- 4*n**4 - m*n**2 = 0. What is n?
-1, -1/4, 0, 2
Let a = 203 + -105. Let z be (a/(-7) - -11)*(-2)/4. Factor 1/4*r**2 - z*r + 9/4.
(r - 3)**2/4
Suppose m + 30 = -m. Let h = 19 + m. Factor 8*x**2 + 10*x**h - 5*x**2 + 5*x**2 + 8*x - 26*x**3.
2*x*(x - 2)*(x - 1)*(5*x + 2)
Let c = -24 + 34. Let j = -8 + c. Find z, given that -2 - z + j*z**2 + 7*z - 6*z**2 = 0.
1/2, 1
Let p(b) be the first derivative of -b**6/30 - 12*b**5/25 - 3*b**4/2 - 28*b**3/15 - 9*b**2/10 - 147. Determine l so that p(l) = 0.
-9, -1, 0
Suppose 25 = 6*c + 13. Let g(v) = -3*v**3 + 15*v**2 + 21*v + 3. Let r(m) = m**3 - 7*m**2 - 10*m - 2. Let k(u) = c*g(u) + 5*r(u). Factor k(a).
-(a + 1)*(a + 2)**2
Let z(g) be the third derivative of -3*g**5/4 - 2015*g**4/24 + 75*g**3 - g**2 - 37. Factor z(l).
-5*(l + 45)*(9*l - 2)
Let i = -17 - -11. Let w be (-1)/(-3) + (-16)/i. Determine x so that 3*x - w*x**3 - 3*x**4 - 2*x - x = 0.
-1, 0
Let f(g) be the second derivative of 13*g + 0 + 1/24*g**4 + 1/3*g**3 + g**2. Determine s so that f(s) = 0.
-2
Let d(a) be the first derivative of 4*a**3/3 - 600*a**2 + 90000*a - 446. Factor d(n).
4*(n - 150)**2
Let d(m) = 2*m**2 + 5*m - 1. Let o be d(-3). Factor 1 - 3 - 11 - 48*w - 23 + 9*w**o.
3*(w - 6)*(3*w + 2)
Suppose -2*b + 15 = 3. Suppose -2*r = -b*r. Factor -2 + 2 + r*i**3 + 2*i**2 + i + i**3.
i*(i + 1)**2
Let 225/2 - 7*s**2 - 1/4*s**3 - 165/4*s = 0. Calculate s.
-15, 2
Let p = 452 - 3160/7. Let a(i) be the first derivative of -p*i**2 - 10/21*i**3 + 8/7*i + 3/14*i**4 - 6. Factor a(g).
2*(g - 2)*(g + 1)*(3*g - 2)/7
Let b(t) = -t**3 + 3*t**2 + 6*t - 6. Let h be b(4). Find a, given that 27*a - 2*a**3 - a**3 - 11*a**2 + 2*a**h - 15 = 0.
-5, 1
Let g be (-231)/(-242) + (-18)/(-33). Let d(x) be the first derivative of 0*x**3 - g*x**2 + 0*x + 3/4*x**4 + 6. Find w, given that d(w) = 0.
-1, 0, 1
Suppose 3*r - 19 = 5*t, r - 9 = -t + 4*t. Suppose x - 4*x = -r. Find n such that 3 - 3 - x + n - 3*n - n**2 = 0.
-1
Let a(v) = v + 39. Let p be a(-33). Let d(b) be the second derivative of 0 + 0*b**4 - 1/20*b**p + 0*b**3 + 2*b + 0*b**5 + 0*b**2. Factor d(u).
-3*u**4/2
Let l(w) be the first derivative of -8 - 1/4*w**4 - 3/2*w**3 + 0*w**2 + 5*w. Let t(u) be the first derivative of l(u). Find g such that t(g) = 0.
-3, 0
Let m be (1/(-9))/((-10)/60). Let b be ((-4)/(-18))/(-2 - (-50)/24). Suppose b + 8/3*i + m*i**2 = 0. Calculate i.
-2
Let z(t) be the second derivative of -t**5/120 - 2*t**4/9 - 13*t**3/9 - 4*t**2 + 29*t - 1. Solve z(o) = 0 for o.
-12, -2
Factor -5*o**4 + 2797*o**2 - 60*o**3 - 240 - 400*o + 2738*o**2 - 5775*o**2.
-5*(o + 2)**3*(o + 6)
Suppose n + 13 = 3*d, -d + 6*d - 11 = -n. Suppose -4*g + 5 = -d. Factor 3*b**4 - b**2 - 2*b**3 + 4*b**2 - 2*b**3 - g*b**3.
3*b**2*(b - 1)**2
Let x(l) be the third derivative of 17*l**7/1050 - l**6/6 + 47*l**5/100 + 3*l**4/20 + 2*l**2 + 40. Let x(c) = 0. What is c?
-2/17, 0, 3
Let f(q) be the third derivative of q**7/126 - q**6/36 + q**5/36 - 51*q**2. Suppose f(z) = 0. Calculate z.
0, 1
Let n(g) = g**4 + 7*g**3 - 5*g**2 + g - 8. Let i(k) = 2*k**4 + 13*k**3 - 11*k**2 + 3*k - 14. Let y(z) = 4*i(z) - 7*n(z). What is q in y(q) = 0?
-5, 0, 1
Let w = 9 - 7. Suppose -3*v + w = -4. What is q in 5*q**3 - 2 + 7*q**5 - 10*q + 15*q**4 - q**5 - q**4 - 12*q**v - q**3 = 0?
-1, -1/3, 1
Let u = 22 - 64. Let k be -4*2/(-40) + u/(-15). Factor -3/7*h**k + 3/7*h**5 + 0*h**2 + 0*h + 0 + 0*h**4.
3*h**3*(h - 1)*(h + 1)/7
Let m be (-12 + 11)*(-1 - 4). Suppose 4*q + 13 = 7*q + 2*k, -25 = -5*q - m*k. Factor 2*n**2 + 3*n**2 + 6*n - q*n**2 - 8.
2*(n - 1)*(n + 4)
Suppose 9 = -2*b + 99. Let i(w) = -9*w**3 - 40*w**2 - 80*w - 4. Let u(n) = 100*n**3 + 440*n**2 + 880*n + 45. Let g(a) = b*i(a) + 4*u(a). Factor g(k).
-5*k*(k + 4)**2
Factor -10/7 + 2/7*r**2 - 8/7*r.
2*(r - 5)*(r + 1)/7
Let p = 67 + -96. Let f be 1/(-4)*(1 - p)/(-2). Find w, given that -3/4*w**3 - f*w + 3/2 + 3*w**2 = 0.
1, 2
Let s = -21311 - -149181/7. Factor -s*p**2 - 36/7 - 24/7*p.
-4*(p + 3)**2/7
Let h(k) be the first derivative of k**7/420 - k**6/45 + k**5/20 + 26*k**3/3 + 15. Let q(y) be the third derivative of h(y). Let q(i) = 0. What is i?
0, 1, 3
Let f(m) = 3*m - 52. Let b be f(18). Let 6/5*x - 4/5 - 2/5*x**b = 0. Calculate x.
1, 2
Let l(d) be the third derivative of -10/3*d**3 - 8*d**2 + 1/12*d**5 + 5/6*d**4 - 1/24*d**6 + 0 + 0*d. Let l(q) = 0. Calculate q.
-2, 1, 2
Let r(n) be the first derivative of n**3/9 + 55*n**2/6 + 18*n + 221. Determine d so that r(d) = 0.
-54, -1
Suppose 0 = 3*v + t + 5 + 8, 0 = -v - 3*t - 7. Let c be (5/2)/((35/v)/(-7)). What is w in -18/7*w**3 + c*w**4 + 0 + 8/7*w - 24/7*w**2 = 0?
-1, 0, 2/7, 2
Let p(c) be the second derivative of 1/6*c**4 + 0 + 24*c - 1/30*c**5 - 2/9*c**3 + 0*c**2. Solve p(r) = 0.
0, 1, 2
Let r(k) be the second derivative of -k**9/10584 - k**8/1960 - k**7/1470 + 5*k**3/3 - 15*k. Let n(a) be the second derivative of r(a). Solve n(d) = 0 for d.
-2, -1, 0
Let 78/5 + 6/5*s**2 + 84/5*s = 0. Calculate s.
-13, -1
Suppose -b + 0*b = 2*b. Suppose 13*x = -b*x. Factor x - 2/9*u**2 + 8/9*u.
-2*u*(u - 4)/9
Let w(x) be the first derivative of 0*x + 1/6*x**2 - 5 + 2/9*x**3 + 1/12*x**4. Determine l so that w(l) = 0.
-1, 0
Let b(h) = -7*h**5 - 18*h**4 - 4*h**3 + 6*h**2 + 11*h + 3. Let l(d) = d**5 + 2*d**4 + 2*d**2 - d - 1. Let x(t) = b(t) + 3*l(t). Find f such that x(f) = 0.
-2, -1, 0, 1
Let 242*d - 8000 - 2277*d**2 + 2272*d**2 + 118*d + 40*d = 0. What is d?
40
Let f(q) = -q + 2. Let s be f(1). Suppose -1 + s + 3*i**2 + 1 - 9*i + 5 = 0. What is i?
1, 2
Let s(r) be the first derivative of 7*r**3/2 + 297*r**2/2 + 84*r - 241. Factor s(y).
3*(y + 28)*(7*y + 2)/2
Suppose i + 4 = 3*i. Suppose 30 - 36 = -i*w. What is c in 4/3*c**w + 0 - 4/3*c**2 + 0*c = 0?
0, 1
Let x be -4 + 0/1 + 16. What is u in 7*u**4 + 8*u**4 - 18*u**4 - 3 + x*u - 18*u**2 + 12*u**3 = 0?
1
Suppose -11*i - 40 = -i. Let y be i + ((-62)/(-7) - 1) + 0. Let 9/7*m**4 + y*m**2 - 6/7*m - 30/7*m**3 + 0 = 0. Calculate m.
0, 1/3, 1, 2
Let f be 5*45/(-36) - -7. Solve -f*n + 0 + 3/4*n**2 = 0 for n.
0, 1
Let k be (-396)/(-189) + -1 + -1. Let c(s) be the first derivative of 0*s + 8 + k*s**3 - 1/7*s**2. Factor c(w).
2*w*(w - 1)/7
Solve 128/5*h + 32/5 - 833/5*h**4 + 1687/5*h**3 - 1014/5*h**2 = 0.
-2/17, 4/7, 1
Let c = -173 - -171. Let t be (c*1/4)/((-2)/12). Factor 0*b**2 + 0 + 8/7*b - 6/7*b**t - 2/7*b**4.
-2*b*(b - 1)*(b + 2)**2/7
Let p = 16/2035 + 1612/2035. Factor -p*u**2 + 0 + 8/5*u.
-4*u*(u - 2)/5
Let 38/7 - 2/7*n - 38/7*n**2 + 2/7*n**3 = 0. What is n?
-1, 1, 19
Let p be -6*((-5)/9 + 2/9). Suppose 0 = -4*c - 5*u - 5, u = c - p*c - 1. Factor 0*v + 0 + 2*v**4 + c*v**2 + 1/2*v**3.
v**3*(4*v + 1)/2
Suppose 4/3*m**4 - 2*m**3 + 0*m + 0*m**2 + 2/3*m**5 + 0 = 0. What is m?
-3, 0, 1
Let l(c) be the third derivative of 1/420*c**7 + 0 + 1/48*c**4 - 4*c**2 + 0*c - 1/40*c**5 - 1/240*c**6 + 1/6*c**3. Let l(y) = 0. What is y?
-1, 1, 2
Suppose -2*t - 46 = -5*t + 4*r, 4*t - 54 = -2*r. Let z = 17 - t. Suppose x**5 - 3*x**2 + 2*x**2 - 4*x**4 + z*x**3 + 0*x**2 + x**4 = 0. Calculate x.
0, 1
Let m(d) be the third derivative of d**10/7560 + d**9/3780 + 17*d**4/24 + 28*d**2. Let g(v) be the second derivative of m(v). Find c, given that g(c) = 0.
-1, 0
What is g in -28/9*g**5 - 212/9*g**3 + 124/9*g**2 + 0*g - 16/9 + 44/3*g**4 = 0?
-2/7, 1, 2
Let p(k) be the second derivative of -k**6/320 + 3*k**5/80 - 9*k**4/64 - 5*k**2/2 + k. Let i(y) be the first derivative of p(y). Let i(m) = 0. What is m?
0, 3
Let m = 40 - 38. Suppose 5*c - 5*c + 8 + 10*c + 0*c**m + 2*c**2 = 0. Calculate c.
-4, -1
Let w = -18 - -22. Factor 48*l - 221*l**2 - 423*l**4 + 295*l**3 - 36*l**4 + 43*l**3 - w + 135*l**5 + 139*l**3.
(l - 2)*(3*l - 1)**3*(5*l - 2)
Suppose -15*l + 13 = -62. Let m(i) = -10*i**3 - 5*i. Let b(p) = p**3 + p. Let h(w) = l*b(w) + m(w). Factor h(u).
-5*u**3
Let 55*r**3 + 3*r**4 + 408 - 54*r - 49*r**3 - 36*r**2 - 327 = 0. What is r?
-3, 1, 3
Let q(u) be the second derivative of 5*u**4/12 - 10*u**3/3 + 69*u. Determine c, given that q(c) = 0.
0, 4
Let g = -129/26 + 723/130. Factor 0 + g*f + 3*f**2.
3*f*(5*f + 1)/5
Let s(p) be the first derivative of p**6/90 + p**5/150 - p**3 - 8. Let o(j) be the third derivative of s(j). Factor o(a).
4*a*(5*a + 1)/5
Let u(d) be the third derivative of -d**8/112 + d**7/10 - 3*d**6/20 + 50*d**2 + 1. Factor u(w).
-3*w**3*(