
(n - 1)*(n + 2)
Suppose -18 = -2*z - 2*z + 2*x, -4*z - x + 3 = 0. Let h be -2*(4/2 - 3). Factor -5*m + 8*m**z - 3*m + 2*m - h*m**3.
-2*m*(m - 3)*(m - 1)
Suppose 29 = 2*o + 5*p, 0 = 42*o - 47*o + p + 5. Let -1/7*c - 1/7*c**o + 2/7 = 0. What is c?
-2, 1
Let t(l) be the third derivative of l**5/45 - 4*l**4/9 - 55*l**2. Find a, given that t(a) = 0.
0, 8
Let f be (-9)/(-10 + 28) - 14/(-4). Let y(a) be the second derivative of 0*a**4 + 0 - 1/40*a**5 + 1/12*a**f - 3*a + 0*a**2. Let y(u) = 0. Calculate u.
-1, 0, 1
Let r(i) = 36*i**2 - 20*i + 16. Let x be (-22 - -34)*(-8)/6. Let f(l) = -4 - 7*l**2 + 2*l + 2*l + 1. Let b(w) = x*f(w) - 3*r(w). Let b(c) = 0. Calculate c.
0, 1
Factor 37 - 44*i + 21 + 4*i**2 - 12 - 6.
4*(i - 10)*(i - 1)
Let w(j) = -j**2 + j + 1. Let d(x) = -x**3 + x**2. Let b(r) = 4*r**3 - 4*r - 5. Let z(s) = b(s) + 5*d(s). Let l(p) = 15*w(p) + 3*z(p). Let l(m) = 0. What is m?
-1, 0, 1
Let w be (-8 + (-2)/2)*(-209)/627. Let 0 + 35/4*i**2 - 45/4*i**w - 5/4*i**5 + 25/4*i**4 - 5/2*i = 0. What is i?
0, 1, 2
Let y(o) be the third derivative of 0 + 0*o + 0*o**3 + 3*o**2 + 1/105*o**5 + 1/14*o**4. Suppose y(z) = 0. What is z?
-3, 0
Solve 20/3*h + 0 + 5/3*h**2 = 0 for h.
-4, 0
Factor -14*j**2 - 6*j**2 + 20*j**4 + 9*j**5 - 5*j**4 - 4*j**5.
5*j**2*(j - 1)*(j + 2)**2
Let l(j) = j**2 + j + 1. Let h(t) be the second derivative of -t**4/6 + 17*t**3/6 - 41*t**2 + 53*t. Let z(q) = 5*h(q) + 5*l(q). Factor z(w).
-5*(w - 9)**2
Let w be 3 + (7 - 3) - 4. Factor -36*a - 23*a**3 - 16*a**4 + 19*a**w - 4*a**5 + 12*a**3 + 48*a**2.
-4*a*(a - 1)**2*(a + 3)**2
Let u(m) be the third derivative of -m**7/210 - 13*m**6/480 - m**5/16 - 7*m**4/96 - m**3/24 + m**2 + 71*m. What is t in u(t) = 0?
-1, -1/4
Let b = 57 + -12. Let -16*c**3 - c**3 + 7*c**3 + b*c**4 = 0. Calculate c.
0, 2/9
Let u(h) be the third derivative of -h**5/75 - 31*h**4/15 - 1922*h**3/15 + 5*h**2 + 1. Factor u(a).
-4*(a + 31)**2/5
Suppose -9*g - 2*g = 23*g - 68. Suppose -1/2*i - 1/6*i**g - 1/3 = 0. Calculate i.
-2, -1
Let q(n) be the third derivative of n**7/70 - n**6/15 - 19*n**5/20 - 3*n**4/4 - 468*n**2. Factor q(t).
t*(t - 6)*(t + 3)*(3*t + 1)
Let l be (650/1560)/(23/(-14) - -2). Factor 0*m**2 + 0*m + 1/3*m**3 + 5/6*m**5 - l*m**4 + 0.
m**3*(m - 1)*(5*m - 2)/6
Factor -563*u**4 - 12*u**2 - 12*u + 4*u**3 + 566*u**4 - u**3.
3*u*(u - 2)*(u + 1)*(u + 2)
Let s(t) be the first derivative of t**6/15 + 2*t**5/25 - 3*t**4/10 - 2*t**3/3 - 2*t**2/5 - 64. Suppose s(h) = 0. What is h?
-1, 0, 2
Let c(w) = 1. Let t(o) = o**2. Let k be t(-2). Let p(z) = 4*z**2 - 8*z + 8. Let q(f) = k*c(f) - p(f). Factor q(b).
-4*(b - 1)**2
Let v be (-30)/(-21) - 164/(-287). Determine l, given that -1/2*l**4 + 0*l**v + 3/4*l**3 + 0*l + 0 = 0.
0, 3/2
What is s in 189*s**3 + 102*s**2 + 12*s - 243/2*s**4 + 0 = 0?
-2/9, 0, 2
Let z(f) = f**3 - 2*f**2 - 3*f - 5. Let d be z(4). Suppose 2*o - d + 2 = -r, o = -r + 8. Factor 6*p**r + p**2 - 2*p**3 - 4*p**4 + 0*p**2 - 2*p**2.
-p**2*(2*p - 1)**2
Suppose 159*b = -201*b + 90*b + 540. Factor 2*o - b*o**3 + 0 + 2/3*o**4 - 2/3*o**2.
2*o*(o - 3)*(o - 1)*(o + 1)/3
Let a(s) be the second derivative of -s**5/110 + 30*s**4/11 - 3600*s**3/11 + 216000*s**2/11 - 2*s - 156. Factor a(c).
-2*(c - 60)**3/11
Let o(k) be the second derivative of -k**7/84 + 5*k**6/24 - 53*k**5/80 + 29*k**4/48 + 11*k**3/24 - 5*k**2/4 - 10*k + 1. Determine s, given that o(s) = 0.
-1/2, 1, 10
Let b be -15 + 740/50 + (-3)/(-5). Solve 0*u + b*u**2 + 0 = 0.
0
Suppose -2*p - 2*f = 8, -3*f - f - 17 = 3*p. Suppose -2*u - p = 2*h + 1, -9 = -h + u. Factor 8*t**3 - 12*t - 7*t**4 + 4 + 4*t + 3*t**h.
-4*(t - 1)**3*(t + 1)
Let o(r) = 3*r**2 - 20*r - 18. Let m(d) = -d. Let z(b) = -5*m(b) + o(b). Factor z(u).
3*(u - 6)*(u + 1)
Let j = -640 + 2561/4. Let w(n) be the third derivative of 0*n**3 + 0 + 0*n - 1/20*n**5 + 8*n**2 + j*n**4. Factor w(c).
-3*c*(c - 2)
Let n(p) be the third derivative of p**6/6 + 5*p**5/12 + 5*p**4/24 + 165*p**2. Let n(d) = 0. Calculate d.
-1, -1/4, 0
Let l(c) be the second derivative of c**6/225 + c**5/75 - c**4/90 - 2*c**3/45 - 2*c - 2. Determine d so that l(d) = 0.
-2, -1, 0, 1
Solve -69*z**4 + 776*z**5 - 1592*z**5 - 6 - 9*z + 75*z**2 + 780*z**5 + 45*z**3 = 0.
-2, -1, -1/4, 1/3, 1
Let j(b) = 7*b**4 + b**3 - 99*b**2 - 189*b + 8. Let k(q) = -15*q**4 - 3*q**3 + 198*q**2 + 378*q - 18. Let l(p) = 9*j(p) + 4*k(p). Factor l(y).
3*y*(y - 7)*(y + 3)**2
Let q be 44/(-14) + 6 - (-3)/21. Let z(w) be the third derivative of -3*w**2 - 3/160*w**6 + 0*w + 0 + 1/20*w**5 + 1/12*w**q + 11/96*w**4. Factor z(i).
-(i - 2)*(3*i + 1)**2/4
Let x(g) be the third derivative of -7*g**2 + 0*g + 0*g**3 + 0*g**4 + 1/20*g**5 + 3/70*g**7 + 0 - 1/112*g**8 - 3/40*g**6. Factor x(t).
-3*t**2*(t - 1)**3
Let u(j) = -57*j**3 - 1386*j**2 + 2754*j - 1374. Let q(w) = 11*w**3 + 277*w**2 - 551*w + 275. Let n(c) = -21*q(c) - 4*u(c). Suppose n(h) = 0. Calculate h.
-93, 1
Let v(n) = -n**4 + 3*n**2 - 2*n. Let l = -15 + 19. Let x(g) = -2*g**4 + 7*g**2 - 13*g + 0*g**l + 8*g. Let d(a) = -5*v(a) + 2*x(a). Factor d(f).
f**2*(f - 1)*(f + 1)
Let i(g) be the third derivative of -g**5/120 + 17*g**4/48 - 5*g**3/2 + 192*g**2 - 1. Solve i(n) = 0 for n.
2, 15
Let z be (72/48)/(85/34). Factor -1/5*f**4 + 0 + f**2 - 1/5*f**3 - z*f.
-f*(f - 1)**2*(f + 3)/5
Let z(i) be the third derivative of -1/6*i**4 + 0 - 11*i**2 - 1/30*i**5 + 0*i + 1/20*i**6 + 0*i**3 + 1/105*i**7 - 1/168*i**8. Find f, given that z(f) = 0.
-1, 0, 1, 2
Let p(l) be the second derivative of 3*l**7/14 + 7*l**6/30 - l**5 + l**4/3 - 2*l + 28. Factor p(m).
m**2*(m - 1)*(m + 2)*(9*m - 2)
Let f(k) be the first derivative of k**6/30 - 2*k**5/5 + 5*k**4/4 + 4*k**3/3 - 8*k**2 - 3*k - 20. Let d(h) be the first derivative of f(h). Factor d(w).
(w - 4)**2*(w - 1)*(w + 1)
Factor 1/3*k**4 - k**2 + 7/3*k**3 + 50/3 - 55/3*k.
(k - 2)*(k - 1)*(k + 5)**2/3
Let x(i) be the first derivative of -3*i**4/8 - 13*i**3/2 - 117*i**2/4 - 81*i/2 + 37. Factor x(o).
-3*(o + 1)*(o + 3)*(o + 9)/2
Let t(d) = -11*d**4 - 35*d**3 + 30*d**2 + 16*d - 8. Let j(q) = 7*q**4 + 23*q**3 - 20*q**2 - 10*q + 5. Let x(y) = -8*j(y) - 5*t(y). Determine u so that x(u) = 0.
-10, 0, 1
Let p(i) be the third derivative of -i**6/240 - 19*i**5/120 - 33*i**4/16 - 27*i**3/4 - 2*i**2 + 11*i. Factor p(s).
-(s + 1)*(s + 9)**2/2
Find r such that -r + 1/6*r**2 - 8/3 = 0.
-2, 8
Let a(q) be the first derivative of q**6/24 + 7*q**5/20 + q**4 + q**3 + 39. Suppose a(h) = 0. What is h?
-3, -2, 0
Suppose -3*w + b + 426 = 0, -b = 2 + 1. Suppose w = -2*t + 145. Suppose 1/2 + 1/4*m**t - 3/4*m = 0. What is m?
1, 2
Let p(s) be the first derivative of 4*s**3/3 - 10*s**2 - 316. Solve p(f) = 0.
0, 5
Factor 13*d**3 + 280*d - 35*d**3 - 289*d - d**5 - 24*d**2 - 8*d**4.
-d*(d + 1)**2*(d + 3)**2
Let d = -13659 + 95633/7. Suppose 12/7 + 22/7*u + 0*u**2 - d*u**3 - 2/7*u**5 - 12/7*u**4 = 0. Calculate u.
-3, -2, -1, 1
Let b = 524 + -521. Let o(p) be the second derivative of 0 - 1/66*p**4 + 2/11*p**2 + 1/33*p**b - 4*p. Find h, given that o(h) = 0.
-1, 2
Let a(f) be the second derivative of f**5/90 - 7*f**4/36 + 2*f**3/3 + 23*f**2 - 36*f. Let q(l) be the first derivative of a(l). Factor q(p).
2*(p - 6)*(p - 1)/3
Suppose -3*i + 4*d = -39, -2*i = -2*d - 8 - 16. Suppose 0 = -28*h + i*h. Factor 0 - 5/2*o**3 + h*o - 5/2*o**4 + 0*o**2.
-5*o**3*(o + 1)/2
Let x = 13/1582 - -6289/4746. Factor -192 - 32*t - x*t**2.
-4*(t + 12)**2/3
Factor 2/3*w**3 + 0 + 1/12*w**4 - 8/3*w - 1/3*w**2.
w*(w - 2)*(w + 2)*(w + 8)/12
Let u(r) be the second derivative of -r**6/15 - 3*r**5/5 - 5*r**4/6 + 100*r. Factor u(c).
-2*c**2*(c + 1)*(c + 5)
Suppose -21 = 3*n - 6, 4*a + 3*n = -3. Factor -211*i + 223*i - 3*i**3 + 7*i**a - 16*i**2.
4*i*(i - 3)*(i - 1)
Let h(d) = -2*d**4 - 2*d**3 + 5*d**2 - d + 3. Let t(j) = j**4 + 2*j**3 - 5*j**2 + 2*j - 4. Let c(g) = 4*h(g) + 3*t(g). Factor c(f).
-f*(f - 1)*(f + 1)*(5*f + 2)
Suppose 0 = -4*c - 4 + 88. Find u, given that -5*u**2 - c*u - 106 - 19 - 29*u = 0.
-5
Let r = 74 - 71. Suppose 0 = -r*k + 15, 6*p - 2*k + 20 = 11*p. Solve -4/3*i - 1/3*i**p - 1 = 0.
-3, -1
Let m = 9 - 8. Let i(h) = -2*h**2 + 2*h - 6. Let j(n) = -6*n + 6. Let q(s) = 7*s - 7. Let a(x) = 6*j(x) + 5*q(x). Let d(y) = m*i(y) + 6*a(y). Factor d(w).
-2*w*(w + 2)
Let i(p) be the second derivative of 1/483*p**7 + 17*p + 0*p**2 - 2/69*p**3 + 1/46*p**4