7
Let d = -4 + 9. Suppose -d*n = -n + 4. Let f(i) = i**2. Let y(p) = 15*p**2 + 27*p + 6. Let x(l) = n*y(l) + 3*f(l). Factor x(s).
-3*(s + 2)*(4*s + 1)
Suppose -8*t = 28 - 84. Suppose 12*s - t*s = 10. Suppose 3*d**3 + 0 + 21/2*d**s - 3/2*d**4 + 6*d = 0. What is d?
-1, 0, 4
Determine u, given that 23/7*u + 11/7*u**2 + 4/7*u**5 - 27/7*u**3 - 6/7 - 5/7*u**4 = 0.
-2, -1, 1/4, 1, 3
Let u(v) = 4*v**3 + 25*v**2 - 6*v + 15. Let n(r) = -9*r**3 - 51*r**2 + 14*r - 35. Let w(c) = -3*n(c) - 7*u(c). Factor w(t).
-t**2*(t + 22)
Let x = -7739 + 7743. Determine g so that -3/2*g + 0 - 3/2*g**3 + 1/4*g**x + 11/4*g**2 = 0.
0, 1, 2, 3
Let p(r) = 18*r - 7*r - 10*r. Let l(a) = a**2 - 27*a + 144. Let h(y) = -5*l(y) - 15*p(y). Factor h(i).
-5*(i - 12)**2
Let z(b) be the second derivative of 0*b**2 - 1/10*b**5 + 4/9*b**3 + 0 + 1/5*b**6 - 4/9*b**4 + 9*b. Factor z(i).
2*i*(i + 1)*(3*i - 2)**2/3
Suppose -4 = -5*i + n + n, 0 = -i - 2*n - 4. Factor 2/3*t - 7/3*t**2 + 8/3*t**3 - t**4 + i.
-t*(t - 1)**2*(3*t - 2)/3
Let v = 164648/5 - 32929. Suppose 24/5*n - 21/5*n**2 + 48/5 + v*n**3 = 0. Calculate n.
-1, 4
Let q(k) be the third derivative of -k**8/504 + 8*k**7/315 - 2*k**6/15 + 17*k**5/45 - 23*k**4/36 + 2*k**3/3 - 156*k**2. Determine z so that q(z) = 0.
1, 2, 3
Let 10109*a + 330*a**2 + 39*a**3 - 11393*a + 42*a**3 - 24*a**4 + 1080 - 3*a**5 = 0. What is a?
-9, -5, 2
Suppose -3*u - 2 = -u. Let j be u + 3 + 0 + (1 - 1). Suppose 3/4*c**j - 3/4*c - 3/2 = 0. Calculate c.
-1, 2
Let c(w) be the second derivative of 19*w - 1/4*w**4 + 0*w**2 + 0 + 1/2*w**3. Factor c(g).
-3*g*(g - 1)
Let h(l) = -l**2 - 12*l + 16. Let k be h(-13). Let z(t) be the first derivative of -8/15*t**k - 4 - t**2 - 2/5*t. Factor z(a).
-2*(a + 1)*(4*a + 1)/5
Let r(g) be the third derivative of 0*g**3 + 0 + 10*g**2 + 0*g**5 + 1/16*g**4 - 1/80*g**6 + 0*g. Determine f so that r(f) = 0.
-1, 0, 1
Let b(w) be the first derivative of -w**7/21 + 4*w**6/15 - w**5/2 + w**4/3 - 19*w - 16. Let h(o) be the first derivative of b(o). Factor h(c).
-2*c**2*(c - 2)*(c - 1)**2
Let w = 23 - 23. Let p be w - (9/(-3) + 0 + 0). Find z, given that 3/2*z**2 + 0 - z - 1/2*z**p = 0.
0, 1, 2
Factor 0 - 15/2*v + 47/4*v**2 - 3/4*v**3.
-v*(v - 15)*(3*v - 2)/4
Let r = -3/16 + 41/48. Let i be (1 + (-3)/7)/(4/14). Factor 0*z - r*z**i + 0.
-2*z**2/3
Solve -2/13*l**4 - 10/13*l + 6/13*l**2 + 2/13*l**3 + 4/13 = 0.
-2, 1
Suppose -9 = 5*m - 19. Factor 18*j**m + 33*j**3 - 5*j**3 - 26*j**2.
4*j**2*(7*j - 2)
Solve -225/4*t**2 + 3/8*t - 3/8*t**3 + 225/4 = 0.
-150, -1, 1
Suppose 0 = -0*y - 17*y + 51. Suppose 5*t = -z - y, -z - 5*t + 1 = 2*z. Factor n - 4/5*n**z - 1/5.
-(n - 1)*(4*n - 1)/5
Suppose -5*p - 2*z = -6, 6 = 2*p + 6*z - 7*z. What is o in 0*o - 15/7*o**4 + 3*o**3 - 6/7*o**p + 0 = 0?
0, 2/5, 1
Let t(k) be the third derivative of -k**8/504 + k**7/63 + 13*k**6/180 + 7*k**5/90 + 258*k**2. Factor t(v).
-2*v**2*(v - 7)*(v + 1)**2/3
Let 9*l**3 - 1453*l**5 + 1448*l**5 + 80 + 15*l**4 + 11*l**3 - 80*l**2 = 0. Calculate l.
-2, -1, 2
Let f be 6 - ((-1 - -1) + 1). Solve -b**f - 3*b**2 + 2*b**5 + 7*b**3 + 3*b**4 + 2*b - 4*b - 6*b**3 = 0 for b.
-2, -1, 0, 1
Factor -2*k**4 + 12*k**3 - 22*k**2 - 45*k - 82 - 23*k + 4*k**4 - 52*k + 282.
2*(k - 2)**2*(k + 5)**2
Suppose -4*g + 20 = 2*q, 18 = 4*q - g + 14. Factor 2/17*o**q + 4/17*o - 2/17*o**3 + 0.
-2*o*(o - 2)*(o + 1)/17
Let l(f) = -f**2 + 9*f. Let c(a) = -5*a**2 + 45*a - 1. Let m(w) = -2*c(w) + 11*l(w). Let g be m(9). Factor -y - 1/3*y**g + 0.
-y*(y + 3)/3
Let k(z) = -173*z - 3285. Let i be k(-19). Solve 76/7*r - 16/7*r**i + 20/7 = 0.
-1/4, 5
Let v(k) be the first derivative of 2*k**7/105 + k**6/10 + k**5/5 + k**4/6 - k**2 - 8. Let b(m) be the second derivative of v(m). Factor b(x).
4*x*(x + 1)**3
Let u(g) = -13*g**3 - 13*g**2 - 13*g + 33. Let p(y) = -9*y**3 - 15*y**2 - 14*y + 34. Let t(f) = 3*p(f) - 2*u(f). Factor t(o).
-(o - 1)*(o + 2)*(o + 18)
Let m(n) be the first derivative of n**4/2 - 20*n**3/3 + 17*n**2 - 16*n - 158. Solve m(o) = 0.
1, 8
Let s(p) be the first derivative of -2*p**3/9 + 64*p**2/3 + 130*p/3 + 26. Factor s(n).
-2*(n - 65)*(n + 1)/3
Find p such that 2/5 + 1/5*p**2 - 3/5*p = 0.
1, 2
Let 240/7 - 236/7*j - 4/7*j**2 = 0. Calculate j.
-60, 1
Suppose 2*w - 7*w - 61 = -3*p, 3 = -w - 4*p. Let j = 12 + w. Factor -4*c + 2*c**2 + j + 1 + 8*c.
2*(c + 1)**2
Let m be (-1)/(-2) - 21/(-6). Suppose -u + 8 = -2*q, u + u = -m*q - 8. Solve -2*o**2 + 43 - 43 + u*o = 0 for o.
0, 1
Find w, given that 4*w**3 - 4*w + 2*w**4 - 2*w**2 - 4*w**5 + 2*w**5 + 4*w**3 - 2*w**3 = 0.
-1, 0, 1, 2
Suppose 5*o + 2 = 6*o. Factor 5*l - 4*l + l**4 - 18*l**2 - l**3 + 17*l**o.
l*(l - 1)**2*(l + 1)
Let k = 6560/11 - 596. Find l, given that -k*l**2 - 2/11*l**4 + 0 + 6/11*l**3 + 0*l = 0.
0, 1, 2
Suppose 5*n + 9 = -3*m, -4*n - 3*m - 3 = -2*m. Let -2/13 + 2/13*u**2 + n*u = 0. Calculate u.
-1, 1
Let -8*q**2 + 65*q**4 - 4*q**5 + q**5 + 2*q**2 - 59*q**4 + 3*q = 0. What is q?
-1, 0, 1
Let -2*p**4 - 2/3*p**2 + 0*p + 0 - 8/3*p**3 = 0. What is p?
-1, -1/3, 0
Let s(q) = -3*q**3 - 9*q**2 + 8*q. Let b(c) = -3*c**3 - 8*c**2 + 7*c. Let r(k) = 7*b(k) - 6*s(k). Factor r(l).
-l*(l + 1)*(3*l - 1)
Let a(d) be the second derivative of d**7/7560 - 7*d**6/4320 + d**5/240 + 47*d**4/12 - 33*d. Let o(j) be the third derivative of a(j). Factor o(f).
(f - 3)*(2*f - 1)/6
Let i(y) be the first derivative of 0*y - 5/24*y**4 - 1 - 1/36*y**5 - 4*y**2 + 0*y**3. Let c(x) be the second derivative of i(x). Factor c(l).
-5*l*(l + 3)/3
Suppose -4*j + 2*j + 30 = 0. Solve j*k - 7*k**2 + 2*k**2 + 6*k**2 + 4*k**2 = 0.
-3, 0
Let m = 33/20 - -57/20. Factor 3*p**4 - m*p**3 - 6*p**2 + 0 + 3/2*p**5 + 6*p.
3*p*(p - 1)**2*(p + 2)**2/2
Suppose -a + 5*w + 43 - 35 = 0, 5*a - 13 = -2*w. Solve 2*b**a + 1/3*b**4 + 4*b**2 + 10/3*b + 1 = 0.
-3, -1
Let k be 5*(32/80 - 0). Factor -3/7*l**k - 3/7*l + 6/7.
-3*(l - 1)*(l + 2)/7
What is m in -2/9*m**2 + 2*m + 8 = 0?
-3, 12
Suppose 0*k + 4*b + 2 = 3*k, 2*k - 6 = -2*b. Determine r so that k + 2/3*r - 2/3*r**3 - 2*r**2 = 0.
-3, -1, 1
Let o(x) = 8*x**3 + 115*x**2 + 199*x + 137. Let t(g) = 2*g**3 + 28*g**2 + 50*g + 34. Let l(q) = 2*o(q) - 9*t(q). Suppose l(d) = 0. Calculate d.
-8, -2, -1
Suppose -4*z - 2*p + 5 = 1, 0 = -2*p - 8. Let x be ((-10)/3)/((-2)/3). Find y such that -7*y**z - 3*y**3 + 0*y**x + y**5 + 5*y + 4*y**5 = 0.
-1, 0, 1
Factor 5/4*p**2 + 14045/4 + 265/2*p.
5*(p + 53)**2/4
Suppose -456 = -5*r - 3*r. Let w = -53 + r. Factor 1/3*x**3 - 2/3*x**5 + 0 + 0*x**2 - 1/3*x**w + 0*x.
-x**3*(x + 1)*(2*x - 1)/3
Find c, given that -129*c**2 - 46*c**3 - 16 - 5*c**4 - 36*c - 44*c - 24*c = 0.
-4, -1, -1/5
Suppose -336 + 258 = -26*c. Factor 6/7*t + 0*t**2 - 2/7*t**c + 4/7.
-2*(t - 2)*(t + 1)**2/7
Let q(u) = 15*u**2 + u + 4. Let n be q(-2). Factor 4*a**3 - 27*a**4 - 31*a**4 + n*a**4.
4*a**3*(a + 1)
Let f(a) be the third derivative of -a**6/360 + a**5/30 + 2*a**3 - 15*a**2. Let b(s) be the first derivative of f(s). Factor b(d).
-d*(d - 4)
Let a be 24/588*-14*14/(-76). Suppose -2/19*x + a*x**3 + 0*x**2 + 0 = 0. Calculate x.
-1, 0, 1
Suppose -4*l = -2*t - 12, -18*t - 5*l + 32 = -12*t. Solve 8/5*r**3 + 2*r**t + 2/5*r**4 + 4/5*r + 0 = 0.
-2, -1, 0
Let l(g) = 2*g**2. Let k be l(-1). Let j = -39 + 41. Suppose -3 + d**j + 3 - 2*d - k*d**4 - d + 1 + 3*d**3 = 0. Calculate d.
-1, 1/2, 1
Let -20*w**4 - 24*w + w**2 + 4*w**5 + 25*w**2 + 4*w**2 - 10*w**2 + 20*w**3 = 0. Calculate w.
-1, 0, 1, 2, 3
Let s(a) be the first derivative of -4*a**5/5 + 4*a**4 + 8*a**3/3 - 24*a**2 - 36*a + 53. Find f such that s(f) = 0.
-1, 3
Suppose 2*f + 4*f - 42 = 0. Let q = 9 + f. What is l in 8*l - 33*l**2 - 2*l**3 + q*l**2 + 6*l**3 + 5*l**2 = 0?
0, 1, 2
Let c be 2/(-6) - 80*(-1)/24. What is m in 1/4 - 1/2*m**5 + 1/4*m**4 - 1/2*m + m**c - 1/2*m**2 = 0?
-1, 1/2, 1
Let b(s) = 2*s**3 - 15*s**2 + 21*s - 13. Let i(k) = k**3 - 8*k**2 + 11*k - 7. Let j(l) = 3*b(l) - 5*i(l). Factor j(h).
(h - 2)**2*(h - 1)
Let y be (1 + 6/(-5))/((486/36)/(-27)). Factor 0 + 0*s**3 - 2/5*s**2 + y*s**4 + 0*s.
2*s**2*(s - 1)*(s + 1)/5
Let p(r) be the first derivative of 3*r**4/4 + 15*r**3 - 3*r**2/2 - 45*r - 138. Find w such that p(w) = 0.
-15, -1, 1
Suppose 10*r = -r + 22. Let g(x) be the third derivative of 4*x**r + 0 - 1/480*x**6 + 0*x**4 - 1/240*x**5 + 0*x**3 + 1/420*x**7 + 0*x. Factor g(l).
l**2*(l - 1)*(2*l + 1)/4
Let q(h) =