*a - 8*a - 6. Let k be (-12)/8*2*a/(-12). Factor -k + 1/4*d - 1/4*d**3 + 1/4*d**2.
-(d - 1)**2*(d + 1)/4
Let a = -14 + 16. Find b such that 145*b**a - 143*b**2 + 1 - 3 = 0.
-1, 1
Suppose 2 = 4*s + 2*k, 2*k + 5 = 3*s - 7. Suppose s*y - 34 + 4 = -n, -2*n = 0. Factor 0 - 7 + 1 + 20*q**4 + 1 + 25*q**3 - 25*q - y*q**2.
5*(q - 1)*(q + 1)**2*(4*q + 1)
Let i(a) = 2*a**2 - 9*a - 37. Let z be i(13). Let p be (4/7)/(4 + z/(-56)). Solve -p*k + 8/5 - 4/5*k**2 = 0 for k.
-2, 1
Let y(o) = 9*o**3 - 7*o**2 - 12*o. Let j(w) = 19*w**3 - 14*w**2 - 25*w - 1. Let v = 47 + -38. Let l(h) = v*y(h) - 4*j(h). Factor l(z).
(z - 2)*(z + 1)*(5*z - 2)
Factor 312*n - 16224 - 3/2*n**2.
-3*(n - 104)**2/2
Let w(k) be the first derivative of -k**4/2 - k**3/3 - k**2/2 + k + 2. Let c be w(-2). Factor u**3 - 5*u**3 - 24*u + c*u**2 + 12 - 4*u**3 + 5*u**3.
-3*(u - 2)**2*(u - 1)
Suppose -5*k = -66 - 9. Let z(f) = -2*f**2 + 1 - 2*f**2 - 2*f**2 + 5*f**2. Let o(b) = 6*b**2 - b - 5. Let q(m) = k*z(m) + 3*o(m). Factor q(u).
3*u*(u - 1)
Let w(f) be the third derivative of f**5/390 + 3*f**4/26 - 304*f**2. Factor w(p).
2*p*(p + 18)/13
Let i be 12*(2/7)/(6/7). Let h(n) be the third derivative of i*n**2 + 0 + 0*n**3 - 1/8*n**4 + 0*n - 1/20*n**5. Find j such that h(j) = 0.
-1, 0
Let r = 4237/12 + -353. Let u(g) be the third derivative of 1/30*g**5 + r*g**4 + 0 + 0*g + 0*g**3 - 5*g**2. Let u(m) = 0. What is m?
-1, 0
Let g be -24*(-3 - (-28)/16). Let k = -28 + g. Find t such that -8*t - 44/5*t**3 - 66/5*t**2 - k*t**4 - 8/5 = 0.
-2, -1, -2/5
Let b(x) be the third derivative of x**6/60 + 3*x**5/10 + 5*x**4/3 - 382*x**2. Factor b(y).
2*y*(y + 4)*(y + 5)
Let 2*q + 50/3*q**2 + 0 = 0. Calculate q.
-3/25, 0
Solve 0 + 4/5*f**3 - 1/5*f**2 + 1/5*f**4 - 4/5*f = 0.
-4, -1, 0, 1
Let l be (6/(-8))/(6/(-40)). Let h(a) = a**4 + a**3 - a + 1. Let w(s) = 2*s**4 + 7*s**3 + s**2 - 5*s + 5. Let d(c) = l*h(c) - w(c). Factor d(x).
x**2*(x - 1)*(3*x + 1)
Suppose 5*c - 33 = 2*w - 8, 0 = 3*w. Let g(n) be the first derivative of 1/12*n**6 - 4/15*n**c - 1/12*n**2 + 0*n**3 + 8 + 1/4*n**4 + 0*n. Factor g(v).
v*(v - 1)**3*(3*v + 1)/6
Factor -21*g**2 - 4*g - 28*g**2 - 54*g**2 - 47*g**3 - 15*g**4 - 29*g**2 + 96*g**2.
-g*(g + 1)*(g + 2)*(15*g + 2)
Let s = -20 + 23. Find h, given that -87*h**2 + 71*h**2 - 5*h**s + 4*h**4 + 8*h + 12 - 3*h**3 = 0.
-1, 1, 3
Let v(i) be the first derivative of -i**3/18 + 17*i**2/3 - 578*i/3 - 30. Factor v(p).
-(p - 34)**2/6
Let m(w) = 2*w**2 - 44*w + 13. Let i(k) = k**2 - 22*k + 6. Let d(o) = 13*i(o) - 6*m(o). Determine z so that d(z) = 0.
0, 22
Let a(i) be the second derivative of -i**8/1120 - 4*i**7/315 + 13*i**6/360 + i**5/10 - 3*i**4/2 - 30*i. Let q(w) be the third derivative of a(w). Factor q(c).
-2*(c - 1)*(c + 6)*(3*c + 1)
Let t(z) be the third derivative of -z**6/540 - z**5/90 - z**4/54 - 107*z**2. Factor t(b).
-2*b*(b + 1)*(b + 2)/9
Suppose 1/2*l**4 + 3/2*l**5 + 6 - 23/2*l**3 + 4*l - 25/2*l**2 = 0. Calculate l.
-2, -1, 2/3, 3
Let t(i) be the third derivative of -i**7/630 + 2*i**6/45 - 8*i**5/15 + i**4/6 - 2*i**2. Let j(h) be the second derivative of t(h). Factor j(v).
-4*(v - 4)**2
Let j = 41 + 49. Let z be 0 + 111/j + 2/12. Find x, given that 0 - 2/5*x**3 + 0*x + x**4 + z*x**5 + 0*x**2 = 0.
-1, 0, 2/7
Let n(j) = -j**2 - 12*j - 3. Let u(f) = -12*f**2 - 132*f - 34. Let d(y) = 68*n(y) - 6*u(y). Solve d(c) = 0.
0, 6
Suppose -10 = -7*g + 11. Let w be g - (60/39 + 1). Factor w + 8/13*p + 2/13*p**2.
2*(p + 1)*(p + 3)/13
Let f(x) be the third derivative of -x**8/560 - x**7/140 - x**3/6 - 5*x**2. Let k(q) be the first derivative of f(q). Factor k(j).
-3*j**3*(j + 2)
Let r(h) = -9*h**2 - 7*h. Let c(o) = o**2 + 3*o - 5. Let j be c(2). Let v(w) = -26*w**2 - 22*w. Let p(f) = j*v(f) - 14*r(f). Factor p(q).
-4*q*(q + 3)
Let z be (-1 - 76/(-20)) + -3. Let v = z - -7/10. Find q, given that -3/4*q**3 + 0*q**4 + v*q**2 + 1/4*q**5 + 0*q + 0 = 0.
-2, 0, 1
Let z be ((-7)/21)/(2/(-12)). Factor i**z - 12*i + 18*i - 2 + i**2 - 6*i**3 + 0*i**3.
-2*(i - 1)*(i + 1)*(3*i - 1)
Let b = -21064 + 21064. Factor 3/4*m - 21/4*m**2 - 39/4*m**4 + b + 3*m**5 + 45/4*m**3.
3*m*(m - 1)**3*(4*m - 1)/4
Let s be 20 + (-60)/(-72) + (-20)/24. Factor -s*h**4 + 84*h**3 + 0*h + 4/3*h**5 + 0 - 196/3*h**2.
4*h**2*(h - 7)**2*(h - 1)/3
Factor 141*j + 8*j**2 - 17*j**2 - 3 + 3*j**3 - 132*j.
3*(j - 1)**3
Let z = 796 - 2386/3. Factor 2*v + z - 2/3*v**5 - 2*v**4 + 4/3*v**2 - 4/3*v**3.
-2*(v - 1)*(v + 1)**4/3
Suppose -34/3*o + 56/3*o**2 - 26/3*o**3 + 4/3 = 0. What is o?
2/13, 1
What is y in -10*y**2 - 18*y**3 + 20*y**3 + 90 - 16*y**2 + 62*y = 0?
-1, 5, 9
Let o = -283 - -283. Let s(q) be the second derivative of o*q**2 - 1/15*q**6 + 0 + 1/10*q**5 + 0*q**3 + 2*q + 0*q**4. Factor s(r).
-2*r**3*(r - 1)
Let r(g) be the second derivative of g**5/30 + 47*g**4/18 - 97*g**3/9 + 49*g**2/3 + 39*g + 1. Find l, given that r(l) = 0.
-49, 1
Suppose 0 = -5*m + 160 + 50. Find g such that -46 - m - g + 90 - g**2 = 0.
-2, 1
Factor 5*l - 84*l**3 + 35*l**4 + 5*l + 15*l**2 + 24*l**3.
5*l*(l - 1)**2*(7*l + 2)
Let -1/2*s + 11/4*s**2 + 0 + 169/4*s**4 + 105/4*s**3 + 77/4*s**5 = 0. What is s?
-1, -2/7, 0, 1/11
Let k be 32/128*(1 + (-7)/(-1)). Let r be (-9)/66*12/(-9). Suppose -r*h**3 - 10/11*h**k - 8/11 - 16/11*h = 0. Calculate h.
-2, -1
Let j(g) be the first derivative of -23 + 2/3*g**2 + 1/9*g**3 + 4/3*g. Find c such that j(c) = 0.
-2
Let y be 0 + 4 - 759/198. Factor -8/3 - y*w**2 + 4/3*w.
-(w - 4)**2/6
Let j(v) = -v**3 - 11*v**2 - 10*v + 3. Let q be j(-10). Let z = 98/99 + -6/11. Solve 28/9*o**4 + 76/9*o**2 + 10/3*o + 26/3*o**q + z = 0.
-1, -1/2, -2/7
Let t(c) be the third derivative of c**8/240 - c**7/70 - 2*c**6/9 + 2*c**5/5 + 5*c**4/8 + 20*c**2. Let o(y) be the second derivative of t(y). Factor o(a).
4*(a - 3)*(a + 2)*(7*a - 2)
Let r(x) be the third derivative of -7*x**2 + 0*x + 1/120*x**5 + 1/480*x**6 - 1/32*x**4 + 0*x**3 + 0. Factor r(f).
f*(f - 1)*(f + 3)/4
Let i(g) be the first derivative of -3*g**5/5 - 9*g**4/4 + 6*g**3 + 12*g**2 + 238. Let i(n) = 0. Calculate n.
-4, -1, 0, 2
Let o be (0 + (-4)/(-5))*50/4. Determine y so that -13*y**2 - 2*y**4 + 7*y**3 + 5*y**3 + o*y**2 - 4*y - 4*y**5 + y**2 = 0.
-2, -1/2, 0, 1
Let g(o) be the second derivative of o**6/120 - 3*o**5/40 + o**4/4 - 5*o**3/12 + 3*o**2/8 - 2*o - 21. Factor g(c).
(c - 3)*(c - 1)**3/4
Let y(k) = 2*k**3 + 3*k**2 - 22*k - 36. Let n(z) = z**3 - 2*z. Let h(s) = -n(s) - y(s). Suppose h(l) = 0. What is l?
-2, 3
Let q be 6/((-96)/(-92))*(-8)/(-1). Let w = q - 44. Let -1/4 + 3/4*r**w + 0*r + 1/2*r**3 = 0. Calculate r.
-1, 1/2
Suppose -121*w = -105*w - 48. Factor 3/8*i**4 + 0*i + 0 + 0*i**2 + 3/8*i**w.
3*i**3*(i + 1)/8
Determine a so that 14 - 3515*a + 3*a**2 + a**2 + 3545*a = 0.
-7, -1/2
Suppose 8/5 - 17/5*j - 1/5*j**3 + 2*j**2 = 0. What is j?
1, 8
Let y(i) be the third derivative of i**6/120 + 7*i**5/30 - 17*i**2 + 2. Factor y(v).
v**2*(v + 14)
Let q be (264/330)/((-3)/(-5)). Factor 0 - 4/3*t + q*t**2.
4*t*(t - 1)/3
Suppose -2*c - x + 52 = 15, -4*c + 3*x + 89 = 0. Factor 36*w**3 - 21*w**3 - c*w**3 - 15*w**2 + 20.
-5*(w - 1)*(w + 2)**2
Let g be (2*1/(-2))/(1/(-9)). Factor g*c - 52*c - 5*c - 2*c**3 - 9*c**2 + 27*c**2 + 40.
-2*(c - 5)*(c - 2)**2
Let o(g) be the first derivative of g**6/3 + 178*g**5 + 39605*g**4 + 14099380*g**3/3 + 313711205*g**2 + 11168118898*g + 143. Factor o(v).
2*(v + 89)**5
Let g be (4/(-3) - -2)/(4/30). Suppose -6*s + 5*w = -s - 20, -5*s - 8 = 2*w. Factor 6*k**4 - 3*k**5 - 5*k**3 + s*k**g + 4*k**3 - 2*k**3.
-3*k**3*(k - 1)**2
Let f(u) = -7*u**4 - 180*u**3 - 728*u**2 - 1184*u - 728. Let r(x) = -2*x**4 - 60*x**3 - 243*x**2 - 394*x - 243. Let k(s) = 3*f(s) - 8*r(s). Factor k(o).
-5*(o + 2)**3*(o + 6)
What is v in -1/9*v**2 + 0 - 26/9*v = 0?
-26, 0
Let q = -67/2 + 35. Let y(f) be the second derivative of -q*f**2 - 1/4*f**4 + 0 + 3*f + f**3. Factor y(r).
-3*(r - 1)**2
Factor 36/5*n - 24/5*n**2 - 1/5*n**4 + 0 - 11/5*n**3.
-n*(n - 1)*(n + 6)**2/5
Let j(n) = n**2 + 10*n - 8. Let p be j(-11). Suppose -5*w + p = u, -15 = -2*u + 4*w - 5*w. Factor k - 14*k**2 - 13*k + u + 18*k**2.
4*(k - 2)*(k - 1)
Let s(q) be the third derivative of 0*q - 1/140*q**7 + 1/224*q**8 + 1/16*q**4 - 1/40*q**6 + 0 + 8*q**2 + 1/20*q**5 - 1/4*q**3. Factor s(j).
3*(j - 1)**3*(j + 1)**2/2
Let x(j) be the third derivative of j**5/