2
Let y(m) be the third derivative of m**9/15120 + m**8/3360 + m**7/2520 - m**4/24 - m**2. Let u(q) be the second derivative of y(q). Suppose u(p) = 0. What is p?
-1, 0
Let y(l) be the third derivative of -l**7/210 - l**6/60 - l**5/60 + 9*l**2. Determine o, given that y(o) = 0.
-1, 0
Let c be 8/(-20) + 8/20. Let d(i) be the third derivative of 0*i**3 + 1/150*i**5 + 2*i**2 + 0*i**4 + 0 + 1/300*i**6 + c*i. Find p such that d(p) = 0.
-1, 0
Let d(k) be the third derivative of -k**6/660 + k**5/110 - k**4/44 + k**3/33 - 4*k**2. Let d(y) = 0. What is y?
1
Let u(c) be the second derivative of c**9/1176 - c**8/392 + c**7/420 - c**6/1260 + c**3 - c. Let f(m) be the second derivative of u(m). Factor f(a).
2*a**2*(a - 1)*(3*a - 1)**2/7
Factor -y**5 - 8*y**2 - 5 + 7*y + 5 - 2 + 2*y**4 + 2*y**3.
-(y - 1)**4*(y + 2)
Let m = -211/4 + 53. Factor 1/2 - m*k**2 - 1/4*k.
-(k - 1)*(k + 2)/4
Suppose 3*d - 2*y + 4*y - 4 = 0, 5*d - 15 = -5*y. Let f be d/4 + (-25)/(-30). Solve f*l**2 - 1/3 + 0*l = 0 for l.
-1, 1
Let u(g) = -7*g**3 + g**2 + 37*g + 24. Let m(a) = -a**3 - a**2 + a. Let z(f) = -5*m(f) + u(f). Find w such that z(w) = 0.
-2, -1, 6
Let 0*x**2 + 4/7*x**3 - 2/7*x**4 - 4/7*x + 2/7 = 0. What is x?
-1, 1
Determine r, given that 4/9*r + 16/9*r**2 - 8/9*r**4 + 4/9*r**5 - 8/9 - 8/9*r**3 = 0.
-1, 1, 2
Let s(z) = 8*z**2 + 24*z - 26. Let j(v) = v**2 + v - 1. Let q(a) = 6*j(a) - s(a). What is g in q(g) = 0?
-10, 1
Let w = 7 + -11. Let q be w/8 + -1 - -2. Factor n**2 + 0 + 0*n - q*n**3.
-n**2*(n - 2)/2
Let u(i) be the third derivative of 0*i + 1/12*i**3 - 1/96*i**6 - 7/96*i**4 + 3/80*i**5 + 1/840*i**7 - 5*i**2 + 0. Find t such that u(t) = 0.
1, 2
Suppose -6/5*d**3 + 0*d + 0*d**4 + 2/5*d**5 - 4/5*d**2 + 0 = 0. What is d?
-1, 0, 2
Let v be (-1520)/200 - 1*-10. Factor v - 12/5*f + 3/5*f**2.
3*(f - 2)**2/5
Let f(d) be the first derivative of d**3/3 - 6*d**2 + 11*d + 1. Let h(u) = -12*u + 12. Let t(z) = 3*f(z) - 2*h(z). Factor t(n).
3*(n - 3)*(n - 1)
Let d(f) be the third derivative of f**7/315 - f**6/60 + f**5/90 + f**4/12 - 2*f**3/9 - 5*f**2. Find a, given that d(a) = 0.
-1, 1, 2
Let -4/7*w**2 + 0*w**3 + 0*w + 2/7 + 2/7*w**4 = 0. Calculate w.
-1, 1
Let q(u) be the second derivative of 0*u**3 - 2*u + 0 - 1/10*u**5 + 1/9*u**6 - 1/9*u**4 + 0*u**2. Find b such that q(b) = 0.
-2/5, 0, 1
Let y(x) be the third derivative of -1/70*x**7 + 0*x + 0*x**3 + 3*x**2 + 1/40*x**6 - 1/60*x**5 + 0*x**4 + 0 + 1/336*x**8. Let y(m) = 0. Calculate m.
0, 1
Let w(s) be the second derivative of -12*s**2 + 9/20*s**5 - 1/2*s**4 + 1/10*s**6 - 6*s**3 + 2*s + 0. Determine q so that w(q) = 0.
-2, -1, 2
Let 0*c**3 - 7*c - 12 + 15*c**2 + 3*c**3 + 4*c - 3 = 0. Calculate c.
-5, -1, 1
Find o such that 10/9*o - 8/9*o**3 - 8/9*o**4 - 2/9*o**5 + 4/9 + 4/9*o**2 = 0.
-2, -1, 1
Let r(x) be the second derivative of 0*x**2 - 1/12*x**4 + 1/10*x**5 + 0 + 0*x**3 - 1/30*x**6 + 4*x. Solve r(q) = 0 for q.
0, 1
Let v = -31 - -21. Let c be 4/v + (-9)/(-10). Determine r so that 0*r + 0 - c*r**3 + 0*r**2 = 0.
0
Factor 1 + 5*l**2 - 5*l**2 + l**4 - 2*l**2.
(l - 1)**2*(l + 1)**2
Let u(m) = m**4 + 14*m**3 + 48*m**2 - 14*m - 54. Let i(c) = 1. Let k(d) = -5*i(d) - u(d). Factor k(a).
-(a - 1)*(a + 1)*(a + 7)**2
Let i(q) be the second derivative of 0 + 0*q**2 - 1/15*q**3 - 1/60*q**4 + 9*q. Solve i(f) = 0 for f.
-2, 0
Factor 14/19*w**3 + 36/19*w**2 + 16/19 + 40/19*w + 2/19*w**4.
2*(w + 1)*(w + 2)**3/19
Let y be -7 - -7 - 2/(-4). Find v, given that v + 0 - y*v**2 = 0.
0, 2
Let c(t) = -7*t**3 - 5*t**2 + 2*t - 6. Let d = -12 + 13. Let f(b) = b**3 + b**2 + 1. Let r(m) = d*c(m) + 6*f(m). Let r(u) = 0. Calculate u.
-1, 0, 2
Let l(g) be the first derivative of 0*g + 1/15*g**5 + 2 + 0*g**2 - 1/9*g**3 + 0*g**4. Factor l(v).
v**2*(v - 1)*(v + 1)/3
Let q(g) be the second derivative of -g**6/75 + 5*g. Suppose q(j) = 0. Calculate j.
0
Let t(z) = 2*z**4 + z**3 + 3*z**2 + 3*z. Let r(x) = 5*x**4 + 2*x**3 + 7*x**2 + 7*x. Let f(h) = -3*r(h) + 7*t(h). Factor f(s).
-s**3*(s - 1)
Let q = 5 - 3. Let n(i) be the third derivative of 0*i + 1/504*i**8 + 0 + 1/105*i**7 - 1/9*i**3 - 1/12*i**4 - 1/45*i**5 + 2*i**q + 1/90*i**6. Factor n(u).
2*(u - 1)*(u + 1)**4/3
Let k(y) = 3*y**2 + 5*y - 2*y**2 - 13*y + 10. Let x be k(7). Solve 0*q**3 + 3*q**4 + q**2 + 0*q**2 - 5*q**4 + q**x = 0.
-1/2, 0, 1
Suppose -n + 0*n + 3 = 0. Factor 9*f**5 - n*f**5 + 40*f**3 + 6 + 26*f**3 - 54*f**4 + 9*f**5 - 24*f**2 - 9*f.
3*(f - 1)**4*(5*f + 2)
Let w be (-5 - -4)/((-1)/2). Suppose -3*f + 2*f + w = 0. Factor 1/2*p**f + 1/2 + p.
(p + 1)**2/2
Let v(j) = 32*j**2 - 88*j - 19. Let d(i) = 16*i**2 - 44*i - 9. Let z(l) = 5*d(l) - 3*v(l). Factor z(b).
-4*(b - 3)*(4*b + 1)
Factor 5*m**2 - 3*m**2 - 3*m**3 + 2*m**3.
-m**2*(m - 2)
Let y(s) be the third derivative of s**5/12 + 35*s**4/24 + 25*s**3/3 + 10*s**2. Let y(q) = 0. What is q?
-5, -2
Let g(n) = -6*n**2 + 4*n + 6. Let f be (5/(-3) - -2)*-3. Let x(y) = y**2 - y - 1. Let o(l) = f*g(l) - 4*x(l). Determine w so that o(w) = 0.
-1, 1
Suppose 2*d + d = 12. Factor 0*j**4 - 4*j**2 + 2*j + 2*j**5 + d*j**4 + j - 5*j.
2*j*(j - 1)*(j + 1)**3
Let y be 12/(-4) - (-6)/1. Find q, given that -16*q**2 + 5*q**y + 4*q + 2*q**3 + 0*q**3 = 0.
0, 2/7, 2
Suppose -r = -d - 8, 2*r - 5*d + 2*d = 20. Let y be ((-6)/(-4) - 2) + 1. Suppose 1/4*h**2 + 0*h + y*h**3 + 0 + 1/4*h**r = 0. Calculate h.
-1, 0
Let i = -13/5 + 3. Let y = 871/5 - 173. Factor y*r**2 + 2/5 - i*r**3 - 6/5*r.
-2*(r - 1)**3/5
Let m(x) = x**2 + x - 42. Let d be m(-7). Factor 0 - 3/5*l**4 - 3/5*l**2 + d*l - 6/5*l**3.
-3*l**2*(l + 1)**2/5
Let a(z) be the third derivative of -z**6/180 - z**5/30 - z**4/12 - z**3/6 - 2*z**2. Let k(u) be the first derivative of a(u). Let k(p) = 0. Calculate p.
-1
Let r(u) be the second derivative of -u**6/75 + 2*u**5/25 - u**4/5 + 4*u**3/15 - u**2/5 - 7*u. Factor r(l).
-2*(l - 1)**4/5
Let v be (2/40)/(36/810). Let s(n) be the first derivative of -1 + v*n**2 - 3/2*n - 1/4*n**3. Factor s(t).
-3*(t - 2)*(t - 1)/4
Let f(l) be the second derivative of -1/6*l**3 + l**2 + l - 1/12*l**4 + 0. Solve f(x) = 0.
-2, 1
Determine q so that -7*q + 3*q - 2*q - 2*q**2 = 0.
-3, 0
Suppose 0*t = -4*t + 8. Suppose 6*x - 3 + 36*x**t + 3 - 39*x**2 = 0. Calculate x.
0, 2
Let l(s) be the second derivative of -s**5/360 + s**4/48 - s**3/18 - 3*s**2/2 - s. Let t(h) be the first derivative of l(h). Factor t(u).
-(u - 2)*(u - 1)/6
Suppose -a = 3*a - 4. Let x(o) = 4*o**2 - 2*o + 1. Let k be x(a). Factor 0*y**5 + 3*y**5 - 5*y - 4*y**k - 2*y**4 + 6*y + 2*y**2.
y*(y - 1)**2*(y + 1)*(3*y + 1)
Let m(i) be the first derivative of -3*i**5/10 + 15*i**4/8 - 3*i**3/2 - 27*i**2/4 + 8. Solve m(k) = 0.
-1, 0, 3
Let c(m) be the third derivative of -m**5/210 + m**4/84 + 2*m**3/21 + 39*m**2. Solve c(o) = 0 for o.
-1, 2
Let q be (0 + 15)*17/85. Suppose -3*y - 13 = -5*a, -2 = -5*a - q*y + 5. Let 2/5*x + 2/5*x**a - 4/5 = 0. Calculate x.
-2, 1
Let s(g) = 2*g**3 - 25*g**2 + 45*g - 5. Let l(t) = -t**2 - t - 1. Let j(n) = -10*l(n) + 2*s(n). Factor j(w).
4*w*(w - 5)**2
Factor 14/9*a**4 + 32/9*a**3 + 16/9*a**2 - 32/9*a - 32/9 + 2/9*a**5.
2*(a - 1)*(a + 2)**4/9
Let d(n) be the first derivative of 0*n**2 - 1/20*n**4 + 0*n**3 + 0*n - 3. Factor d(j).
-j**3/5
What is z in 9/4 + 3/4*z**2 + 21/4*z**3 - 3*z**4 - 21/4*z = 0?
-1, 3/4, 1
Let b be 4*21/(-224) + (-15)/(-8). Let b*y**2 - 4*y**3 + 0 + 3/2*y**4 + y = 0. What is y?
-1/3, 0, 1, 2
Let t(o) = -o**2 + 5*o - 2. Let g be t(3). Factor 4*i**g - 12 - 2*i**5 + 6*i**3 - 8*i - 8*i**2 + 12.
-2*i*(i - 2)**2*(i + 1)**2
Determine n, given that -2/11*n**2 - 4/11 - 6/11*n = 0.
-2, -1
Solve 6*j**2 - 6*j**2 + 0*j**5 - 6*j**4 + 3*j**5 + 3*j**3 = 0.
0, 1
Let r(l) be the first derivative of -3*l**4/8 - 5*l**3/4 - 3*l**2/4 + 1. What is g in r(g) = 0?
-2, -1/2, 0
Let l(b) be the second derivative of -b**4/84 + b**2/14 + 10*b. Suppose l(f) = 0. Calculate f.
-1, 1
Let w(k) = -4*k**3 - 7*k**2 - 2*k + 6. Let a(r) = r**3 + 2*r**2 + r - 2. Let s be 171/(-12) + (-1)/(-4). Let o(p) = s*a(p) - 4*w(p). What is h in o(h) = 0?
-2, 1
Let d be (-1)/(-2) + (-3)/(-2). Let j be (0 - -2) + (3 - d). Factor -6*a**j - 2*a**2 + 0*a**2 - 2*a**3.
-2*a**2*(4*a + 1)
Let c(k) be the second derivative of -k**9/45360 + k**8/20160 + k**7/7560 - k**6/2160 + k**4/6 + 2*k. Let x(v) be the third derivative of c(v). Factor x(y).
-y*(y - 1)**2*(