*r + 4. Factor -3*q**2 - 5*q**2 + u*q**3 - 3*q**3 - 5*q - 2*q - 2.
-(q + 1)**2*(3*q + 2)
Let i(f) = f**2. Let u(w) = 8*w**2 - 2*w. Suppose -2*y - 1 - 1 = 0. Let l(k) = y*u(k) + 10*i(k). Factor l(b).
2*b*(b + 1)
Let c(t) = -t**3 + t**2 + t - 1. Let i(z) = -4*z**4 + 5*z**3 + 19*z**2 - 37*z + 17. Let a(g) = 5*c(g) + i(g). Factor a(j).
-4*(j - 1)**3*(j + 3)
Let r(u) = 32*u**4 - 48*u**3 + 18*u**2 - 2*u. Let y(n) = -96*n**4 + 144*n**3 - 54*n**2 + 6*n. Let f = 22 + -30. Let z(k) = f*r(k) - 3*y(k). Solve z(h) = 0.
0, 1/4, 1
Let d(w) = 6*w**3 - 2*w. Let q = 27 - 17. Let a = -6 + q. Let i(k) = -13*k**3 + k**2 + 5*k. Let t(r) = a*i(r) + 9*d(r). Factor t(b).
2*b*(b + 1)**2
Let t = -3 + 10. Let m = -5 + t. Solve r**3 + 8*r + 24*r**m - 2*r**3 + 11*r**3 = 0.
-2, -2/5, 0
Let t = 50 + -45. Factor 0*p**2 + 0 + 1/2*p**4 + 0*p**3 + 0*p - 1/2*p**t.
-p**4*(p - 1)/2
Let w(b) be the third derivative of b**8/112 + b**7/105 - b**6/30 - b**5/30 + b**4/24 - 4*b**2. Find v such that w(v) = 0.
-1, 0, 1/3, 1
Let 21/5*k**5 - 4/5*k + 34/5*k**4 - 16/5*k**2 + 1/5*k**3 + 0 = 0. What is k?
-1, -2/7, 0, 2/3
Let a(r) = -r**2 - 11*r - 6. Let u be a(-10). Factor -u*x**5 + 191 - 191 + 4*x**3 - 4*x**4 + 4*x**2.
-4*x**2*(x - 1)*(x + 1)**2
Let o(p) be the first derivative of p**8/1008 - p**7/315 + p**6/360 + p**2/2 + 2. Let s(t) be the second derivative of o(t). Factor s(z).
z**3*(z - 1)**2/3
Let o = 2/567 + 559/2268. Determine r so that 1/4*r**2 + 0 + 1/2*r - o*r**3 = 0.
-1, 0, 2
Suppose 6 = 2*i - 2. Let d(m) be the third derivative of 1/70*m**5 - 2/21*m**3 + 2*m**2 - 1/84*m**i + 0*m + 0. Factor d(h).
2*(h - 1)*(3*h + 2)/7
Let c(g) be the second derivative of g**7/84 - g**6/60 - g**5/40 + g**4/24 - 15*g. Factor c(i).
i**2*(i - 1)**2*(i + 1)/2
Let o(v) be the second derivative of -v**5/20 - v**4/12 + v**3/6 + v**2/2 - 7*v. Factor o(a).
-(a - 1)*(a + 1)**2
Let k = -447 - -452. Suppose 3*a**2 + 0 - 3/2*a - 3*a**4 + 0*a**3 + 3/2*a**k = 0. What is a?
-1, 0, 1
Let g be (-3)/(6/(-8)) - -2. Factor 3*k**2 + 4*k**2 + 7*k - g - 2*k + 4.
(k + 1)*(7*k - 2)
Let c(g) be the first derivative of 4/5*g + 2/15*g**3 - 5 - 3/5*g**2. Factor c(f).
2*(f - 2)*(f - 1)/5
Suppose -25 = 17*l - 22*l. Suppose -4*m - 2 = -3*s - 0, s = l*m - 3. Factor -4/3 - 2/3*j**2 + s*j.
-2*(j - 2)*(j - 1)/3
Let o(z) be the third derivative of -z**8/141120 + z**7/5880 - z**6/560 - z**5/20 - z**2. Let k(a) be the third derivative of o(a). Solve k(r) = 0 for r.
3
Let j(t) be the second derivative of 1/33*t**3 - 1/110*t**5 + 0 + 0*t**2 - 6*t + 0*t**4. Suppose j(u) = 0. What is u?
-1, 0, 1
Suppose 31*n + 45 = 107. Suppose 3/4 + 1/4*k**n + k = 0. Calculate k.
-3, -1
Solve 4/3*k**3 + 0*k + 0 + 8/3*k**2 = 0.
-2, 0
Factor -2*p**3 - 4*p + 638 + 6*p**2 - 638.
-2*p*(p - 2)*(p - 1)
Let j be 58/(-116) + 50/36. Factor 8/9*p + 2/3*p**2 + 2/9*p**4 - j*p**3 - 8/9.
2*(p - 2)**2*(p - 1)*(p + 1)/9
Let j(s) = -s**2 + s + 1. Let b(n) = 8*n + 6. Let t(c) = -b(c) + 2*j(c). Factor t(u).
-2*(u + 1)*(u + 2)
Let c(a) = -a + 1. Let i be c(2). Let p = 2 - i. Suppose -2/3*v**4 + 0 + 0*v + 1/3*v**p + 0*v**2 + 1/3*v**5 = 0. What is v?
0, 1
Let u(j) be the first derivative of -1/15*j**5 + 0*j - 1/72*j**6 - 1 - 1/2*j**2 - 1/9*j**3 - 1/8*j**4. Let v(x) be the second derivative of u(x). Factor v(m).
-(m + 1)**2*(5*m + 2)/3
Factor -2/3*j**2 + 0*j + 0 - 2/3*j**5 + 2/3*j**4 + 2/3*j**3.
-2*j**2*(j - 1)**2*(j + 1)/3
Let a(r) be the first derivative of r**5/210 - r**4/28 + 5*r**2 + 6. Let w(t) be the second derivative of a(t). Suppose w(k) = 0. Calculate k.
0, 3
Let u(f) = -4*f**3 + 7*f**2 - 2*f - 6. Let w(p) = 3*p**3 - 6*p**2 + 3*p + 6. Let d(m) = -6*u(m) - 7*w(m). Factor d(g).
3*(g - 2)*(g + 1)**2
Let g(p) be the first derivative of p**5/30 + p**4/6 + p**3/3 + 3*p**2/2 - 3. Let d(x) be the second derivative of g(x). Let d(f) = 0. What is f?
-1
Let f = 34/5 + -432/65. Factor f - 2/13*q**2 + 0*q.
-2*(q - 1)*(q + 1)/13
Let y(h) be the third derivative of -h**8/10080 - h**7/2520 + 2*h**5/15 + h**2. Let r(a) be the third derivative of y(a). Suppose r(k) = 0. What is k?
-1, 0
Let i(d) = d**3 - 9*d - 5. Let w be i(-4). Let z = w + 38. Let 1/4*p**z + 0 + 1/4*p**4 - 1/4*p**3 + 0*p - 1/4*p**2 = 0. Calculate p.
-1, 0, 1
Let n = 188/3 + -62. Factor n*q - 4/3 + 2*q**2.
2*(q + 1)*(3*q - 2)/3
Let h be (0 - -3)/(-3) + 5. Solve -3*c**5 + 2*c**3 - 21*c**2 + 8*c + 8 - 7*c**5 + 26*c**h - 13*c**2 = 0.
-1, -2/5, 1, 2
Let s(z) be the second derivative of 3*z - 3/2*z**4 + 0 + 7/10*z**5 + 0*z**2 + 2/3*z**3. Factor s(h).
2*h*(h - 1)*(7*h - 2)
Let u(w) be the first derivative of -1/12*w**3 + 0*w**2 + 4 + 1/4*w. Factor u(j).
-(j - 1)*(j + 1)/4
Suppose -3*n + 3*t + 18 = -3, -5*n = 2*t - 7. What is l in 4*l**3 - n*l**4 - 2*l + l**2 + 0*l + 0*l**4 = 0?
-2/3, 0, 1
Let n(c) = 24*c**3 + 33*c**2 + 6*c - 9. Let o(k) = k**3 - k - 1 - 4*k + 4*k + 3*k**2 - 4*k**2. Let j(h) = n(h) - 3*o(h). Solve j(q) = 0 for q.
-1, 2/7
Let i(l) be the second derivative of l**5/140 + l**4/21 + 5*l**3/42 + l**2/7 + l. Factor i(v).
(v + 1)**2*(v + 2)/7
Let c = -2/51 + 19/51. Let v = 33 - 97/3. Factor c*h**2 - 1/3*h - v.
(h - 2)*(h + 1)/3
Let t(q) be the third derivative of 2*q**7/105 + q**6/15 - q**4/3 - 2*q**3/3 + 4*q**2. Find y, given that t(y) = 0.
-1, 1
Let n(y) be the third derivative of -3*y**6/50 - y**5/5 - 7*y**4/30 - 2*y**3/15 + 2*y**2. Determine f, given that n(f) = 0.
-1, -1/3
Let r(g) = g**3 + 2*g. Let j(z) = 2*z**3 + 3*z. Let o(w) = 3*j(w) - 5*r(w). Factor o(c).
c*(c - 1)*(c + 1)
Factor 3/5*u**5 + 3/5*u**4 - 6/5*u**2 + 3/5*u - 6/5*u**3 + 3/5.
3*(u - 1)**2*(u + 1)**3/5
Determine c so that -16/3*c**2 + 8/3*c + 0 - 2/3*c**4 + 10/3*c**3 = 0.
0, 1, 2
Let s(p) be the second derivative of -3*p**5/80 - p**4/16 + p**3/8 + 3*p**2/8 + 13*p. Factor s(l).
-3*(l - 1)*(l + 1)**2/4
Let n(h) be the first derivative of 5/9*h**3 + 4/3*h - 4/3*h**2 - 1/12*h**4 - 1. Factor n(b).
-(b - 2)**2*(b - 1)/3
Let y = 1/4 + 0. Let j(b) be the first derivative of 1 + 5/8*b**2 + 3/16*b**4 - y*b - 7/12*b**3. Solve j(c) = 0 for c.
1/3, 1
Let v(d) be the third derivative of d**6/150 + 2*d**5/75 - d**4/30 - 4*d**3/15 - 28*d**2. Factor v(f).
4*(f - 1)*(f + 1)*(f + 2)/5
Let b(a) be the third derivative of 0*a**6 + 1/315*a**7 + 0*a**3 + a**2 - 1/90*a**5 + 0 + 0*a + 0*a**4. Suppose b(n) = 0. Calculate n.
-1, 0, 1
Factor -1/2*c**2 - 2 - 2*c.
-(c + 2)**2/2
Let d(a) be the second derivative of 7*a**4/36 - 5*a**3/18 - a**2/3 - 6*a. Determine v so that d(v) = 0.
-2/7, 1
Suppose -1 = 6*i - 13. Let h be ((-18)/15)/(6/(-20)). Suppose -1 + b**4 - 3*b**4 + 4*b**4 - 3*b**h + 2*b**i = 0. Calculate b.
-1, 1
Factor -9*z**2 + 3*z - 1/4.
-(6*z - 1)**2/4
Suppose 4*v - 14 = 2*a - 2, 4*v = -a + 12. Suppose -4*g**v - 3*g**3 + 4*g**3 + 3*g**4 = 0. Calculate g.
0, 1
Let f(s) be the third derivative of -s**8/144 - s**7/21 - 29*s**6/360 + 11*s**5/90 + s**4/2 + 4*s**3/9 + 10*s**2. Determine p so that f(p) = 0.
-2, -1, -2/7, 1
Let l be (6/(-9))/((-4)/12). Factor -89*o**3 - l*o**4 + 101*o**3 - 7*o**4 + 2*o + 11*o**2.
-o*(o - 2)*(3*o + 1)**2
Factor 3*r**3 + 3*r**5 - 5*r**4 - 2*r**4 + r**4.
3*r**3*(r - 1)**2
Suppose 0*q - 2 = 3*p + q, 5*p = -3*q - 6. Let n = -3/2 + 11/6. Factor -1/3*b**2 + p*b + n.
-(b - 1)*(b + 1)/3
Let x(d) be the third derivative of -d**8/560 + 4*d**7/175 - 11*d**6/100 + 6*d**5/25 - 9*d**4/40 - 10*d**2. What is m in x(m) = 0?
0, 1, 3
Let p = -40 - -42. Let m(w) be the third derivative of 0*w + 0 + 0*w**3 + p*w**2 - 1/150*w**5 - 1/30*w**4 + 1/525*w**7 + 1/150*w**6. Let m(r) = 0. Calculate r.
-2, -1, 0, 1
Suppose 2/5*n**3 - 12/5*n + 4/5 - 3/5*n**4 + 9/5*n**2 = 0. Calculate n.
-2, 2/3, 1
Suppose 2*p = 3*p + 6. Let t = p + 8. Factor t*x - 3*x**2 - 2 + 0*x + 2.
-x*(3*x - 2)
Let i be (-260)/(-364) + (0 - -1*1). Factor 9/7*o - i*o**2 + 3/7.
-3*(o - 1)*(4*o + 1)/7
Let g(m) be the second derivative of 2/15*m**6 + 1/6*m**4 - 7/20*m**5 + 1/6*m**3 + 10*m + 0 + 0*m**2. Factor g(p).
p*(p - 1)**2*(4*p + 1)
Let x(g) = -g**3 + 6*g**2 - 27*g + 16. Let i(a) = -a**2 - a. Let k(y) = -3*i(y) + x(y). Factor k(q).
-(q - 4)**2*(q - 1)
Factor -6/11*s**2 + 6*s - 60/11.
-6*(s - 10)*(s - 1)/11
Let k(c) be the first derivative of -3/20*c**4 + 0*c**2 + 10 + 2/15*c**3 + 1/25*c**5 + 0*c. Let k(f) = 0. Calculate f.
0, 1, 2
Suppose -4*y + 0*y = m - 10, 14 = 3*y + 4*m. Let -2*n - 4*n**2 + n**2 - n