e third derivative of -o**5/420 + o**4/84 - o**3/42 - 3*o**2. Factor t(z).
-(z - 1)**2/7
Find g, given that 2/3*g**3 + 0*g**2 + 0 + 2/3*g**5 + 0*g + 4/3*g**4 = 0.
-1, 0
Let l(t) be the third derivative of t**10/120960 - t**8/26880 - t**4/24 + 4*t**2. Let g(y) be the second derivative of l(y). Factor g(s).
s**3*(s - 1)*(s + 1)/4
Let h(b) be the second derivative of b**6/60 + b**5/15 - b**2/2 + 2*b. Let k(m) be the first derivative of h(m). Factor k(j).
2*j**2*(j + 2)
Let m(t) = t**2 - 4*t - 9. Let w(j) = 4*j**2 - 11*j - 27. Let u be 4/(-2) - (-2 + 7). Let n(r) = u*m(r) + 2*w(r). Factor n(i).
(i + 3)**2
Let l(c) = -c + 5. Let d be l(3). Let -d*h - 8*h**3 - 6*h**2 + 10*h - 2*h**4 + 1 + 7 = 0. Calculate h.
-2, -1, 1
Let q(g) be the second derivative of 0 - 4/5*g**2 + 1/30*g**4 + 0*g**3 - g. Find b, given that q(b) = 0.
-2, 2
Let y(h) be the first derivative of 1/24*h**6 - 3/16*h**4 + 1/4*h**2 - 1/20*h**5 + 1/12*h**3 + 0*h - 5. Solve y(w) = 0 for w.
-1, 0, 1, 2
What is r in -4*r**2 - 9*r**2 + 20*r**2 - 2*r**3 - 11*r**2 - 2*r = 0?
-1, 0
Let k be (-46)/(-120) - 24/180. Suppose 1/4*a**2 + 0*a + 0 - k*a**3 = 0. Calculate a.
0, 1
Suppose 2*v - 220 = 7*v. Let i(u) = -u**2 - 3*u + 3. Let n(x) = -8*x**2 - 22*x + 22. Let z(m) = v*i(m) + 6*n(m). Factor z(a).
-4*a**2
Let m(c) be the third derivative of c**6/225 - c**5/75 + c**4/60 - c**3/6 - 6*c**2. Let s(z) be the first derivative of m(z). Factor s(u).
2*(2*u - 1)**2/5
Suppose -3*m - 4 = -5*m. Factor -3*a**3 - 4*a**m + a**2 - 6*a - 2*a**2 - 4*a**2.
-3*a*(a + 1)*(a + 2)
Let x(s) be the third derivative of s**7/560 + s**6/120 - s**5/80 - s**4/8 + s**3/3 + 6*s**2. Let b(w) be the first derivative of x(w). Factor b(m).
3*(m - 1)*(m + 1)*(m + 2)/2
Let x(u) = 25*u**2 + 28*u + 13. Let b(y) = 37*y**2 + 42*y + 19. Let o(s) = -5*b(s) + 7*x(s). Factor o(j).
-2*(j + 1)*(5*j + 2)
Find f, given that -3*f + 1/2 + 53/8*f**2 - 55/8*f**3 + 27/8*f**4 - 5/8*f**5 = 0.
2/5, 1, 2
Factor -d**2 + 8/5*d + 1/5*d**3 - 4/5.
(d - 2)**2*(d - 1)/5
Suppose -4*s - 4 = -6*s. Factor 24*q - 12*q**3 - s*q**3 - 10 + 18 - 14*q**2 - 4*q**2.
-2*(q - 1)*(q + 2)*(7*q + 2)
Let m(j) be the second derivative of -j**5/140 + j**4/28 + j**3/42 - 3*j**2/14 - 6*j. Suppose m(q) = 0. Calculate q.
-1, 1, 3
Let t(y) be the third derivative of y**8/1008 + y**7/315 - y**6/180 - 2*y**5/45 - 7*y**4/72 - y**3/9 + 4*y**2. Factor t(w).
(w - 2)*(w + 1)**4/3
Suppose 0*s + s - 4*s = 0. Let x(m) be the second derivative of s + 1/40*m**6 + 3/40*m**5 - 3/8*m**2 - 3*m - 1/4*m**3 + 0*m**4. Factor x(y).
3*(y - 1)*(y + 1)**3/4
Suppose u - 2*u + 2 = 0, 5*s = -2*u + 284. Suppose 4*p - 3*z = 24, 5*p - 5*z + 21 = s. Factor -2*w - 3*w**2 - 3*w**p - 2*w**4 + w + w**4 + 0*w**4.
-w*(w + 1)**3
Let u(j) be the first derivative of 1/13*j**2 - 7 - 4/13*j + 2/39*j**3. Factor u(o).
2*(o - 1)*(o + 2)/13
Let m(z) = -39*z**3 + 13*z**2 + 44*z - 3. Let p(i) = 59*i**3 - 19*i**2 - 66*i + 5. Let s(g) = -7*m(g) - 5*p(g). Factor s(q).
-2*(q - 1)*(q + 1)*(11*q - 2)
Let -4/9 + 34/9*v**2 + 2*v + 4/3*v**3 = 0. What is v?
-2, -1, 1/6
Let z(p) be the first derivative of p**5/80 + p**4/24 - 3*p - 1. Let g(f) be the first derivative of z(f). Factor g(q).
q**2*(q + 2)/4
Let n = 44 - 41. Let i(a) be the second derivative of 1/6*a**4 - 1/10*a**5 + 0 + 0*a**2 + 0*a**n - 3*a. Factor i(s).
-2*s**2*(s - 1)
Suppose 4*b - 2 + 38 = -3*l, 3*l + 30 = -2*b. Let o be (-8)/(-5) - l/20. Solve w + 1 + 2*w + w**3 + 3*w**o + w - w = 0.
-1
Let s(m) = m - 5. Let j be s(3). Let p be (j + 1)*1 - -1. Factor p*k - 2/5 + 2/5*k**2.
2*(k - 1)*(k + 1)/5
Let p(s) = 8*s**2 + 11*s - 29. Let l(d) = -4*d**2 - 5*d + 15. Let w(x) = 5*l(x) + 3*p(x). Let w(z) = 0. Calculate z.
-3, 1
Let j(s) be the third derivative of -s**9/756 + s**7/70 - s**6/45 - 7*s**3/6 - s**2. Let f(u) be the first derivative of j(u). Solve f(y) = 0.
-2, 0, 1
Suppose k + 0*k - 1 = 0. Let u = 1 + k. Factor 6*w**2 - w**3 - 4*w**u + 2*w**3 - 2*w**4 - w.
-w*(w - 1)*(w + 1)*(2*w - 1)
Let n(s) be the first derivative of s**5/5 - 7*s**4/12 + s**3/3 + s**2/2 + 4*s + 4. Let o(b) be the first derivative of n(b). What is f in o(f) = 0?
-1/4, 1
Let d(k) be the second derivative of -1/18*k**6 + 1/6*k**5 + 1/126*k**7 - 1/6*k**2 + 5/18*k**3 + k - 5/18*k**4 + 0. Factor d(r).
(r - 1)**5/3
Let y = 2/179 + 344/1253. Factor -2/7*b**2 + 0*b + y.
-2*(b - 1)*(b + 1)/7
Solve -10*u**4 + 2*u**5 - 17*u**4 - 24*u**3 - 6*u + 27*u**2 + 19*u**5 + 9*u**3 = 0.
-1, 0, 2/7, 1
Let p(t) be the first derivative of -t**4/10 + 4*t**3/5 - 9*t**2/5 + 56. Solve p(l) = 0 for l.
0, 3
Let j be (650/(-120))/13 + 4/6. Suppose -2*y = -x - 0*y, y = -2*x + 5. Solve -1/4*o + 1/2*o**x - j = 0 for o.
-1/2, 1
Let p be ((-7)/84)/((4/(-3))/4). Factor 1/4*g**2 - 1/4*g**4 + p*g - 1/4*g**3 + 0.
-g*(g - 1)*(g + 1)**2/4
Let a(g) be the third derivative of -g**5/15 + 4*g**4/3 - 8*g**3 + 11*g**2 - g. Suppose a(l) = 0. What is l?
2, 6
Let t = -4 - -16. Let y(r) = r - 9. Let m be y(t). Find s, given that -4 - m + 3*s**2 + 4 = 0.
-1, 1
Let q(n) = -n + 1 + 2*n**2 + n**2 - 4*n**2. Let c be q(0). Suppose -w + 15*w**2 + 10*w - c + 3 + 3*w**4 + 11*w**3 = 0. What is w?
-1, -2/3
What is r in 1/2 + 11/4*r - 9/4*r**4 - 11/4*r**3 + 7/4*r**2 = 0?
-1, -2/9, 1
Let n = -457 - -9599/21. Let t(g) be the first derivative of -n*g**3 - 1/7*g**2 - 2 + 4/7*g. Let t(k) = 0. What is k?
-2, 1
Suppose -2*j + 3*j - 6 = 0. Let s = j + -1. Factor -10*h**4 + 2*h**3 + h**s + 5*h**5 + 0*h**4 + 2*h**2.
2*h**2*(h - 1)**2*(3*h + 1)
Let a(x) be the first derivative of 5*x**4/4 - 20*x**3/3 + 10*x**2 + 11. Factor a(q).
5*q*(q - 2)**2
Let i(f) be the first derivative of f**7/840 + f**6/120 + f**5/60 + 4*f**3/3 - 1. Let s(m) be the third derivative of i(m). Find l such that s(l) = 0.
-2, -1, 0
Let v(t) be the second derivative of -t**7/105 + t**5/50 + 4*t. Factor v(o).
-2*o**3*(o - 1)*(o + 1)/5
Let q(l) = -70*l**5 + 125*l**3 + 55*l**2 + 55*l - 55. Let t(h) = -5*h**5 + 9*h**3 + 4*h**2 + 4*h - 4. Let f(g) = 4*q(g) - 55*t(g). Find c such that f(c) = 0.
-1, 0, 1
Suppose 4 = -0*k + 2*k. Let v be 2*2/4 + 1. Factor -2*h**2 + h**3 + 3*h + h**v - 2*h**k - 1.
(h - 1)**3
Let h = 8731/30 - 291. Let r(b) be the second derivative of h*b**5 + 0*b**2 + 3*b + 0 + 2/27*b**4 + 1/27*b**3. Factor r(v).
2*v*(v + 1)*(3*v + 1)/9
Suppose 16 = 5*f - 2*r - 2*r, 5*f = 3*r + 17. Let u = f + -2. Suppose u*t - 2*t**2 - 3*t**3 - t**3 + 2*t**3 + 2*t**4 = 0. What is t?
-1, 0, 1
Factor 3/2*z**5 + 0*z**4 + 0*z**2 - 3*z**3 + 0 + 3/2*z.
3*z*(z - 1)**2*(z + 1)**2/2
Factor 1/2*q**5 + 0*q**2 + 0 + 0*q - 1/4*q**4 - 1/4*q**3.
q**3*(q - 1)*(2*q + 1)/4
Let x(f) = 10*f**4 + 19*f**3 - 5*f**2 + 11*f + 11. Let v(r) = r**4 + r**3 + r**2 + r + 1. Let w(k) = 22*v(k) - 2*x(k). Factor w(t).
2*t**2*(t - 4)**2
Suppose -6*o**2 + 5*o**2 - o**4 - o + 3*o**2 - 5*o**2 - 3*o**3 = 0. Calculate o.
-1, 0
Let c(n) = n**2 + 8*n + 8. Let f be c(-8). Factor f + 3*g**4 - 8 - g**4 + g**3 + g**5.
g**3*(g + 1)**2
Let l(i) be the second derivative of -i**7/210 + 2*i**6/75 - 3*i**5/100 - i**4/15 + 2*i**3/15 - 22*i. Determine u so that l(u) = 0.
-1, 0, 1, 2
Solve -4*o**5 - 22 + 42*o**3 + 22 - 26*o**3 = 0.
-2, 0, 2
Let j(l) be the first derivative of 2*l**5/35 - 5*l**4/14 + 2*l**3/7 + 5*l**2/7 - 8*l/7 - 6. What is p in j(p) = 0?
-1, 1, 4
Solve -2/17*r**4 - 4/17*r + 0*r**3 + 0 + 6/17*r**2 = 0 for r.
-2, 0, 1
Let p(u) be the second derivative of -u**4/54 + u**3/9 - 15*u. Factor p(t).
-2*t*(t - 3)/9
Let n(x) be the first derivative of -5*x**3/3 - 15*x**2/2 + 11. Factor n(u).
-5*u*(u + 3)
Let i(m) be the third derivative of -7*m**6/180 + m**5/30 - m**3/3 + m**2. Let a(r) be the first derivative of i(r). Suppose a(b) = 0. What is b?
0, 2/7
Let u be 2 + -2 - (-42)/105. Solve -u*p**3 + 0*p**2 - 2/5*p**5 + 0*p - 4/5*p**4 + 0 = 0 for p.
-1, 0
Suppose j - 3*j = 32. Let z be 72/j*2/(-3). Solve 4 - 3*u + 2*u - z*u**2 + u**2 - u = 0 for u.
-2, 1
Let u(b) be the first derivative of 2 - 1/120*b**6 + 0*b**4 + b**2 - 1/60*b**5 + 0*b + 0*b**3. Let p(v) be the second derivative of u(v). Factor p(m).
-m**2*(m + 1)
Factor 0*h + 0*h**3 + 4/5*h**2 - 3/5*h**4 + 0 + 1/5*h**5.
h**2*(h - 2)**2*(h + 1)/5
Let l(k) be the third derivative of k**7/10080 + k**6/1440 + k**5/480 - 5*k**4/24 - 3*k**2. Let t(b) be the second derivative of l(b). Factor t(h).
(h + 1)**2/4
Let c(b) = -b -