -13*b**3 - 1 - 4 + 20*b - i*b**2 - 7*b**3 + l*b**4 = 0. Calculate b.
-1, 1/2, 1
Suppose 61*n = 31*n. Factor 9/2*a**2 + 3/2*a + n.
3*a*(3*a + 1)/2
Suppose 26*m = 28 + 33 - 9. Let n(h) = h**3 + 2*h**2 - 3*h - 3. Let l be n(-2). Factor -m*o + 0 - 2/9*o**l + 4/3*o**2.
-2*o*(o - 3)**2/9
Let p be (-117)/(-65)*(-10)/(-3). Let k(w) be the first derivative of 2*w**2 + 8/3*w**3 + 0*w - 2/3*w**p + 5 - 8/5*w**5 + 0*w**4. Factor k(i).
-4*i*(i - 1)*(i + 1)**3
Suppose 0 - 124*a**2 - 537*a + 529*a + 0 = 0. Calculate a.
-2/31, 0
Let g(o) be the third derivative of -5*o**8/252 - o**7/6 - o**6/72 + 7*o**5/12 + 25*o**4/72 - 308*o**2. Suppose g(x) = 0. What is x?
-5, -1, -1/4, 0, 1
Let k(n) be the first derivative of -5*n**4/4 - 25*n**3/3 + 15*n**2 + 58. Factor k(g).
-5*g*(g - 1)*(g + 6)
Factor 1/2*h**4 - 9/2*h**2 + 3/2*h**3 - 27/2*h + 0.
h*(h - 3)*(h + 3)**2/2
Solve -2/5*z - 8/5 + 11/5*z**2 + z**3 = 0 for z.
-2, -1, 4/5
Let f(t) be the second derivative of 4*t**4/3 - 94*t**3 + 70*t**2 + 2*t - 54. Factor f(v).
4*(v - 35)*(4*v - 1)
Let o(m) be the second derivative of m**7/84 + m**6/12 + m**5/10 - 62*m + 2. What is v in o(v) = 0?
-4, -1, 0
Factor 0 + 16/7*a + 4/7*a**4 + 32/7*a**2 + 20/7*a**3.
4*a*(a + 1)*(a + 2)**2/7
Let w(a) be the third derivative of 0 + 1/18*a**3 + 1/630*a**7 + 5*a**2 - 1/90*a**6 + 0*a - 1/18*a**4 + 1/30*a**5. Factor w(l).
(l - 1)**4/3
Let o = 14 + -12. Solve -2*k + o*k**2 + k + k - 4*k + 2 = 0.
1
Let z(m) be the second derivative of -m**6/480 + m**5/240 - 8*m**2 - 14*m. Let r(w) be the first derivative of z(w). Find i such that r(i) = 0.
0, 1
Suppose 2*a = -2*m + 4*a + 604, 2*m + 2*a = 608. Determine q, given that 3*q**3 + m - 4*q + 6*q**2 + q**3 - 309 = 0.
-3/2, -1, 1
Let g(c) be the first derivative of -44/9*c**3 - 8*c**2 - 16/3*c - 10 + 2/9*c**6 - 1/3*c**4 + 4/5*c**5. Factor g(x).
4*(x - 2)*(x + 1)**3*(x + 2)/3
Let b(r) be the second derivative of -57*r**4 - 260*r**3/3 - 48*r**2 + 11*r - 24. Suppose b(w) = 0. Calculate w.
-4/9, -6/19
Let u(q) = -8 - 3*q**2 + 4*q**2 - 1 - 2*q**2 - 13*q. Let a be u(-12). Find x, given that -a + 3/2*x**2 - 3/2*x = 0.
-1, 2
Let z be (-6*2/(-15))/(366/915). Determine q so that 0*q + 1/4*q**z - 1/4 = 0.
-1, 1
Let p = 2210 + -2210. Factor -2/3*q**3 - 8/3*q + p + 8/3*q**2.
-2*q*(q - 2)**2/3
Let m = 17 - 15. Suppose -b + t = -1 - 3, -t = -2*b + 8. Determine g so that -b*g - m + 5/2*g**2 = 0.
-2/5, 2
Let j(h) be the first derivative of 3/2*h**2 + 4/5*h**3 + 6/5*h + 11 + 3/20*h**4. Let j(k) = 0. What is k?
-2, -1
Let r be 2*(-33)/(-176)*4. Suppose 3/2*k**3 + 0 + 0*k - r*k**4 + 0*k**2 = 0. Calculate k.
0, 1
Let l(n) be the second derivative of 3*n + 0 + 1/138*n**4 + 0*n**2 - 1/23*n**3. Let l(x) = 0. What is x?
0, 3
Let t be 5*-2*(-6)/15. Let t - n**2 - 2 + 3*n + 3*n - 7*n = 0. Calculate n.
-2, 1
Let n(k) be the second derivative of k**6/75 + 2*k**5/25 - k**4/30 - 16*k**3/15 - 12*k**2/5 + 2*k + 53. Determine b so that n(b) = 0.
-3, -2, -1, 2
Let x be (-1)/3 - 80/(-24). Suppose 7*i = x*i + 8. Suppose -11*a - a - 3 - 5 + 10*a**i - 4*a = 0. What is a?
-2/5, 2
Factor -96 - 42 + 52 + 0 + 284*p - 194 - 4*p**2.
-4*(p - 70)*(p - 1)
Let v be ((-34)/8)/(19/(-76)). Suppose 0 = -a + 3*w + 7, 5*a = 8*a - 5*w - v. What is g in 2/3*g + 7/3*g**2 + 1/3*g**5 + 0 + 3*g**3 + 5/3*g**a = 0?
-2, -1, 0
Let a(h) be the second derivative of 1/30*h**4 + 0 + 25*h - 2/5*h**3 + h**2. Factor a(f).
2*(f - 5)*(f - 1)/5
Solve 32*h**2 + 9 + 816*h**3 + 5400*h**4 + 2500*h**5 - 20 + 11 = 0.
-2, -2/25, 0
Let x(l) be the third derivative of 3/4*l**4 + 5/2*l**3 + 0 + 0*l + 1/20*l**5 - 15*l**2. Suppose x(b) = 0. Calculate b.
-5, -1
Let k = -46 + 57. Suppose z - k = 4*x, 1 = -4*x - 7. Factor 3/4*u**z - 3/4*u + 1/2 + 5/4*u**4 - 7/4*u**2.
(u - 1)*(u + 1)**2*(5*u - 2)/4
Suppose -77 = -3*l - 5*u, -3*u - 21 = -4*l + 43. Factor -3*o + l - 8*o**2 - 21 - 6*o + o.
-2*(2*o + 1)**2
Let b(i) = -3*i**4 - i**3 + i**2 + 19*i - 16. Let p(g) = 2*g**4 - g**2 - 9*g + 8. Let t be 0 - (16/(-6) + (-1)/3). Let o(z) = t*b(z) + 5*p(z). Factor o(y).
(y - 2)**2*(y - 1)*(y + 2)
Let m(u) be the second derivative of -u**6/6 - u**5 - 5*u**4/4 + 17*u + 2. Factor m(i).
-5*i**2*(i + 1)*(i + 3)
Let j(o) be the third derivative of -o**7/168 - 7*o**6/48 - 61*o**5/48 - 35*o**4/8 - 15*o**3/2 + 10*o**2 + 1. Determine g so that j(g) = 0.
-6, -1
Let 16/9*y - 28/9*y**2 + 28/9*y**4 - 4/9*y**3 + 0 - 4/3*y**5 = 0. What is y?
-1, 0, 1, 4/3
Suppose -q + 0*q = -2. Let j be 1/(-3) - 16/(-48). Suppose 8*f + 4 - 3 + 1 + j + 6*f**q = 0. Calculate f.
-1, -1/3
Factor -58/7 - 8*x + 2/7*x**2.
2*(x - 29)*(x + 1)/7
Let u(o) = -o**3 - 10*o**2 + 19*o + 22. Let p be u(-10). Let c be 2/7 + (-582)/p. Solve 21/4*w**5 - c*w**3 - 27/4*w**2 - 3/2*w + 0 + 27/4*w**4 = 0.
-1, -2/7, 0, 1
Let i be (-1)/((-5)/30) - 4. Factor 2*b**2 + i*b - 3*b**2 + 9 - 9.
-b*(b - 2)
Let f(u) be the first derivative of -2/21*u**4 - 1/630*u**6 + 8/3*u**3 + 0*u + 0*u**2 - 6 - 2/105*u**5. Let n(a) be the third derivative of f(a). Factor n(s).
-4*(s + 2)**2/7
Let a be (-4085)/(-423) + -4 - 5. Let r = a - 10/47. Find b, given that 2/9*b**2 - r*b + 4/9*b**3 - 2/9 = 0.
-1, -1/2, 1
Let h(v) be the first derivative of -v**4/2 - 38*v**3/3 + 20*v**2 + 248. Factor h(p).
-2*p*(p - 1)*(p + 20)
Suppose 16 = 2*b + 2*c, -48 = -5*b - 0*b - 3*c. Let a = -10 + b. What is f in 3*f**2 - 4 + 1 + f**a - 1 = 0?
-1, 1
Let q(b) be the third derivative of -b**7/525 + b**5/75 - b**3/15 + 84*b**2. What is s in q(s) = 0?
-1, 1
Let b = 342733/5634 + 35/626. Let s = b - 182/3. Solve -s*h**2 + 0 - 2/9*h = 0.
-1, 0
Let d = 2235/12287 - 1/12287. Solve -d*i**3 + 0*i**2 + 0 + 2/11*i**4 + 0*i = 0.
0, 1
Let s(n) = n**2 - 18*n + 34. Let t(g) = -6*g - 50. Let b be t(-11). Let v be s(b). Factor 0 - 2/5*q - 2/5*q**v.
-2*q*(q + 1)/5
Let k(o) be the third derivative of o**5/390 - 121*o**3/39 + 1005*o**2. Determine w, given that k(w) = 0.
-11, 11
Let b(h) be the third derivative of h**8/1680 - h**7/350 + h**5/75 + 47*h**2. Factor b(f).
f**2*(f - 2)**2*(f + 1)/5
Let d(g) = 287*g**2 - 204*g + 34. Let t be ((-48)/40)/(6/20). Let x(p) = 286*p**2 - 204*p + 33. Let a(o) = t*x(o) + 6*d(o). Let a(j) = 0. What is j?
6/17
Let y(h) = -15*h**3 - 8*h**2 - 5*h + 15. Let b(r) = 2*r**3 + 2*r**2 - r - 1. Let p(f) = 35*b(f) + 5*y(f). Suppose p(t) = 0. Calculate t.
2
Let k(i) be the first derivative of -12/7*i**3 - 2*i**2 - 33 + 8/7*i. What is u in k(u) = 0?
-1, 2/9
Let n(r) = -6*r**5 - 3*r**4 + 2*r**3 - 4*r**2 + 4*r + 2. Let q(x) = x**5 + x**4 - x. Let f = -21 + 20. Let c(l) = f*n(l) - 5*q(l). Factor c(b).
(b - 2)*(b - 1)**2*(b + 1)**2
Let b be 35/(-10)*36/(-21). Factor 48 - 3*l**3 + 21*l**2 - l + b*l**2 + 0*l**2 - 71*l.
-3*(l - 4)**2*(l - 1)
Let s(p) =