derivative of 3*x**7/70 - x**6/40 - x**5/4 + x**4/8 + x**3 - 7*x**2. Factor r(g).
3*(g - 1)**2*(g + 1)*(3*g + 2)
Let u = -377 + 1141/3. Determine y so that -u*y + 2/3 + 8/3*y**2 = 0.
1/4, 1
Factor -2*u**4 - 11*u**3 - 12*u**3 + 0*u**4 + 25*u**3.
-2*u**3*(u - 1)
Suppose 2*w = 14 + 4. Let a be 95/(-35) - w/(-3). Factor 0 - 4/7*m**2 + 2/7*m + a*m**3.
2*m*(m - 1)**2/7
Suppose 0*w = 3*w - 57. Suppose 3*t + 1 = -5*a, -a = 3*t - 0*a - w. Factor 8*p - t*p - 1 + p**2.
(p - 1)*(p + 1)
Let y(c) = -c + 3. Let r be y(0). Suppose v**5 - 2*v**4 + v**r - 6*v + 0*v**4 + 6*v = 0. What is v?
0, 1
Suppose x + 0*x = 2. Let o be 0/((0 - 1)*2). Let 0*y**x + 0*y + 2/5*y**4 + o - 2/5*y**3 = 0. Calculate y.
0, 1
Suppose 0 = 2*q + 3 - 11. Factor -3*i**2 + i - 5*i**q + 1 - 5*i**3 + 2*i**4 + i**4.
-(i + 1)**3*(2*i - 1)
Suppose 10*b - 31*b + 42 = 0. Factor -2/3*q**4 + 0*q**b + 0 - 4/3*q**3 + 0*q.
-2*q**3*(q + 2)/3
Let w(l) be the third derivative of -l**6/320 + l**5/80 + l**4/64 - l**3/8 - 6*l**2. Factor w(n).
-3*(n - 2)*(n - 1)*(n + 1)/8
Let i(v) be the second derivative of 0*v**5 + 0*v**6 - 2*v + v**2 + 1/210*v**7 + 0*v**3 + 0 + 0*v**4. Let j(k) be the first derivative of i(k). Factor j(n).
n**4
Let c(w) = -5*w**4 + 4*w**3 - 5*w**2 - 2. Let k(x) = -81*x**4 + 63*x**3 - 81*x**2 - 33. Let i(h) = 33*c(h) - 2*k(h). Factor i(y).
-3*y**2*(y - 1)**2
Suppose 4*w - 20 = -2*h, -3*h + 2*w = h - 10. Let s(a) be the second derivative of 7/6*a**3 + 5/12*a**h + 0 + a**2 - a. Factor s(b).
(b + 1)*(5*b + 2)
Factor -10*v**2 - 4*v**5 + 5*v + 6*v**5 - 7*v**5 + 10*v**4.
-5*v*(v - 1)**3*(v + 1)
Let k(z) = -z**5 - 2*z**4 - 3*z**3 - 4*z**2 - 2*z. Let q(n) = 6*n**5 + 11*n**4 + 17*n**3 + 25*n**2 + 13*n. Let j(r) = 39*k(r) + 6*q(r). Factor j(w).
-3*w**2*(w + 1)**2*(w + 2)
Solve 4/5*k**2 + 0*k**3 + 0 - 4/5*k**4 + 2/5*k**5 - 2/5*k = 0 for k.
-1, 0, 1
Let p be (-5)/(-2)*(-24)/(-150). Factor -4/5*s**2 + 0*s + p*s**3 + 0.
2*s**2*(s - 2)/5
Let l(j) be the third derivative of -j**9/60480 - j**8/20160 - j**5/30 - 2*j**2. Let s(b) be the third derivative of l(b). Factor s(v).
-v**2*(v + 1)
Let o(r) = -3*r**2 + 5*r. Let b be o(1). Factor n + 1/2*n**b + 1/2.
(n + 1)**2/2
Let t(g) be the first derivative of 0*g**3 - 1/24*g**6 + 0*g - 1 - 1/8*g**2 + 1/8*g**4 + 0*g**5. Determine m, given that t(m) = 0.
-1, 0, 1
Suppose 0 = 4*c - 5*c + 4. Let f be 4/(36 - -4)*c. Factor 6/5*h - f*h**2 + 2/5 - 6/5*h**3.
-2*(h - 1)*(h + 1)*(3*h + 1)/5
Let d be 4*((-2 - -1) + 14/8). Factor 0 + 0*j + 2/3*j**2 + 1/3*j**d.
j**2*(j + 2)/3
Let t(x) be the second derivative of -3*x**4/28 - x**3/7 - 2*x. Solve t(y) = 0 for y.
-2/3, 0
Let x = -40 + 68. Let k(o) = -3*o**2 - 16*o + 19. Let u(f) = -16*f**2 - 88*f + 104. Let b(j) = x*k(j) - 5*u(j). Solve b(h) = 0.
-3, 1
Let g(k) be the second derivative of k**4/60 + 2*k**3/15 + 3*k**2/10 - 13*k. Suppose g(s) = 0. What is s?
-3, -1
Let z(n) = -6*n + 2*n**2 - n**2 - 2*n**2. Let j(v) = -v. Let f(h) = 5*j(h) - z(h). Solve f(r) = 0 for r.
-1, 0
Let x(k) = -k**5 - k**3 - k**2 + 1. Let a(d) = 6*d**5 + 12*d**4 + 27*d**3 - 3*d**2 - 3*d - 9. Let z(n) = a(n) + 15*x(n). Solve z(m) = 0.
-1, -2/3, 1
Let s(m) be the first derivative of -m**3/15 + 3*m**2/10 - 2*m/5 - 8. Let s(w) = 0. What is w?
1, 2
Let h(a) = a**3 + 4*a**2 + 4*a. Let f(n) = -5*n**3 - 20*n**2 - 20*n. Let s(q) = 4*f(q) + 22*h(q). Factor s(c).
2*c*(c + 2)**2
Let a(p) be the third derivative of p**7/14 + p**6/24 - p**5/4 - 5*p**4/24 + 7*p**2. Factor a(h).
5*h*(h - 1)*(h + 1)*(3*h + 1)
Let a(f) be the second derivative of f**7/33 + 16*f**6/165 + 2*f**5/55 - 7*f**4/33 - f**3/3 - 2*f**2/11 + 5*f. Determine v so that a(v) = 0.
-1, -2/7, 1
Let b = 4 - 2. Suppose 2*h - 3*h = -b. Factor 5*a**2 - 3*a**h - 4*a - 2 - 4*a**2.
-2*(a + 1)**2
Factor 1/5*a**5 + 0*a**2 + 0*a**3 - 1/5*a**4 + 0 + 0*a.
a**4*(a - 1)/5
Factor -1/2*f**2 + 0 + 0*f - 1/2*f**3.
-f**2*(f + 1)/2
Let h(s) be the first derivative of s**3 - 69*s**2/14 + 18*s/7 + 4. Factor h(k).
3*(k - 3)*(7*k - 2)/7
Let v(h) = -21*h**2 - 11*h. Let y(i) = -64*i**2 - 34*i. Let m(n) = 11*v(n) - 4*y(n). Determine d so that m(d) = 0.
-3/5, 0
Let z(g) be the second derivative of g**5/90 + g**4/6 + g**3 - 4*g**2 + g. Let s(b) be the first derivative of z(b). Solve s(c) = 0 for c.
-3
Let l(a) = a**2 + 22*a + 59. Let b be l(-19). What is k in -1/3*k**3 + 0 + 0*k + 2/3*k**b = 0?
0, 2
Let x(r) be the second derivative of r**7/14 - 3*r**6/5 + 33*r**5/20 - r**4/2 - 6*r**3 + 12*r**2 - 38*r. Solve x(a) = 0 for a.
-1, 1, 2
Let g(b) be the first derivative of 3*b**6/2 + 3*b**5/5 - 9*b**4 - 4*b**3 + 46. Determine x, given that g(x) = 0.
-2, -1/3, 0, 2
Suppose -3*z + z + 3*o + 32 = 0, 4*z - 5*o = 64. Let m be (-6)/(-8) + (-4)/z. Determine y, given that m*y**2 - 3/2*y + 1 = 0.
1, 2
Let j(l) be the first derivative of -l**6/18 + 2*l**5/15 - 2*l**3/9 + l**2/6 - 10. Solve j(o) = 0 for o.
-1, 0, 1
Suppose 3*n = 2*n + 12. Factor -n*s**3 + 1 + 4*s**3 + 2*s**4 - 1 + 12*s**2 + 2 - 8*s.
2*(s - 1)**4
Let w be (-14)/(-63) + 466/9. Factor w*b**2 - 4*b**4 - 61*b + 13*b + 16 - 24*b**3 + 8*b**4.
4*(b - 2)**2*(b - 1)**2
Factor 1/3*g + 0*g**4 - 2/3*g**3 + 0*g**2 + 0 + 1/3*g**5.
g*(g - 1)**2*(g + 1)**2/3
Factor 5*o**4 + 4*o**2 - o**4 - o**4 - 2*o**3 - 7*o**2 + 2*o.
o*(o - 1)*(o + 1)*(3*o - 2)
Factor 3*a**2 - 6 + 9*a**3 + 1 + 0 - 9*a - 1 + 3*a**4.
3*(a - 1)*(a + 1)**2*(a + 2)
Let x(u) = 3*u**5 - 4*u**4 - u**3 - 6*u**2 + 6*u - 6. Let y(i) = 3*i + 2*i - 4*i - 1 - i**2 - i**4. Let b(k) = -x(k) + 6*y(k). Solve b(t) = 0 for t.
-1, 0, 1/3
Factor -48/7*g - 18/7*g**2 - 32/7 - 2/7*g**3.
-2*(g + 1)*(g + 4)**2/7
Let i = 10 + -6. Let q = 6 - i. Factor j**q - 3*j**4 - 3*j**3 + 3*j - 4*j**3 + 2 - 4*j**2.
-(j + 1)**3*(3*j - 2)
Let y be (-2 + -1 - -4) + 3. Factor y*u**2 + 0 - 1 - 2*u**2 - u**2.
(u - 1)*(u + 1)
Let h(z) = 4*z**2 + 12*z + 3. Let c(t) = 4*t**2 + 11*t + 2. Let a(n) = 5*c(n) - 4*h(n). Factor a(s).
(s + 2)*(4*s - 1)
Let s be 28/98 + 122/4326. Let q = 2/103 + s. Solve q*n + 0 - 1/3*n**2 = 0 for n.
0, 1
Let a(f) be the first derivative of -6859*f**4 + 1444*f**3 - 114*f**2 + 4*f + 10. Find m, given that a(m) = 0.
1/19
Let n(j) be the third derivative of 0*j**3 - 4*j**2 + 1/140*j**6 + 0*j**4 + 0*j**7 + 0 + 1/105*j**5 - 1/1176*j**8 + 0*j. Factor n(b).
-2*b**2*(b - 2)*(b + 1)**2/7
Factor 0 - 1/3*i + 1/6*i**2 + 1/6*i**3.
i*(i - 1)*(i + 2)/6
Factor -3*x**2 - x**2 - 4 - 4*x**4 + 12*x**2.
-4*(x - 1)**2*(x + 1)**2
Let r(l) = 1. Let v(m) = 2*m**2 - 6*m - 10. Let f(t) = -10*r(t) - v(t). Find z, given that f(z) = 0.
0, 3
Let f(z) be the second derivative of z**6/2 - z**5/4 - 5*z**4/4 + 5*z**3/6 + 2*z. Factor f(l).
5*l*(l - 1)*(l + 1)*(3*l - 1)
Suppose -2*z + 7*z = -2*w + 11, 4*w = 2*z + 10. Let d be (-4 + -2)/(w - 7). Factor d*n - 3/2*n**2 + 1/2*n**3 - 1/2.
(n - 1)**3/2
Let r(i) be the third derivative of i**8/90720 + i**7/11340 + i**6/3240 - i**5/20 - i**2. Let b(w) be the third derivative of r(w). Factor b(x).
2*(x + 1)**2/9
Let n(w) be the second derivative of w**5/20 + w**4/4 + 43*w. Factor n(t).
t**2*(t + 3)
Let w(f) be the third derivative of -1/160*f**6 + 0*f + 0 + 7*f**2 - 1/40*f**5 + 1/4*f**3 + 1/32*f**4. Factor w(o).
-3*(o - 1)*(o + 1)*(o + 2)/4
Let d = -7 - -11. Determine n, given that -3 + 2*n - d*n - 1 + 2*n**2 = 0.
-1, 2
Let p(i) be the first derivative of -i**4/18 - 4*i**3/27 - i**2/9 - 10. Find s, given that p(s) = 0.
-1, 0
Determine n, given that -3/5*n**3 + 12/5*n**2 + 0 - 3/5*n**4 + 12/5*n = 0.
-2, -1, 0, 2
Let y = -2 + 3. Let b be (-10)/70*(y - 33). Factor -2/7 - 16/7*j - 48/7*j**2 - 64/7*j**3 - b*j**4.
-2*(2*j + 1)**4/7
Let n = 21 - 18. Factor 0*k**3 - 3*k**n + k**3 - 2 + 3*k + k**3.
-(k - 1)**2*(k + 2)
Let z(d) be the second derivative of d**2 + 1/12*d**4 + 0 + 3*d + 1/2*d**3. Let z(s) = 0. Calculate s.
-2, -1
Let c(t) be the third derivative of 1/240*t**5 + 0*t + 1/32*t**4 + 0 + 1/12*t**3 + 2*t**2. Suppose c(u) = 0. What is u?
-2, -1
Let h(r) be the second derivative of r**4/84 - r**3/42 - 3*r**2/7 + 11*r. Determine s so that h(s) = 0.
-2, 3
Let w(a) be the second derivative of -3*a**5/100 - 9*a**4/20 - 27*a**3/10 - 81*a**2/10 + 35*a. Suppose w(k) = 0. What is k?
-3
Let s(c) be the first derivative of -c**5/60 - c**4/12 - c**3/6 + 3*c**2/2 + 1. Let r(o) be the second derivative of s(o). Factor r(n).
-(n + 1)**2
Factor 75/2*f + 7/2*f**3 - 9 