.
-1
Let j = -12839/30 - -428. Let h(d) be the third derivative of -5/84*d**4 + 0 - 1/21*d**3 - j*d**5 - d**2 - 1/140*d**6 + 0*d. Find w, given that h(w) = 0.
-1, -1/3
Let q(p) be the third derivative of p**5/105 - p**4/6 + 30*p**2. Find a, given that q(a) = 0.
0, 7
Suppose -3 - 1 = c. Let n(k) = -k**2 - 4*k - 3. Let t(i) = i**2 + 5*i + 4. Let w(h) = c*t(h) - 5*n(h). Suppose w(l) = 0. Calculate l.
-1, 1
Let g be 0/((0 + -6)/(-6)). Solve 0 + 1/3*x**3 + 1/3*x**2 + g*x = 0 for x.
-1, 0
Let t(h) be the second derivative of -h**7/2940 + h**6/1260 - h**3/6 - 4*h. Let z(f) be the second derivative of t(f). Solve z(p) = 0 for p.
0, 1
Let u(d) be the first derivative of 2/15*d**5 + 0*d**2 + 1/9*d**6 - 3 + 0*d + 0*d**4 + 0*d**3. Factor u(j).
2*j**4*(j + 1)/3
Let x(i) be the second derivative of i**6/10 + 3*i**5/2 + 33*i**4/4 + 20*i**3 + 24*i**2 + 3*i - 2. Let x(w) = 0. Calculate w.
-4, -1
Let i(n) be the third derivative of n**6/60 + n**5/5 + n**4 + 8*n**3/3 + n**2. Let i(d) = 0. What is d?
-2
Let b(t) be the third derivative of 0 + 0*t**3 + 4*t**2 + 0*t + 1/1995*t**7 - 1/1140*t**6 + 1/228*t**4 - 1/570*t**5. Factor b(m).
2*m*(m - 1)**2*(m + 1)/19
Let n(g) = -4*g**2 - 4*g + 2. Let v(l) = 13*l**2 - 4*l**2 - 3 + 8*l + l. Let j be ((-5)/(-2))/((-3)/(-6)). Let m(a) = j*n(a) + 2*v(a). Factor m(t).
-2*(t - 1)*(t + 2)
Let n(m) be the second derivative of m**4/3 + 2*m**3/3 - 3*m. Determine x so that n(x) = 0.
-1, 0
Let d(l) be the second derivative of 9*l**6/5 + 9*l**5/5 - 2*l**4 - 8*l**3/3 + 24*l. Factor d(p).
2*p*(3*p - 2)*(3*p + 2)**2
Let j(s) be the second derivative of -s**6/105 - 2*s**5/35 - s**4/14 + 4*s**3/21 + 4*s**2/7 + 10*s. Suppose j(q) = 0. What is q?
-2, -1, 1
Let v = 64/273 - -2/39. What is m in v*m**4 + 0*m + 0 - 2/7*m**2 + 0*m**3 = 0?
-1, 0, 1
Let j = -55 - -38. Let x(q) = 7*q**2 - 2*q. Let f(m) = 20*m**2 - 6*m. Let s(u) = j*x(u) + 6*f(u). Suppose s(y) = 0. Calculate y.
0, 2
Suppose 26*j - 32*j + 30 = 0. Let -2*r**4 - 4*r**2 + 2*r - 2/5 + 4*r**3 + 2/5*r**j = 0. Calculate r.
1
Suppose 4*r + 2*r + 0*r = 0. Find s such that 2/5*s**3 + 0*s**2 - 4/5*s**4 + r + 0*s = 0.
0, 1/2
Let p(c) = -2*c - 5. Let u be p(-5). Suppose -3*q**2 - 5 + 2*q + 0*q + u = 0. What is q?
0, 2/3
Let n(t) be the second derivative of -t**9/5040 + t**4/6 - 4*t. Let v(f) be the third derivative of n(f). Let v(w) = 0. Calculate w.
0
Let v = 497/759 + 3/253. Suppose 8/3*l + 2 + v*l**2 = 0. Calculate l.
-3, -1
Let n be (-7496)/33 + (-9)/(-27). Let b = n + 227. Determine w so that 2/11*w**4 + 0 + b*w**2 + 4/11*w**3 + 0*w = 0.
-1, 0
Suppose -4*x = 3*z - 2*z - 44, 5*x - 46 = z. Let y be 222/57 - 10/(-95). Suppose 5*o**3 + 2*o**4 + o**3 + 2*o + x*o**2 - y*o**2 = 0. Calculate o.
-1, 0
Let o(t) = -5*t**4 - 16*t**3 + 5*t**2 + 16*t. Let q(j) = -j**3 + j. Let f(s) = -o(s) - 4*q(s). Determine x so that f(x) = 0.
-4, -1, 0, 1
Let g(u) be the third derivative of 0*u + 0 + 1/150*u**5 - 1/840*u**8 + 0*u**3 + 1/175*u**7 + 0*u**4 - 1/100*u**6 + 3*u**2. Solve g(b) = 0.
0, 1
Factor 7*q + 5*q**5 + 3*q - 20*q**4 - 20*q**2 - 5*q + 30*q**3.
5*q*(q - 1)**4
Let q(v) be the third derivative of -v**5/15 + 6*v**3 + 37*v**2. What is u in q(u) = 0?
-3, 3
Let c(w) be the first derivative of 0*w + 0*w**3 + 1/240*w**5 + 0*w**4 + 2 + w**2. Let f(r) be the second derivative of c(r). What is d in f(d) = 0?
0
Let f = 6 + -4. Let d = 2 + f. Let 22*t**3 + 3*t**5 + 5*t + t - 1 - 18*t**2 - 13*t**d + t = 0. Calculate t.
1/3, 1
Let h(r) = -r**3 - 4*r**2 + 5*r. Let v be h(-5). Factor 5/3*g**2 - 1/3*g**5 + 2/3*g - 1/3*g**4 + g**3 + v.
-g*(g - 2)*(g + 1)**3/3
Let c(f) be the third derivative of f**7/5040 + f**4/12 + f**2. Let q(v) be the second derivative of c(v). Determine i, given that q(i) = 0.
0
Suppose -2*t = -4*y + 15 - 3, -16 = t - 4*y. Factor -6 - t*b - 2/3*b**2.
-2*(b + 3)**2/3
Let v = -5891/11 - -536. Let p(m) be the first derivative of -20/33*m**3 - 5/11*m**2 - 3 - 2/11*m - 1/33*m**6 - 2/11*m**5 - v*m**4. Find o such that p(o) = 0.
-1
Let g(v) be the second derivative of -v**7/7 - v**6/3 + v**5/2 + 5*v**4/6 - 2*v**3/3 - 18*v. What is c in g(c) = 0?
-2, -1, 0, 1/3, 1
Find a, given that 2*a**3 + 7*a**2 + 6*a - 9*a**2 - 6*a**2 = 0.
0, 1, 3
Find u such that -2*u - 2*u**2 + 4/3 + 14/3*u**3 - 2*u**4 = 0.
-2/3, 1
Let g(r) be the third derivative of r**8/80640 + r**7/6720 + r**6/1440 - r**5/15 + 4*r**2. Let b(h) be the third derivative of g(h). Solve b(i) = 0.
-2, -1
Let j(q) = q**4 - 11*q**3 + 32*q**2 - 20*q + 8. Let t(n) = n**4 - 11*n**3 + 33*n**2 - 19*n + 8. Let r(p) = -6*j(p) + 5*t(p). Factor r(x).
-(x - 8)*(x - 1)**3
Find a, given that 6/7*a**3 + 0 - 4/7*a**2 + 0*a - 2/7*a**4 = 0.
0, 1, 2
Factor 43 + 24*l**3 - 96*l + 27 + 4*l**4 - 6 + 4*l**2.
4*(l - 1)**2*(l + 4)**2
Suppose y - 25 = -4*y - 5*t, 2*t - 6 = 0. Suppose 2*c + y = 2*o, 5*o = -5*c + 16 + 9. Solve 0 - 1/4*p**c + 1/2*p = 0.
0, 2
Let b(l) be the first derivative of l**3 + 0*l - 2 + 3*l**2 - 9/4*l**4. Factor b(m).
-3*m*(m - 1)*(3*m + 2)
Suppose -k = 3*k + 16. Let n(p) = -7*p**2 + p - 2. Let d(x) = -6*x**2 + x - 1. Let u(w) = k*d(w) + 3*n(w). Factor u(v).
(v - 1)*(3*v + 2)
Let n(u) = -u - 1. Let l be n(-3). Factor m - l*m - 3*m - 2 - 2*m**2.
-2*(m + 1)**2
Let q be 1 - (0 + (-39)/(-45)). Let d(f) be the second derivative of 1/5*f**2 + q*f**3 + 0 + 1/30*f**4 + 2*f. Suppose d(h) = 0. Calculate h.
-1
Suppose 2*b = 2*g + 10, -4*g - 28 = -3*b - 2*b. Let j(v) = -v + 12. Let r be j(12). Suppose -10*n**3 - 8/5*n + r - b*n**2 = 0. What is n?
-2/5, 0
Let u = 42 + -16. Let h = -77/3 + u. Factor -h*j**3 + j**2 + 1/3 - j.
-(j - 1)**3/3
Let p = 38 + -36. Let t(x) be the first derivative of 1/6*x**3 + 1/4*x**p + 0*x + 1. Let t(a) = 0. What is a?
-1, 0
Let x(u) = -2*u**3 - 4*u**2 + 6*u + 3. Let j be x(-3). Suppose 1/4*d**j + 9/4*d**2 + 27/4*d + 27/4 = 0. Calculate d.
-3
Let y be (-1)/(35/5 - 11). Factor y*b**4 - 1/4*b**2 - 1/4*b**3 + 1/4*b + 0.
b*(b - 1)**2*(b + 1)/4
Let h = -2 - -5. Suppose -3*a**2 + h*a**2 - 3*a**3 = 0. Calculate a.
0
Let r be (3/(-1))/(7 + (-120)/10). Find v, given that r*v**2 + 3/5 + 6/5*v = 0.
-1
Suppose 5*b + 2*x - 11 = -x, b = 4*x + 16. Factor 2/3*l + 0*l**3 + 0 - l**2 + 1/3*l**b.
l*(l - 1)**2*(l + 2)/3
Let w(t) = 2*t**4 - 12*t**3 + 23*t**2 - 3*t. Let m(q) = q**2 + q. Let p(z) = -10*m(z) + 2*w(z). Factor p(k).
4*k*(k - 4)*(k - 1)**2
Factor -3/4*y + 1/2 + 1/4*y**2.
(y - 2)*(y - 1)/4
Let i(f) be the second derivative of f**7/21 + f**6/15 - 4*f**5/5 - 4*f**4/3 + 16*f**3/3 + 16*f**2 + 6*f. Determine h so that i(h) = 0.
-2, -1, 2
Let l be 0 + 1 + 2 + -2. Let u be 2 + 4*l/2. Factor 3*m**4 - 6*m**4 + m**u.
-2*m**4
Let u be (84/(-16) + 5)*-6. Let l(o) be the first derivative of -2 - 1/2*o**6 + 3/2*o**4 + 0*o**5 + 0*o - u*o**2 + 0*o**3. Find n such that l(n) = 0.
-1, 0, 1
Let k(y) be the second derivative of y**5/15 + 5*y**4/24 + y**3/6 - y**2/2 + 2*y. Let l(m) be the first derivative of k(m). Factor l(a).
(a + 1)*(4*a + 1)
Let l(z) = -z**3 + 4*z**2 - z - 3. Let f = 18 + -15. Let r be l(f). Factor 4/5*g**r + 0*g - 2/5*g**2 + 0 - 2/5*g**4.
-2*g**2*(g - 1)**2/5
Let m = 67/57 + 3/19. Find o, given that 1/3*o**3 + 0 + 4/3*o - m*o**2 = 0.
0, 2
Suppose -4*c = 4 - 12. Factor -5*w - 7*w**2 + c*w**2 - 8 + 3*w**2 - 3*w.
-2*(w + 2)**2
Solve 0*x + 0*x**3 + 8/7 - 10/7*x**2 + 2/7*x**4 = 0.
-2, -1, 1, 2
Let v(s) = -1. Suppose 5*j + 7 = -m + 4*j, j - 8 = 2*m. Let w(p) = -p**2 + p + 5. Let l(c) = m*v(c) - w(c). Find n such that l(n) = 0.
0, 1
Let c(n) be the third derivative of -n**7/1260 - n**6/180 + n**4/6 + 5*n**2. Let m(a) be the second derivative of c(a). Suppose m(u) = 0. Calculate u.
-2, 0
Let s(t) be the second derivative of -t**7/63 + t**6/45 + t**5/30 - t**4/18 - 5*t. Let s(l) = 0. What is l?
-1, 0, 1
Let r(s) be the first derivative of -1/6*s**6 - 2/3*s**3 - 3 + s + 1/5*s**5 - 1/2*s**2 + 1/2*s**4. Factor r(k).
-(k - 1)**3*(k + 1)**2
Let f(n) = -n**3 - 4*n**2 - 2*n - 2. Let z be f(-5). Suppose -3*s = m - 11, -m + z = 4*s + 4*m. Determine v, given that -3*v - v**2 + 3*v - v**s = 0.
0
Let k(g) be the first derivative of 2*g**3/3 - g**2 - 4*g - 16. Factor k(h).
2*(h - 2)*(h + 1)
Let t(q) be the third derivative of q**7/525 + q**6/150 - q**5/150 - q**4/30 + 4*q**2. Factor t(u).
2*u*(u - 1)*(u + 1)*(u + 2)/5
Let q(f) = f**3 - f**2 - f. Let x(g) = -3*g**3 + g**2 + 3*g + 1. 