). Let o(u) = -2*u**q + u**3 - 2*u - 6*u**3 + 2*u**2 + 3*u**3. Let r(s) = s**4 + 2*s**3 - s**2 + s. Let f(z) = 3*o(z) + 4*r(z). Factor f(l).
-2*l*(l - 1)**2*(l + 1)
Let q(t) = 14*t**2 + 12*t + 12. Let f(k) be the third derivative of k**5/60 + k**4/24 + k**3/6 - 2*k**2. Let i(x) = -12*f(x) + q(x). Factor i(o).
2*o**2
Let u(c) = -c**4 - 3*c**3 + 4*c**2 - 5*c - 5. Let h(v) = 2*v**4 + 2*v**3 - 4*v**2 + 6*v + 6. Let a(m) = 5*h(m) + 6*u(m). Factor a(j).
4*j**2*(j - 1)**2
Suppose p - 48 = 4*p. Let q be p/10 + -3 + 5. Factor -q*z - 4/5 + 2/5*z**2.
2*(z - 2)*(z + 1)/5
Suppose -4*i = 3*p - 2 - 2, -2*p - 2*i + 4 = 0. Factor 2/3 - 10/3*u - 20/3*u**3 + 20/3*u**2 + 10/3*u**p - 2/3*u**5.
-2*(u - 1)**5/3
Let s(f) be the second derivative of -f**7/168 + 3*f**5/80 - f**4/24 - 2*f. Factor s(g).
-g**2*(g - 1)**2*(g + 2)/4
Let i = -12 + 18. Suppose 3*b + 31 = 5*x + i, -3*x - b + 15 = 0. Find a, given that -1/3*a**x + 2/3*a**2 + 0 + 1/3*a + 0*a**3 - 2/3*a**4 = 0.
-1, 0, 1
Let x(v) be the first derivative of -2*v**5/35 + 2*v**3/21 + 11. Determine d so that x(d) = 0.
-1, 0, 1
Let o(b) be the third derivative of -b**6/24 - 3*b**5/4 - 25*b**4/8 - 35*b**3/6 + b**2 - 2. Let o(g) = 0. Calculate g.
-7, -1
Let x(d) be the third derivative of d**7/630 - d**6/180 + d**5/180 + 10*d**2. Factor x(k).
k**2*(k - 1)**2/3
Let p(v) be the third derivative of -v**10/4320 + v**9/15120 + v**8/5040 - v**5/60 - v**2. Let z(m) be the third derivative of p(m). Factor z(o).
-o**2*(5*o - 2)*(7*o + 2)
Let a(x) be the first derivative of -4 - 1/5*x - 1/15*x**3 + 1/5*x**2. Solve a(j) = 0.
1
Let b(p) = 5*p**3 - p**2. Let m(f) = f**3 - 2. Let h(o) = -o**3 + 1. Let s(i) = -2*h(i) - m(i). Let y(t) = -2*b(t) + 9*s(t). Factor y(z).
-z**2*(z - 2)
Let n be ((-55)/25 + (2 - 1))/(-3). Factor -2/5*c**2 - 2/5*c + n*c**3 + 2/5.
2*(c - 1)**2*(c + 1)/5
Let d = 10004/261 - -1/261. Let w = d - 38. Solve 0*p + 0 - w*p**2 = 0.
0
Suppose c**4 + 87*c - 3*c**2 - 2 - 85*c + 2 = 0. Calculate c.
-2, 0, 1
Let y(k) = k**2 + 0*k + 2*k + 0*k - 8 + 5. Suppose -5 = -3*d + 7. Let w(p) = -1. Let h(q) = d*w(q) - y(q). Factor h(x).
-(x + 1)**2
Let t(w) = -w**3 - 3*w**2 + 4. Let u be t(-3). Find x such that -5*x**u + 6*x**2 + 26*x**4 + 6*x**4 + 33*x**3 = 0.
-1, -2/9, 0
Determine r so that -2/3*r**2 + 7/6*r + 1/3 = 0.
-1/4, 2
Let o be (-1)/((-70)/22 + 2/11). Solve -2/3 - 1/3*b + o*b**2 = 0.
-1, 2
Let u = -16 + -19. Let g be ((-6)/u)/(6/20). Let -2/7*p**2 + g*p + 0 - 4/7*p**3 + 2/7*p**4 = 0. Calculate p.
-1, 0, 1, 2
Let g(y) be the second derivative of -3/2*y**2 + 0 + 3/2*y**5 + 2*y - 5/2*y**4 + 5/2*y**3 - 1/2*y**6 + 1/14*y**7. Factor g(k).
3*(k - 1)**5
Let j(n) be the third derivative of -1/3*n**3 + 0 - 1/8*n**4 - 1/60*n**5 + 0*n + 3*n**2. Let j(o) = 0. Calculate o.
-2, -1
Suppose -133*f = -129*f. Solve 1/3*l**2 - 2/3*l**3 + 0*l + 1/3*l**4 + f = 0.
0, 1
Let o(q) be the third derivative of -45*q**8/112 + 39*q**7/35 + q**6/40 - 7*q**5/2 + 11*q**4/2 - 4*q**3 - 5*q**2. Let o(n) = 0. Calculate n.
-1, 2/5, 2/3, 1
Let a(x) be the first derivative of -25*x**6/6 - 7*x**5 - 5*x**4/2 - 35. Factor a(i).
-5*i**3*(i + 1)*(5*i + 2)
Factor -2/3 + c**2 + 5/3*c.
(c + 2)*(3*c - 1)/3
Let h = -7 + 3. Let g = 7 + h. Factor -1 + 8 - g*d**2 + 0*d**2 - 1 + 3*d.
-3*(d - 2)*(d + 1)
Suppose -5*y = 5*f, 3*f + 2*f - 18 = y. Suppose -10*s = -11*s + f. Determine c, given that -2/3*c**2 + 2/3*c**s + 1/3 + 1/3*c**4 - 1/3*c - 1/3*c**5 = 0.
-1, 1
Let m(p) be the first derivative of -p**4/4 + 2*p**3/3 - p**2/2 + 1. Factor m(j).
-j*(j - 1)**2
Let n be (-39)/(-4) + 3/12. Factor 4*k**3 - 1 + 12*k**4 - 1 + 5*k**5 - n*k**2 - 8*k - k.
(k - 1)*(k + 1)**3*(5*k + 2)
Find j, given that -3/5*j**2 + 12/5*j - 12/5 = 0.
2
Let q = -182 - -537. Let i = q + -2481/7. Factor -2/7*f**2 + 2/7*f + i.
-2*(f - 2)*(f + 1)/7
Let a(j) be the second derivative of 4*j**5/225 + j**4/90 - j**3/45 + 2*j**2 - 9*j. Let i(m) be the first derivative of a(m). Factor i(r).
2*(2*r + 1)*(4*r - 1)/15
Suppose 2 + 10 = 4*h. Factor -4*x**3 - 6*x**4 + 2 + 4*x + h*x**2 - 2*x**5 + x**2 - 2*x + 4*x.
-2*(x - 1)*(x + 1)**4
Let g be -1 - 9/((-45)/5). Determine y so that 1/4*y**2 - 1/4 + g*y = 0.
-1, 1
Let b = -205/264 - -9/11. Let f(w) be the first derivative of -3/20*w**5 + 3/16*w**4 + 0*w**2 + 0*w + b*w**6 - 2 - 1/12*w**3. Suppose f(i) = 0. What is i?
0, 1
Let r(w) = -15*w**2 + 105*w - 142. Let o(l) = 10*l**2 - 70*l + 95. Let z(q) = 8*o(q) + 5*r(q). Find c such that z(c) = 0.
2, 5
Let p(q) = q - 1. Let s(z) = -z**2 + z - 4. Let k(x) = 5*p(x) + s(x). Suppose k(y) = 0. Calculate y.
3
Let y(f) be the third derivative of f**7/70 - 3*f**6/20 + 3*f**5/5 - 5*f**4/4 + 3*f**3/2 + 13*f**2. Factor y(n).
3*(n - 3)*(n - 1)**3
Suppose 153*x**3 + 80*x**4 + 6*x + 10*x + 4*x**3 + 112*x**2 + 55*x**3 = 0. What is x?
-2, -2/5, -1/4, 0
Let x(a) = -5*a**3 + 10*a**2 - a. Let q(h) = 10*h**3 - 20*h**2 + 3*h. Let t(j) = -4*q(j) - 7*x(j). Factor t(p).
-5*p*(p - 1)**2
Suppose -5*p - 8 = -4*i, -5 = -4*i - p + 3. Let w be i/(-5) - 6/(-15). Let 1/4*g**4 + 0*g**2 + 0 - 1/4*g**3 + w*g = 0. Calculate g.
0, 1
Factor 0 + 2/9*q**2 + 2/3*q.
2*q*(q + 3)/9
Let w(r) be the second derivative of -r**2 + 3/2*r**3 + 0 - 1/10*r**6 - 3*r + 11/20*r**5 - 5/4*r**4. Factor w(i).
-(i - 1)**3*(3*i - 2)
Let o = 7/13 + -9/65. Let p(i) be the first derivative of i**4 - 2/5*i**5 + 2 + i**2 - o*i - 4/3*i**3 + 1/15*i**6. Let p(q) = 0. Calculate q.
1
Factor 0 + 0*f - 1/2*f**4 - 1/2*f**3 + f**2.
-f**2*(f - 1)*(f + 2)/2
Let q(o) be the first derivative of -1/9*o**3 + 3 - 1/3*o - 1/3*o**2. Suppose q(x) = 0. Calculate x.
-1
Let a(g) be the second derivative of -g**2 - 1/3*g**3 + 1/24*g**4 + 0 - g + 1/60*g**5. Let d(p) be the first derivative of a(p). Factor d(o).
(o - 1)*(o + 2)
Let s(q) = -11*q**2 - 8*q - 4. Let v(j) = -2 - 6*j - 3*j**2 + 0*j**2 + 2*j - 3*j**2. Let r(n) = -4*s(n) + 7*v(n). Factor r(u).
2*(u + 1)**2
Find s such that -30*s**2 + 12*s**3 - 3/2 + 51/4*s = 0.
1/4, 2
Let w = -1137 + 1137. Factor 2/7*t**2 - 6/7*t + w.
2*t*(t - 3)/7
Let d(q) = 3*q + 58. Let j be d(-18). Let y be 5/2 + 1 + -2. Factor 0*g - 1/2*g**5 + 3/2*g**j + 1/2*g**2 - y*g**3 + 0.
-g**2*(g - 1)**3/2
Suppose -n**3 + 3*n**2 + 229*n - 1 + 2 - 232*n = 0. Calculate n.
1
Suppose 4*b - 4 = 3*f + 7, -3*b + 4*f + 10 = 0. Let r(i) be the first derivative of 1/3*i**4 - 1/3*i**b + 2 - 2/9*i**3 + 0*i. Factor r(g).
2*g*(g - 1)*(2*g + 1)/3
Let j = 3 - 3. Suppose 27 = u + 5*v, 23 = -u + 4*v + 5. Factor j*m**u + 4*m**2 - 2*m**2.
2*m**2
Suppose -5*s = -4*s - 7. Let j(a) = -3*a**2 - 15*a - 3. Let w(h) = 8*h + 3 - 2 - h + h**2. Let r(t) = s*w(t) + 3*j(t). Factor r(i).
-2*(i - 1)**2
Suppose 1 = 4*x + 3*r - 7, 0 = -5*x + r + 10. Let u(p) = p**3 + 9*p**2 + 2. Let n be u(-9). Factor x*f**2 - 2 - n*f + 2.
2*f*(f - 1)
Solve 1/3*p**2 + 2/3*p - 1/2*p**4 + 1/6 - 2/3*p**3 = 0 for p.
-1, -1/3, 1
Let m = 1/43 - -251/301. Factor 2/7 - 8/7*f**2 + m*f.
-2*(f - 1)*(4*f + 1)/7
Suppose 7 + 37 = 4*w. Let i(j) = -35*j**2 - 56*j - 10. Let g(y) = 7*y**2 + 11*y + 2. Let k(b) = w*g(b) + 2*i(b). Find x such that k(x) = 0.
-1, -2/7
Let g(o) be the first derivative of -3*o**5/5 - 3*o**4 - 4*o**3 + 11. Suppose g(n) = 0. What is n?
-2, 0
Let b(s) = -s**3 - 3*s**2 + 4*s - 3. Let j be b(-5). Factor -j*f**2 + 3*f**3 + 21*f**2 + 8 - 5*f**3.
-2*(f - 1)*(f + 2)**2
Let c(r) = -r**3 + 12*r**2 - 15*r + 6. Let j(u) = 3*u**3 - 48*u**2 + 60*u - 24. Let a(p) = 9*c(p) + 2*j(p). Let a(f) = 0. Calculate f.
1, 2
Suppose 28 - 1 = -3*l. Let m be 12/(-9)*l/6. Factor 0 - 2/7*d + 4/7*d**m - 2/7*d**3.
-2*d*(d - 1)**2/7
Let k(n) be the second derivative of n**7/2520 - n**6/360 - n**4/3 + 9*n. Let b(y) be the third derivative of k(y). Factor b(t).
t*(t - 2)
Find o such that -1/2*o**5 + 0*o**2 + 1/2*o**3 + 0 + 0*o + 0*o**4 = 0.
-1, 0, 1
Let g(n) = n**3 + 43*n**2 + 83*n + 44. Let s be g(-41). Let 2*o + 10/7*o**s - 2/7*o**4 - 4/7 - 18/7*o**2 = 0. What is o?
1, 2
Let d(u) be the first derivative of -u**6/3 - 6*u**5/5 - 3*u**4/2 - 2*u**3/3 - 32. Suppose d(z) = 0. What is z?
-1, 0
Let r(x) be the second derivative of x**8/2352 - x**7/1470 - x**6/420 + x**2 - 6*x. Let v(b) be the first derivative of r(b). What is k in v(k) = 0?
-1, 0, 2
Factor 2/5 - 1/5*u - 1/5*u**2.
-(u - 1)*(u + 2)/5
Factor 3*p**3 - 5*p**2 - 11*p**2 + 3 - 3*p + 0*p + 13*p**2.
3*(p - 1)**2*(p + 1)
Suppose w 