for d.
-1
Let v(p) be the first derivative of p**3/3 - p**2 + p - 9. Factor v(j).
(j - 1)**2
Suppose 5 = 3*s + 2. Factor -2*h**2 + 0 + s - 4 - h**2 + 6*h.
-3*(h - 1)**2
Let o = 114 + -112. Determine c, given that 2/3*c**o + 4/3 - 2*c = 0.
1, 2
Let n be (-12)/(-168) + 3/6. Determine m, given that 0 + 2/7*m**2 + n*m = 0.
-2, 0
Let v be 22/(-77) - (-8)/14. Solve -4/7*l**2 + 4/7*l**3 - 2/7*l + 2/7 - 2/7*l**5 + v*l**4 = 0 for l.
-1, 1
Let p(l) be the first derivative of 5 + 0*l**2 + 0*l - l**3 + 0*l**4 + 3/5*l**5. Factor p(c).
3*c**2*(c - 1)*(c + 1)
Let z(m) be the second derivative of -m**6/15 + m**5/5 + 2*m**4/3 - 2*m**3/3 - 3*m**2 - 13*m + 1. Suppose z(l) = 0. Calculate l.
-1, 1, 3
Let r(a) be the second derivative of a**6/200 - a**4/30 + 2*a**3/3 + 2*a. Let p(q) be the second derivative of r(q). Factor p(t).
(3*t - 2)*(3*t + 2)/5
Let c(i) = -3*i**3 - 5*i**2 - 7*i + 5. Let g(q) = 4*q**3 + 6*q**2 + 8*q - 6. Let j(h) = 6*c(h) + 5*g(h). Find r, given that j(r) = 0.
-1, 0, 1
Suppose 4*w + 4*c - 25 + 5 = 0, 5*w + c - 5 = 0. Determine l so that -2*l - 5 + 5 + w*l + 2*l**3 = 0.
-1, 0, 1
Let q = 13/9 + -7/9. Suppose 0 = 2*x + 2*x. Factor 0 + 0*k**4 + 0*k**2 + 2/3*k**3 + x*k - q*k**5.
-2*k**3*(k - 1)*(k + 1)/3
Suppose -r = 8*r - 27. Let s(h) be the second derivative of -4/5*h**2 + 4/15*h**3 - r*h - 7/15*h**6 + 0 - 2/25*h**5 + 13/10*h**4. Solve s(c) = 0 for c.
-1, -2/5, 2/7, 1
Let g be 12/8 - (-12)/(-9). Let -1/6*o**4 + g*o + 1/6*o**5 + 1/3*o**2 - 1/6 - 1/3*o**3 = 0. Calculate o.
-1, 1
Let q = 29 + -45. Let j be ((-3)/(-1))/((-36)/q). Solve 0 - 2/3*g**2 + j*g = 0 for g.
0, 2
Let d = 651/524 + 1/131. Solve -1/4*q + 1/2 + 3/4*q**4 - d*q**2 + 1/4*q**3 = 0.
-1, 2/3, 1
Let j(y) be the third derivative of -y**7/4410 + y**6/2520 + y**4/3 + 7*y**2. Let p(r) be the second derivative of j(r). Determine x, given that p(x) = 0.
0, 1/2
Let w(c) be the third derivative of c**5/20 - c**4/3 + 2*c**3/3 + 9*c**2. Suppose w(f) = 0. Calculate f.
2/3, 2
Let t(n) be the second derivative of 2*n**6/5 - 3*n**5/20 - n**4 + n**3/2 - 12*n. Factor t(k).
3*k*(k - 1)*(k + 1)*(4*k - 1)
Solve 2/5*y**2 + 2/5 - 4/5*y = 0 for y.
1
Let p be (-27)/(-27) + 2/6. Factor p*k + 2/3 + 2/3*k**2.
2*(k + 1)**2/3
Let d(f) = -f**3 + 7*f**2 - 7*f + 9. Let g be d(6). Let t(q) be the second derivative of 1/5*q**5 - q + 0 + q**2 + 0*q**4 - 1/15*q**6 - 2/3*q**g. Factor t(n).
-2*(n - 1)**3*(n + 1)
Let v(l) be the second derivative of l**8/5880 - l**6/1260 - 5*l**3/6 + 7*l. Let o(u) be the second derivative of v(u). Let o(h) = 0. What is h?
-1, 0, 1
Suppose -2*g - 18 = -2*v - 2*v, 0 = 5*g - v + 9. Let d = g + 3. Factor 8*a**5 + d*a**2 + 12*a**3 + 8*a**4 - 2*a**4 + 12*a**4.
2*a**2*(a + 1)**2*(4*a + 1)
Let d(g) be the third derivative of 2*g**2 + 1/945*g**7 + 0*g**4 + 0*g**3 - 1/270*g**5 + 0*g**6 + 0*g + 0. Factor d(s).
2*s**2*(s - 1)*(s + 1)/9
Let i = 8 - 5. Let h(y) be the second derivative of 0*y**i + 0 + 0*y**2 - 2*y + 1/6*y**4. Factor h(o).
2*o**2
Let m(g) = -g**2 + g. Let j(x) = -4*x + 4. Let b be 2/((4 - 1) + -4). Let h(q) = b*m(q) - j(q). Find z such that h(z) = 0.
-2, 1
Let t be (40/24)/((-15)/(-36)). Let z(l) be the second derivative of 1/8*l**t + 0 - 1/2*l**2 + 3*l + 1/12*l**3. Let z(p) = 0. Calculate p.
-1, 2/3
Let 0 - 1/6*g**4 - 1/6*g**2 + 1/3*g**3 + 0*g = 0. Calculate g.
0, 1
Let m(z) be the third derivative of z**7/840 - z**6/160 - z**5/240 + z**4/32 - 5*z**2. Factor m(x).
x*(x - 3)*(x - 1)*(x + 1)/4
Let h(f) be the first derivative of -f**3/12 + 3*f**2/8 - 1. Solve h(k) = 0 for k.
0, 3
Let m(l) = -5*l**3 - l**2. Let y(f) = f**2 - 6*f - 8. Let s be y(7). Let x(r) = r**3. Let a(u) = s*m(u) - 6*x(u). Factor a(k).
-k**2*(k - 1)
Find f, given that -3/4*f**2 + 1/4*f**4 + 0*f**3 + 0 - 1/2*f = 0.
-1, 0, 2
Suppose 0 = 2*m - 3*m. What is n in -2/5*n**3 + m*n - 2/5*n**2 + 0 = 0?
-1, 0
Suppose -x - 5 = -4*q, -q = -4*q + 15. Let k be (-6)/(-15) + 39/x. Find g such that -k*g**3 - 25*g**2 + g**3 + 23*g**2 = 0.
-1, 0
Let b(u) be the third derivative of -u**9/80640 + u**8/20160 - u**7/20160 - u**5/12 + 6*u**2. Let a(o) be the third derivative of b(o). Factor a(p).
-p*(p - 1)*(3*p - 1)/4
Suppose -7 = 4*z - 23. Let n(a) = 4*a**2 + a + 7. Let x(k) = -3*k**2 - k - 6. Let p(m) = z*n(m) + 5*x(m). Find y such that p(y) = 0.
-1, 2
Let a = 33 + -31. Let f(i) be the first derivative of -2/3*i**3 - a + 0*i + 0*i**2. Suppose f(z) = 0. Calculate z.
0
Let -27/4 - 1/4*i**3 - 9/4*i**2 - 27/4*i = 0. What is i?
-3
Let h(a) be the first derivative of a**6/3 - 2*a**5/5 - 3*a**4/2 + 2*a**3/3 + 2*a**2 - 25. Suppose h(c) = 0. What is c?
-1, 0, 1, 2
Factor -2/5 + 4/5*d**3 + 0*d**2 + 2/5*d**4 - 4/5*d.
2*(d - 1)*(d + 1)**3/5
Solve -2/3*v**2 + 2/3 + 2/9*v - 2/9*v**3 = 0 for v.
-3, -1, 1
Solve 34*h**3 + 21*h - 12*h**2 - 6 - 19*h**3 - 3*h**4 + 4*h**2 - 19*h**2 = 0 for h.
1, 2
Find p, given that -8*p - 2*p**2 + 3*p**2 + 12*p + 3 = 0.
-3, -1
Let q(o) = -o**2 + o + 1. Let g(b) = -b**3 + b**2 + 2*b - 3. Let n(x) = -g(x) - q(x). Factor n(i).
(i - 1)**2*(i + 2)
Let w(q) = -3*q + 26. Let g be w(8). Factor -g*p**3 + 6*p**2 + 4 - 8*p + 1/4*p**4.
(p - 2)**4/4
Let y = -1/49 + 149/98. Let h(z) be the second derivative of 4*z - y*z**2 + 1/2*z**3 + 0 + 1/2*z**4. What is m in h(m) = 0?
-1, 1/2
Let t(p) be the second derivative of p + 0*p**2 + 0 + 3/10*p**5 + 1/3*p**3 + 1/2*p**4 + 1/15*p**6. Factor t(z).
2*z*(z + 1)**3
Let p = -27/20 - -8/5. Solve -1/4*y**3 + 1/4*y + 1/4*y**2 - p = 0 for y.
-1, 1
Let l(j) be the third derivative of -1/24*j**3 - 1/240*j**6 + 1/240*j**5 - j**2 + 1/48*j**4 + 0 + 0*j. Factor l(i).
-(i - 1)*(i + 1)*(2*i - 1)/4
Factor -4/9*f + 2/9 + 2/9*f**2.
2*(f - 1)**2/9
Let q be -3 - (25/(-20) - 2). Let j(l) be the first derivative of 1/9*l**3 - 1/18*l**6 + 2 + 0*l**2 + 0*l - q*l**4 + 1/5*l**5. Factor j(s).
-s**2*(s - 1)**3/3
Let j(o) = o**3 - 6*o**2 - 8*o + 9. Let h be j(7). Factor l - l**h + l + 4 + l - 6.
-(l - 2)*(l - 1)
Suppose -3*u = -d + 4 + 7, u + 2*d + 13 = 0. Let b = u + 7. Factor 0 + 0*x**b - 1/2*x**3 + 0*x.
-x**3/2
Let u be (72/810)/(256/(-130) - -2). Factor -16/3*v + 2 - 4/9*v**3 + u*v**2.
-2*(v - 3)**2*(2*v - 1)/9
Let w be 144/15 + 2/5. Suppose 10 = 4*t + 2*y, 4 = -2*t - 2*y + w. Factor 0 + 2/5*x**t + 0*x.
2*x**2/5
Let z(o) = -o**3 - 15*o**2 - o - 15. Let m be z(-15). Factor m - 3*w + 3/2*w**2.
3*w*(w - 2)/2
Let m be (-2 + 3)/((-5)/(-10)). Let u(h) = h**3 - 2*h**2 + 2*h - 2. Let n(s) = s**3 + s - 1. Let d(j) = m*n(j) - u(j). Let d(q) = 0. What is q?
-2, 0
Let z(h) be the third derivative of -h**5/180 - 5*h**4/72 - 2*h**3/9 - 23*h**2. Factor z(k).
-(k + 1)*(k + 4)/3
Let w(q) be the first derivative of -q**3/4 - q**2/4 + q/4 - 5. Factor w(y).
-(y + 1)*(3*y - 1)/4
Let q(g) = 7*g**4 + 8*g**3 + 4*g**2 - 19*g + 11. Let j(s) = 4*s**4 + 4*s**3 + 2*s**2 - 10*s + 6. Let m(r) = -11*j(r) + 6*q(r). Factor m(t).
-2*t*(t - 2)*(t - 1)*(t + 1)
Suppose 0 = 5*i - i - 8. Factor 2*t - 6*t**2 - t**2 + i*t**2.
-t*(5*t - 2)
Suppose -20*o**2 + 72*o**3 + 71*o**3 + 7*o + 2 - 132*o**3 = 0. Calculate o.
-2/11, 1
Let t(r) = -6*r**3 - 19*r**2 - 35*r - 17. Let b(s) = 21*s**3 + 66*s**2 + 123*s + 60. Let f(j) = 5*b(j) + 18*t(j). Let f(k) = 0. What is k?
-2, -1
Suppose -3*n = 3*p - 6, n - 3*p = -2*p + 4. Factor 2*g**5 - 6*g**5 - 2*g**2 - 6*g**4 + 2*g**5 + 0*g**n - 6*g**3.
-2*g**2*(g + 1)**3
Let q be (-8)/(-1 - 1) - 1. Let l(k) = -2 - k - q*k**3 - 3 + 5*k**2 + 3*k - k**3. Let u(o) = o**3 + o**2 + o - 1. Let g(j) = -l(j) - u(j). Factor g(t).
3*(t - 2)*(t - 1)*(t + 1)
Let z(s) = s**2 - 5*s - 4. Let v be z(6). Suppose 8*r + r**v - 2*r - 4 + r**2 - 4*r = 0. Calculate r.
-2, 1
Let i(w) be the first derivative of -w**4/6 + w**3 - 2*w**2 + 2*w - 6. Let u(n) be the first derivative of i(n). Determine t so that u(t) = 0.
1, 2
Suppose 4/5*t**3 - 3/5*t**2 + 4/5*t**4 + 1/5 - 2/5*t = 0. Calculate t.
-1, 1/2
Factor 2/5*y**5 - 16/5*y**4 - 64/5*y**2 + 0 + 32/5*y + 48/5*y**3.
2*y*(y - 2)**4/5
Let g = -317/1290 + 12/43. Let b(h) be the second derivative of 0*h**2 + 0 + 1/15*h**3 - h - g*h**4. Factor b(o).
-2*o*(o - 1)/5
Let z(t) be the first derivative of 3*t**6/2 + 3*t**5/5 - 9*t**4/4 - t**3 - 9. Solve z(l) = 0 for l.
-1, -1/3, 0, 1
Solve 38/17*u**3 + 32/17*u + 2/17*u**5 + 50/17*u**2 + 14/17*u**4 + 8/17 = 0 for u.
-2, -1
Let k(d) be the third derivative of -d**6/204 + 2*d**5