3 + 3*f**4 - 4*f**2 - 7*f**4 - 205*f**3 = 0.
0, 1
Let q(j) = j**2 - 6*j + 5. Let h(a) be the first derivative of -2*a**3/3 + 13*a**2/2 - 11*a - 4. Let b(s) = -3*h(s) - 7*q(s). Factor b(g).
-(g - 2)*(g - 1)
Let s(j) be the second derivative of j**7/210 - j**6/50 + j**5/100 + j**4/20 - j**3/15 - 32*j. Factor s(t).
t*(t - 2)*(t - 1)**2*(t + 1)/5
Let n = -1 - -7. Let o = n - 3. Find s such that s**5 + 4*s**4 - 5*s**4 - s**o + 3*s**4 + 2*s**3 = 0.
-1, 0
Let l(w) = 6*w - 10. Let j be l(2). Factor -1/3*o**j + 1/3*o + 0.
-o*(o - 1)/3
Let q = -455 + 1821/4. Find t such that -q*t**5 + 0*t**3 + 0 + 0*t + 0*t**2 + 1/4*t**4 = 0.
0, 1
Let r(g) be the first derivative of -g**5/5 - 5*g**4 - 44*g**3 - 160*g**2 - 256*g + 54. Suppose r(w) = 0. Calculate w.
-8, -2
Suppose 4*i - i = 6. Let u(l) = -l**2 + 11*l - 10. Let f be u(10). Factor 0*o - 14/5*o**5 + 4/5*o**3 + i*o**4 + f*o**2 + 0.
-2*o**3*(o - 1)*(7*o + 2)/5
Factor -2*h**2 - 2 - 5*h - 6 + 1 + 4.
-(h + 1)*(2*h + 3)
Let v = 1/43 - -36/301. What is c in -1/7 + v*c**3 + 1/7*c**2 - 1/7*c = 0?
-1, 1
Let h(t) be the first derivative of -15/16*t**4 - 1/8*t**6 + 0*t**2 + 6 + 0*t + 3/5*t**5 + 1/2*t**3. Let h(c) = 0. What is c?
0, 1, 2
Let p(c) be the first derivative of -3*c**5/20 - c**4/4 - 6*c + 5. Let h(n) be the first derivative of p(n). Factor h(y).
-3*y**2*(y + 1)
Let v(a) be the third derivative of -a**8/630 + a**7/175 + a**6/450 - a**5/50 + a**4/90 + 4*a**2. Solve v(b) = 0 for b.
-1, 0, 1/4, 1, 2
Let l(v) = -v**4 - v**3 + v**2 + 1. Let w(g) = 8*g**4 + 16*g**3 + 20*g**2 + 27*g - 7. Let k(h) = 28*l(h) + 4*w(h). What is b in k(b) = 0?
-3, 0
Let a be (-2)/3*3/(-4). Let i(b) be the first derivative of -2 - 1/4*b**4 + 0*b**3 + a*b**2 + 0*b. Find d, given that i(d) = 0.
-1, 0, 1
Let a(v) = 3*v**5 - 15*v**4 + 45*v**3 - 3*v**2 - 12*v. Let w(r) = r**3 + r**2 - r. Let q(s) = -2*s + 4. Let d be q(-7). Let y(g) = d*w(g) - a(g). Factor y(o).
-3*o*(o - 2)*(o - 1)**3
Let d = 20 + -11. Suppose d*j = 4*j + 10. Factor 2*y**3 - 7*y**j - y**4 - y - y**3 + 8*y**2.
-y*(y - 1)**2*(y + 1)
Let t(l) be the first derivative of 5*l**3/3 + 5*l**2 + 5*l - 4. Factor t(r).
5*(r + 1)**2
Let y(b) be the first derivative of 4*b**5/15 - 5*b**4/6 + 4*b**3/9 - 7. Factor y(m).
2*m**2*(m - 2)*(2*m - 1)/3
Let d(r) be the second derivative of 1/168*r**7 + r - 1/24*r**3 + 1/60*r**6 + 0*r**5 + 0 + 0*r**2 - 1/24*r**4. Factor d(l).
l*(l - 1)*(l + 1)**3/4
Let a(b) be the first derivative of -b**3 + 0*b**2 + 0*b**5 - 1/180*b**6 + 0*b + 1/12*b**4 - 2. Let g(j) be the third derivative of a(j). Factor g(s).
-2*(s - 1)*(s + 1)
Let m(i) be the first derivative of -i**6/6 + 9*i**5/20 - 3*i**4/8 + i**3/12 - 5. What is h in m(h) = 0?
0, 1/4, 1
Let t(q) be the third derivative of q**5/330 + 2*q**4/33 - 27*q**2 - 2. Determine i so that t(i) = 0.
-8, 0
Suppose -p - 4*v - 6 = 8, 3*v = -2*p - 3. Factor 5 - 2 + 4*j**2 - p*j - j**2.
3*(j - 1)**2
Let b be (2 + (-234)/105)/(10/(-25)). What is z in 0*z**3 - 2/7*z + 4/7*z**2 + 2/7*z**5 - b*z**4 + 0 = 0?
-1, 0, 1
Factor -2/3 - 16/3*i**2 + 3*i - 2*i**4 + 14/3*i**3 + 1/3*i**5.
(i - 2)*(i - 1)**4/3
Let p(f) be the third derivative of 0*f + 0*f**4 - 5*f**2 + 1/150*f**5 + 0 + 0*f**3 - 1/600*f**6. What is h in p(h) = 0?
0, 2
Factor 44*o**5 - 2 - 25*o**2 + 125*o**5 + 9*o + 355*o**3 - 2 - 455*o**4 - 49*o.
(o - 1)**3*(13*o + 2)**2
Let c(t) = t**2 + 4*t + 2. Let q be c(-3). Let r(k) = k**4 + 0*k - 2*k + 2 + 3 - 4. Let f(h) = h**4 - h**3. Let m(s) = q*r(s) + 2*f(s). Solve m(n) = 0.
-1, 1
Suppose -30 = -5*d - 4*l, 2*d = -0*d + 3*l - 11. Suppose 0*s**3 + 0*s**d + 0 + 0*s**4 + 0*s + 1/3*s**5 = 0. Calculate s.
0
Let y(f) be the third derivative of -f**5/120 + f**4/48 + f**3/6 - f**2. Factor y(k).
-(k - 2)*(k + 1)/2
Let u be (-4)/2 - 1*-2. Let t be -1 + u - 3/(-1). Factor -3*c + 2*c - c + 2*c**t.
2*c*(c - 1)
Let y(o) = o**2 - 2*o. Suppose -4*i - 2 = -14. Let z be y(i). Factor 0 - s**2 + 0*s**2 + z*s - 2.
-(s - 2)*(s - 1)
Let g(z) be the first derivative of -15*z**4/2 + 5*z**3/3 + 10*z**2 + 5*z + 13. Factor g(m).
-5*(m - 1)*(2*m + 1)*(3*m + 1)
Let z(v) be the second derivative of -v**5/20 + v**4/12 - 5*v. Factor z(w).
-w**2*(w - 1)
Let h(r) be the first derivative of r**6/6 + 2*r**5/5 - 2*r**3/3 - r**2/2 - 2. Find n, given that h(n) = 0.
-1, 0, 1
Factor -10*g**4 - 5*g + 15*g**3 + 3*g - 4*g + g.
-5*g*(g - 1)**2*(2*g + 1)
Let w(u) be the first derivative of -9*u**4/10 - 14*u**3/5 - 16*u**2/5 - 8*u/5 - 5. Find b such that w(b) = 0.
-1, -2/3
Let f(r) be the first derivative of 2/9*r**3 + 1/6*r**4 + 4 - 2/3*r**2 + 0*r. Factor f(k).
2*k*(k - 1)*(k + 2)/3
Suppose 5*j + 4*b + 9 = -1, 3*b = j - 17. Factor 1/6*x**j + 1/6 + 1/3*x.
(x + 1)**2/6
Let n = -15416/2793 + 105/19. Let q(p) be the second derivative of 0*p**5 - 2/105*p**6 + 1/21*p**4 + 0*p**2 + 1/21*p**3 - 2*p - n*p**7 + 0. Factor q(b).
-2*b*(b - 1)*(b + 1)**3/7
Let j(r) be the third derivative of -r**8/1512 + r**6/54 + 2*r**5/27 + 5*r**4/36 + 4*r**3/27 + 25*r**2. Factor j(o).
-2*(o - 4)*(o + 1)**4/9
Solve 70*q**2 - 4*q**5 - 6*q**4 + 4*q**3 - 2*q**4 - 62*q**2 = 0 for q.
-2, -1, 0, 1
Let m(d) be the second derivative of d**7/5040 + d**6/720 + d**5/240 + d**4/12 - 2*d. Let u(c) be the third derivative of m(c). Factor u(s).
(s + 1)**2/2
Let v(i) be the first derivative of 2 + 25/8*i**3 + 3/8*i - 15/8*i**2. Factor v(x).
3*(5*x - 1)**2/8
Suppose 2*m + 4 = 3*m. Let u be (2/(-15))/((-5)/720). Let u*w**3 - 6/5*w - 38/5*w**2 - 56/5*w**m + 4/5 = 0. Calculate w.
-2/7, 1/2, 1
Let s(i) = i**5 + i**3 + 2*i**2 + 2*i + 2. Let d(v) = 2*v**5 + v**4 + 2*v**3 + 3*v**2 + 3*v + 3. Let m(a) = -4*d(a) + 6*s(a). Solve m(y) = 0.
-1, 0
Suppose -5*v = -2*y, -2*y = 3*y - 4*v - 17. Suppose 3*m - 22 = -y*j, -4*j - j + 3*m = 2. Factor 1/5*g**j + 0 - 1/5*g.
g*(g - 1)/5
Let a(s) be the third derivative of 1/840*s**7 + 0*s**4 - 2*s**2 + 1/240*s**5 + 0 - 1/240*s**6 + 0*s + 0*s**3. Solve a(c) = 0 for c.
0, 1
Let h be (-26)/8 + 3/12. Let y = h + 6. Factor -v**5 + 2*v - 2*v**2 + y*v**3 - 2*v.
-v**2*(v - 1)**2*(v + 2)
Let c(u) = u**3 - 3*u**2 + 4*u - 2. Let a be c(3). Let s = a + -8. Factor -1/4*x**3 + 1/4 - 1/4*x**s + 1/4*x.
-(x - 1)*(x + 1)**2/4
Let q(k) be the second derivative of -3/40*k**5 - 8*k + 1/24*k**4 + 0*k**2 - 1/84*k**7 + 1/20*k**6 + 0*k**3 + 0. Factor q(h).
-h**2*(h - 1)**3/2
Let v(d) = -d**2 - 3*d + 4. Let m be v(-4). Let t be 1/2*(17 + -11). Factor -f**2 - 2*f**4 - 1/2*f + 7/2*f**t + m.
-f*(f - 1)**2*(4*f + 1)/2
Let j(r) be the second derivative of r**6/135 + r**5/30 + r**4/18 + r**3/27 + 32*r. Factor j(t).
2*t*(t + 1)**3/9
Let c(j) be the second derivative of 3*j**5/100 - 3*j**3/10 - 3*j**2/5 + 2*j. Suppose c(x) = 0. Calculate x.
-1, 2
Let k be 2*1/6*3. Let l(z) = 5*z. Let w be l(k). Factor -4*b**3 + b**4 + b**2 - 2*b - 2*b + w*b**2 + 1.
(b - 1)**4
Let b be 8/(-14) + 145/70. Find z such that -1 + z**2 - b*z = 0.
-1/2, 2
Let l(a) = a**2 + a. Let y(w) = 7*w**2 + 10*w. Let u(r) = -4*l(r) + y(r). Solve u(d) = 0.
-2, 0
Solve 6/5*y**2 - 1/5 + 14/5*y**3 + 3/5*y**5 - 1/5*y + 11/5*y**4 = 0 for y.
-1, 1/3
Let y = -16 - -20. Factor 25*t**2 + 3*t - 2*t**4 + 3*t**y - 5*t - 28*t**2.
t*(t - 2)*(t + 1)**2
Let o = 4771/30 + -159. Let f(z) be the second derivative of -o*z**4 + 0*z**3 + 2*z + 0 + 1/5*z**2. Find x, given that f(x) = 0.
-1, 1
Let o be 2/24*(-872)/78. Let u = o + 15/13. Factor -2/9*z - 2/9 + 2/9*z**2 + u*z**3.
2*(z - 1)*(z + 1)**2/9
Let m(x) = -5*x**2 - 5*x + 3. Let r(o) = o**2 - 11*o + 5. Let g be r(11). Let z(d) = 9*d**2 + 9*d - 5. Let l(w) = g*m(w) + 3*z(w). Let l(a) = 0. Calculate a.
-1, 0
Factor -2/3*q + 4 - 2/3*q**2.
-2*(q - 2)*(q + 3)/3
Suppose 0*o = -o. Suppose o*s + 6 = 2*s - 2*r, 0 = -2*s - 3*r + 6. Factor -4*d**s - 2*d**4 - d**2 - 2*d**2 + d**2.
-2*d**2*(d + 1)**2
What is t in 1/2*t + 0 + 1/4*t**2 = 0?
-2, 0
Factor 2 + 0*g - 3/2*g**2 + 1/2*g**3.
(g - 2)**2*(g + 1)/2
Let x(y) be the second derivative of y**6/6 + y**5/4 - 5*y**4/4 - 5*y**3/6 + 5*y**2 - 5*y. Factor x(a).
5*(a - 1)**2*(a + 1)*(a + 2)
Let t(q) be the first derivative of q**6/4 + 9*q**5/5 + 3*q**4 - 8*q**3 - 36*q**2 - 48*q + 40. Suppose t(c) = 0. What is c?
-2, 2
Solve 2/7 - 6/7*s - 2/7*s**3 + 6/7*s**2 = 0 for s.
1
Let g(o) be the third derivative of -o**6/240 - o**5/120 + o**4/48 + o**3/12 - 3*o**2. Factor g(q).
-(q - 1)*(q + 1)**2/2
Let s = -4 + 4