d**7/420 - d**5/40 - d**4/24 + 40*d**2. Factor o(x).
x*(x - 2)*(x + 1)**2/2
Let n(a) be the first derivative of -a**5/10 + a**3/6 + 8. Factor n(d).
-d**2*(d - 1)*(d + 1)/2
Let l(j) be the first derivative of 3*j**4/8 - 3*j**3 + 48*j + 34. Factor l(t).
3*(t - 4)**2*(t + 2)/2
Let j(t) = 13*t**3 + 4*t**2 + 13*t + 11. Let m(p) = 2*p**3 + 2*p**3 + 2*p**2 + 3*p**3 + 6 + 7*p. Let a(y) = 6*j(y) - 11*m(y). Factor a(r).
r*(r + 1)**2
Factor 0*c + 0*c**2 - 1/11*c**4 + 0 + 2/11*c**3 - 1/11*c**5.
-c**3*(c - 1)*(c + 2)/11
Let a be 6/21*11 + -3. Let d(v) be the first derivative of a*v**2 + 0*v - 1 + 1/14*v**4 - 4/21*v**3. Find i such that d(i) = 0.
0, 1
Let g(z) be the second derivative of z**5/20 + z**4/12 - z**3/6 - z**2/2 + 9*z. Determine l, given that g(l) = 0.
-1, 1
Let z be 1*((-15)/(-35) - 1). Let s = -6/35 - z. Factor 2/5*a**3 + 0*a**2 + 0 + 0*a**4 - s*a**5 + 0*a.
-2*a**3*(a - 1)*(a + 1)/5
Let i = 7/18 - 1/18. Solve -2/3*w**4 + i*w - 1/3*w**5 + 2/3*w**2 + 0*w**3 + 0 = 0 for w.
-1, 0, 1
Let q(n) be the first derivative of -4*n**5/5 + 3*n**4/2 + 4*n**3/3 - 38. Suppose q(y) = 0. Calculate y.
-1/2, 0, 2
Let q(f) = 16*f**3 + 28*f**2 + 16*f + 4. Let j(a) = a**4 - 15*a**3 - 28*a**2 - 17*a - 5. Let p(u) = -4*j(u) - 5*q(u). Solve p(t) = 0.
-3, -1, 0
Let h be -2 + 3 + -1 - -2. Factor 0*k**h - k**3 + 4*k**2 - 5*k**2 + 2*k**4.
k**2*(k - 1)*(2*k + 1)
Let z = -480/11 - -44. Determine n so that -2/11*n**4 - 2/11*n - 2/11*n**5 + 4/11*n**3 + z*n**2 - 2/11 = 0.
-1, 1
Let o(a) = 3*a - 5. Let s be o(3). Suppose -2*n = j - 0*n - 2, -5*n = s*j - 5. Let -2/3*z**2 + j + 0*z = 0. Calculate z.
0
Let m(z) be the first derivative of z**4/3 + 4*z**3/9 - 4*z**2/3 - 6. Find i, given that m(i) = 0.
-2, 0, 1
Factor 0 + 12/7*r - 2*r**2.
-2*r*(7*r - 6)/7
Let g(b) be the second derivative of 0 - 4*b - 4/21*b**3 + 4/7*b**2 + 1/42*b**4. What is l in g(l) = 0?
2
Let q be (-1)/(0 - -1)*0. Suppose q = 4*d - 7 - 1. Factor 2*i + 4/5 + 6/5*i**d.
2*(i + 1)*(3*i + 2)/5
Let u(a) be the second derivative of a**8/7840 + a**7/1764 + a**6/2520 - a**5/420 - a**4/12 + 2*a. Let b(n) be the third derivative of u(n). Factor b(q).
2*(q + 1)**2*(3*q - 1)/7
Let p = 3 - 0. Suppose -5*g + 5*j = 2 - 32, -p*g = -4*j - 22. Factor 9*u**g - 9*u**2 + u**3 + 8*u**5 - 6*u**4.
u**3*(2*u - 1)*(4*u - 1)
Let i(a) be the second derivative of 0 - 1/2*a**3 - 1/180*a**6 - 2*a + 0*a**2 + 0*a**5 + 1/12*a**4. Let n(k) be the second derivative of i(k). Factor n(d).
-2*(d - 1)*(d + 1)
Let x(i) = 14*i**4 + 32*i**3 + 32*i**2 + 8*i. Let t(v) = 9*v**4 + 21*v**3 + 21*v**2 + 5*v. Let c(u) = 8*t(u) - 5*x(u). Find f, given that c(f) = 0.
-2, 0
Let v = 133 + -133. Factor -1/2*p**5 + v*p - 3/2*p**4 + 0 - p**3 + 0*p**2.
-p**3*(p + 1)*(p + 2)/2
Let j(a) be the second derivative of -2*a**7/105 + a**6/10 - a**5/5 + a**4/6 + 3*a**2 - 2*a. Let u(r) be the first derivative of j(r). Solve u(v) = 0.
0, 1
Let z(i) = -7*i**2 - 2*i. Let r(c) = 52*c**2 + 10*c. Let m(q) = 21*q**2 + 4*q. Let k(x) = -12*m(x) + 5*r(x). Let u(f) = -6*k(f) - 7*z(f). Factor u(s).
s*(s + 2)
Factor -2*s + s - 18*s**4 + 2*s**2 + s**5 - 4*s**2 + 20*s**4.
s*(s - 1)*(s + 1)**3
Let t(r) = 3*r**4 + 3*r**2 - r**2 - 2 - r - 3*r**2 - 3*r**3. Let y(s) = 13*s**4 - 13*s**3 - 4*s**2 - 5*s - 9. Let g(x) = -9*t(x) + 2*y(x). Factor g(i).
-i*(i - 1)**2*(i + 1)
Let p be ((-68)/(-35))/2 - (-52)/(-91). What is f in 2/5*f - 2/5*f**2 - 2/5*f**3 + p = 0?
-1, 1
Let g(o) = o + 2. Let q be g(0). Factor 0 + 0*k - 1/2*k**q.
-k**2/2
What is f in -4/5*f**3 + 2/5*f**4 + 2/5*f**5 + 0*f**2 + 0*f + 0 = 0?
-2, 0, 1
Let x(q) be the second derivative of q**4/32 + q**3/4 + 3*q**2/4 - 5*q. Suppose x(m) = 0. What is m?
-2
Let s(j) be the third derivative of -8*j**8/21 + 16*j**7/105 + 41*j**6/15 + 107*j**5/30 + 25*j**4/12 + 2*j**3/3 - 4*j**2. Determine o so that s(o) = 0.
-1, -1/4, 2
Let j(z) be the second derivative of z**6/135 + z**5/45 - 2*z**3/27 - z**2/9 + 8*z. What is r in j(r) = 0?
-1, 1
Let o(a) be the third derivative of 0*a + 1/300*a**6 + 9*a**2 + 0 + 1/75*a**5 + 1/60*a**4 + 0*a**3. Determine w so that o(w) = 0.
-1, 0
Factor 0 + 1/3*r**2 + 0*r.
r**2/3
Let z(i) = 2*i + 33. Let j be z(-15). What is a in -2/3*a**j + 2/3*a**4 - 2/3*a**2 + 0 + 2/3*a**5 + 0*a = 0?
-1, 0, 1
Let d(f) be the first derivative of f**4/4 + 4*f**3/3 + 2*f**2 + 2*f + 2. Let o be d(-2). Factor 0 + x**3 - x - x**4 + x**o + 0.
-x*(x - 1)**2*(x + 1)
Let v(r) = -r**5 + r**3. Let s(t) = 8*t**5 - t**4 - 8*t**3 + t**2. Let q(b) = 2*s(b) + 14*v(b). Factor q(l).
2*l**2*(l - 1)**2*(l + 1)
What is n in -20*n**3 + 73*n**4 - 8 - 77*n**4 - 36*n**2 + 9*n - 37*n = 0?
-2, -1
Factor 20*u**2 - 2791*u + 320*u**3 + 2791*u + 1105*u**4 - 1445*u**5.
-5*u**2*(u - 1)*(17*u + 2)**2
Let j = 36/55 - -6/11. Factor 3/5*k - 3/5*k**5 + j*k**4 + 0 + 0*k**3 - 6/5*k**2.
-3*k*(k - 1)**3*(k + 1)/5
Let v(x) be the second derivative of -x**8/20160 + x**7/7560 - x**4/6 + 4*x. Let b(u) be the third derivative of v(u). Factor b(s).
-s**2*(s - 1)/3
Let m(r) be the second derivative of r**8/20160 - r**6/2160 - r**4/4 - r. Let i(j) be the third derivative of m(j). Factor i(b).
b*(b - 1)*(b + 1)/3
Let w(m) be the first derivative of m**6/315 - m**5/60 - m**4/42 + 2*m**3/3 - 1. Let n(d) be the third derivative of w(d). Factor n(k).
2*(k - 2)*(4*k + 1)/7
Let b(t) be the third derivative of t**8/33600 - t**7/6300 - t**4/6 - 2*t**2. Let a(q) be the second derivative of b(q). Factor a(z).
z**2*(z - 2)/5
Factor 2*x**5 - 7*x**4 - x**5 - 13*x**2 + 4*x + 4268*x**3 - 4253*x**3.
x*(x - 4)*(x - 1)**3
Suppose 2 - 4 = -n. Let o = n + -2. What is b in -2/3*b + o*b**2 + 2/3*b**3 + 0 = 0?
-1, 0, 1
Let q(b) = b. Let c be q(4). Suppose 4*i - 5*r - 63 = -9, 24 = i + c*r. Suppose -7*s**5 - 6*s**3 - i*s**4 - 2*s**2 - 5*s**3 + 0*s**2 + 0*s**3 = 0. What is s?
-1, -2/7, 0
Let k(s) = -s + 1. Let j be k(-3). Factor -3*z**3 - 3*z - z + j*z**3 + 3*z.
z*(z - 1)*(z + 1)
Let q(f) be the third derivative of -f**6/30 + 3*f**5/40 + f**4/8 + f**3/6 + f**2. Let x(o) be the first derivative of q(o). Factor x(k).
-3*(k - 1)*(4*k + 1)
Let k(y) be the third derivative of y**5/270 + 5*y**4/27 + 100*y**3/27 - 42*y**2. Find p such that k(p) = 0.
-10
Suppose -w - 4 = -8. Suppose 2*f - 11 = 3*j, f = -w*j + 6*j + 6. Factor -2/7*v**3 - 2/7*v**5 + 0 - 4/7*v**f + 0*v + 0*v**2.
-2*v**3*(v + 1)**2/7
Factor 0*o**4 + 4/7*o**2 + 2/7*o**5 - 4/7 - 8/7*o**3 + 6/7*o.
2*(o - 1)**3*(o + 1)*(o + 2)/7
Let b(q) = q + 14. Let g be b(-12). Factor 3/2*m**g - 3 - 3/2*m.
3*(m - 2)*(m + 1)/2
Let c(o) be the second derivative of -o**4/12 + 4*o**3/3 - 5*o**2/2 + 2*o. Let a be c(7). Factor -a*i**2 + 2*i + i**2 - i.
-i*(i - 1)
Let p(s) = -3*s + 1. Let x be p(1). Let w(u) = -9*u**2 - 9*u + 5. Let i(g) = -4*g**2 - 4*g + 2. Let a(o) = x*w(o) + 5*i(o). Factor a(f).
-2*f*(f + 1)
Find s such that -3*s**2 + 11*s**3 - s**2 + 2*s**4 - 13*s**3 = 0.
-1, 0, 2
Let h = 0 + -5. Let z(n) = 3*n**5 - n**3 + 2*n**2. Let s(k) = -7*k**5 + 2*k**3 - 5*k**2. Let c(x) = h*z(x) - 2*s(x). Factor c(g).
-g**3*(g - 1)*(g + 1)
Factor 2/17*b**4 + 0*b**2 - 2/17 - 4/17*b + 4/17*b**3.
2*(b - 1)*(b + 1)**3/17
Let m(l) = -l + 1. Let s be m(-3). Suppose 3*q - 5*w - 29 = 0, 3*q - s*w - 25 = -0*q. Factor 5*y**4 - 2*y**5 - 2*y**3 - 4*y**4 + 0*y**3 + q*y**4.
-2*y**3*(y - 1)**2
Let s(p) be the first derivative of -1 + 1/27*p**6 + 0*p + 1/9*p**2 - 1/9*p**4 + 0*p**5 + 0*p**3. Factor s(t).
2*t*(t - 1)**2*(t + 1)**2/9
Determine k so that 0 + 33/2*k**3 - 18*k**2 + 6*k - 9/2*k**4 = 0.
0, 2/3, 1, 2
Suppose -28*i = -33*i. Let s = -1 + 3. Determine x so that -s*x**2 + i*x - x**2 + 2*x + x**3 + 0*x = 0.
0, 1, 2
Suppose 4*y - 20 = -y. Suppose -y*u + 1 = -7. Factor i**2 - 5*i**2 + 2*i**3 - 2*i**2 + 6*i - u.
2*(i - 1)**3
Let c(u) be the third derivative of -5*u**2 - 1/168*u**8 + 0*u + 2/15*u**5 - 1/12*u**4 - 1/10*u**6 + 0 + 0*u**3 + 4/105*u**7. Factor c(j).
-2*j*(j - 1)**4
Let v = 770 - 767. Factor -2/5 - 6/5*t**4 + 9/5*t - 16/5*t**2 + 1/5*t**5 + 14/5*t**v.
(t - 2)*(t - 1)**4/5
Let f(y) = y**2 + 7*y - 2. Let v(h) = h**2 + 6*h - 2. Let q(b) = -5*f(b) + 6*v(b). Let q(w) = 0. What is w?
-2, 1
Let v(n) be the second derivative of 3*n**5/20 + n**4/2 + n. Determine c, given that v(c) = 0.
-2, 0
Let -8/5 + 2/5*r**5 + 32/5*r + 38/5*r**3 - 10*r**2 - 14/5*r**4 = 0. What is r?
1, 2
Find n, given that -16/3 + 8*n - 4*n**2