 j(i) = 105*i**4 - 50*i**3 - 90*i**2 + 35*i. Let q(h) = -2*j(h) - 15*k(h). Factor q(l).
5*l*(l - 1)*(l + 1)*(3*l - 1)
Let v(b) be the first derivative of -75*b**3/4 - 15*b**2/2 - b - 1. Factor v(d).
-(15*d + 2)**2/4
Let t(c) be the second derivative of -c**8/20160 + c**7/7560 - c**4/6 - 2*c. Let m(q) be the third derivative of t(q). What is l in m(l) = 0?
0, 1
Let h(u) be the third derivative of -u**7/70 + 3*u**6/20 - 9*u**5/20 + u**4/2 - 9*u**2. Suppose h(b) = 0. Calculate b.
0, 1, 4
Let i(k) be the third derivative of k**6/40 + k**5/4 - 3*k**4/4 - k**2 - 31*k. Suppose i(x) = 0. What is x?
-6, 0, 1
Let n = 2 - -1. Suppose -n = -2*u + 1. Determine z, given that u*z**4 - 2*z**2 - 5*z**2 + 5*z**2 = 0.
-1, 0, 1
Let z(b) be the first derivative of -5*b**4/4 + 15*b**2/2 + 10*b + 9. Factor z(s).
-5*(s - 2)*(s + 1)**2
Let n = -1 - -8. Let k(z) = -13*z**5 - 8*z**4 - 5*z**3 - 5*z. Let q(f) = 19*f**5 + 12*f**4 + 7*f**3 + 7*f. Let u(h) = n*k(h) + 5*q(h). Factor u(m).
4*m**4*(m + 1)
Let z = 5 - 0. Let t(r) = r - 3. Let y be t(z). Suppose 6*v - 2 + 2*v**2 + 4 - y*v = 0. What is v?
-1
Let z be 8/(-14)*(-21)/54. Find m such that -2/9*m**3 + 2/9*m - 2/9*m**2 + z = 0.
-1, 1
Let z be (3 - 0)*(-140)/(-30). Let i be 4/z + 38/14. What is w in 2/3*w**i + 0 - 4/3*w + 2/3*w**2 = 0?
-2, 0, 1
Let z(i) be the second derivative of -i**4/6 - 2*i**3/3 + 8*i**2 + 6*i. Factor z(v).
-2*(v - 2)*(v + 4)
Factor 0 - 1/5*n**2 + 0*n - 1/5*n**3.
-n**2*(n + 1)/5
Let x be (2/3)/((-12)/(-54)). Suppose x*w + 2 = -2*u, -2*u + 0*u = -w + 10. Solve 0 - 2/9*q**w + 4/9*q = 0.
0, 2
Suppose 2*u - u = 4*h - 2, 0 = -u - 5*h + 25. Factor -3*v**3 - v - 6 + u*v + 0*v.
-3*(v - 1)**2*(v + 2)
Let i(z) = -4*z**5 + 20*z**4 - 36*z**3 + 28*z**2 - 8*z + 6. Let r(k) = 1. Let m(p) = i(p) - 6*r(p). Suppose m(n) = 0. Calculate n.
0, 1, 2
Suppose 4*j - 24 = -4*y, -5*j + 20 = -y + 2. Suppose 2/5 + 2*w**4 + 4*w**y + 4*w**3 + 2*w + 2/5*w**5 = 0. Calculate w.
-1
Let x(w) be the first derivative of -w**9/1512 + w**8/600 - w**7/1050 - 5*w**3/3 + 5. Let h(n) be the third derivative of x(n). Factor h(d).
-2*d**3*(d - 1)*(5*d - 2)/5
Let j = 2 - -1. Factor -2*h**2 + j*h + 0 - h**2 + 0.
-3*h*(h - 1)
Let r(a) be the second derivative of 5*a**7/42 + 5*a**6/6 + 9*a**5/4 + 35*a**4/12 + 5*a**3/3 - 16*a. Factor r(d).
5*d*(d + 1)**3*(d + 2)
Let y(w) be the first derivative of -3*w**3 + 27*w**2 - 81*w - 11. Let h(m) = 6*m**2 - 36*m + 54. Let g(f) = -8*h(f) - 5*y(f). Determine p so that g(p) = 0.
3
Let a(d) be the first derivative of 2*d**3/15 - 4*d**2/5 + 8*d/5 - 2. Find n such that a(n) = 0.
2
Let k(p) = -p + 12. Let i be k(13). Let u be (0 + 1 + i)/1. Find t such that u - 2/9*t**4 - 2/9*t**2 + 0*t + 4/9*t**3 = 0.
0, 1
Find j such that -8/7 - 2/7*j**2 + 8/7*j = 0.
2
Let g(o) = -o**2. Let j(t) = 2*t**3 - 2*t - 6. Let i(f) = 6*g(f) - j(f). Determine w so that i(w) = 0.
-3, -1, 1
Factor 0*g**2 + 0 - 1/2*g + 1/2*g**3.
g*(g - 1)*(g + 1)/2
Let m = -13 - -18. Suppose -5*q = m*l, -q = 3*l - 0*l - 6. Factor -2*v**3 + 4*v + 2*v**l - 2*v**3 + 2*v**2.
-2*v*(v - 2)*(v + 1)
Let z(x) be the second derivative of x**9/504 + x**8/420 + x**7/1260 - 3*x**3/2 + 4*x. Let t(k) be the second derivative of z(k). Solve t(f) = 0 for f.
-1/3, 0
Let k(y) be the first derivative of y**6/480 + y**5/80 - y**3/6 - y**2 - 3. Let d(i) be the second derivative of k(i). What is u in d(u) = 0?
-2, 1
Let q(f) be the third derivative of f**8/1680 - f**7/420 + f**5/60 - f**4/24 - 2*f**3/3 - 4*f**2. Let y(k) be the first derivative of q(k). Factor y(d).
(d - 1)**3*(d + 1)
Let a(u) be the first derivative of 0*u**4 - 2/65*u**5 + 0*u**2 - 2/13*u + 4/39*u**3 + 4. Factor a(c).
-2*(c - 1)**2*(c + 1)**2/13
Suppose 0 = 6*r - 10*r + 8. Let t(h) = -2*h - 1. Let u be t(-2). What is o in -u*o + 3*o**2 - 3*o**r - 3*o**2 = 0?
-1, 0
Let w(t) be the third derivative of -5*t**8/336 + t**6/12 - 5*t**4/24 + 5*t**2. Factor w(p).
-5*p*(p - 1)**2*(p + 1)**2
Let v(o) be the first derivative of o**6/27 + 14*o**5/45 + o**4 + 40*o**3/27 + 8*o**2/9 + 3. Determine t so that v(t) = 0.
-2, -1, 0
Let x = -2/15 - -4/5. Factor -2/3*r + 0 + 0*r**2 + x*r**3.
2*r*(r - 1)*(r + 1)/3
Let m(h) = 5*h + 5*h + h + 8 - 3*h + 6*h**2. Let q(v) = -11*v**2 - 16*v - 16. Let t be (3 + 1)*(0 + -1). Let c(k) = t*q(k) - 7*m(k). Factor c(n).
2*(n + 2)**2
Let b(q) be the first derivative of 100*q**3/3 + 60*q**2 + 36*q - 11. Find s, given that b(s) = 0.
-3/5
Let g be 4/8*-4 + -5. Let s = 7 + g. Solve -1/5*n**3 + s - 4/5*n**2 + 4/5*n**4 + 1/5*n = 0 for n.
-1, 0, 1/4, 1
Let m(a) be the second derivative of 1/12*a**4 + a + 1/60*a**5 + 0*a**2 + 0 + 1/9*a**3. What is d in m(d) = 0?
-2, -1, 0
Suppose 0*n - 5*n = -25. Determine x so that 0*x + 4*x - 5*x + n*x + 2*x**2 = 0.
-2, 0
Suppose -11*y - 6 = -13*y. Let p(f) be the second derivative of 0 + f + 0*f**2 + 1/105*f**6 - 1/42*f**4 + 1/21*f**y - 1/70*f**5. Determine d so that p(d) = 0.
-1, 0, 1
Let l = 51/305 + 2/61. Factor -1/5*f**5 + 2/5*f**4 + l*f + 0 - 2/5*f**2 + 0*f**3.
-f*(f - 1)**3*(f + 1)/5
Suppose 0 = 2*n + n. Let j = 479 + -479. Factor j*y**3 - 2/9*y**4 + 2/9*y**2 + n*y + 0.
-2*y**2*(y - 1)*(y + 1)/9
Let d(w) = -2*w**2 - 5*w. Let f(p) = 0 - 2 + p + 2. Let r(k) = 2*d(k) + 6*f(k). Factor r(m).
-4*m*(m + 1)
Determine s, given that 2/7*s**2 + 32/7 + 16/7*s = 0.
-4
Let a(g) be the second derivative of -g**7/294 - g**6/105 + g**4/42 + g**3/42 + 30*g. Find z, given that a(z) = 0.
-1, 0, 1
Factor -50 + 50 + 3*w**2 - 3*w.
3*w*(w - 1)
Let n be 364/(-189) - -2*1. Let p = n + 23/54. Factor 1/4*k**2 + 1/4 + p*k.
(k + 1)**2/4
Let z(i) be the second derivative of -i**5/70 - i**4/42 + 2*i**3/21 - 2*i. Determine j, given that z(j) = 0.
-2, 0, 1
Let u be 27/15 - 3/(-15). Suppose -o**4 - 2*o - 2*o**3 - o**5 + 2*o**u + 5*o + 1 - 2*o**4 = 0. Calculate o.
-1, 1
Suppose 0 = 2*b - 5*o + 4 + 3, -2*b - 4*o + 20 = 0. Let 4/5*c + 6/5*c**2 + 0 - 16/5*c**3 + 6/5*c**b = 0. Calculate c.
-1/3, 0, 1, 2
Let k be 18/(-27) - (-8)/3. Factor -8/5*z**k + 0 + 2/5*z**3 + 6/5*z.
2*z*(z - 3)*(z - 1)/5
Let l(u) be the third derivative of -u**7/105 + u**5/10 + u**4/6 + 9*u**2. Solve l(d) = 0.
-1, 0, 2
Let f(g) be the first derivative of -g**6/120 + g**5/40 - g**4/48 - g - 2. Let t(n) be the first derivative of f(n). Let t(c) = 0. Calculate c.
0, 1
Let m be (1008/(-490) + 2)/((-2)/40). Factor 12/7*t**2 + 2/7*t**4 - 16/7 - m*t + 10/7*t**3.
2*(t - 1)*(t + 2)**3/7
Let i(r) be the third derivative of -r**5/240 - r**4/48 + 2*r**2. Factor i(d).
-d*(d + 2)/4
Let g(d) be the second derivative of -d**6/120 - d**5/20 - d**4/8 + d**3 - 9*d. Let z(j) be the second derivative of g(j). Solve z(u) = 0 for u.
-1
Let w(l) be the second derivative of -2*l**7/147 + 4*l**5/35 - 2*l**4/21 - 2*l**3/7 + 4*l**2/7 - 8*l. Determine n so that w(n) = 0.
-2, -1, 1
Solve 2*b - 2*b**5 - 2*b**2 + b**5 - b + 2*b**4 = 0.
-1, 0, 1
Let p(j) be the first derivative of -3/8*j**4 + 0*j**2 - 3 + 0*j - 1/3*j**3 - 1/10*j**5. What is t in p(t) = 0?
-2, -1, 0
Let z(d) be the first derivative of 3*d**4/4 + d**3 + 27. Factor z(j).
3*j**2*(j + 1)
Let n(u) be the first derivative of u**6/30 - 3*u**5/25 - u**4/5 + 6. Suppose n(f) = 0. Calculate f.
-1, 0, 4
Determine l, given that 16*l + 106*l**3 + 16*l**2 - 110*l**3 - 2*l**4 - 2*l**4 = 0.
-2, -1, 0, 2
Let h(i) be the first derivative of 3*i**5/5 - 3*i**4/2 - 3*i**3 + 12*i**2 - 12*i - 5. Factor h(l).
3*(l - 2)*(l - 1)**2*(l + 2)
Let q(m) be the second derivative of m**7/42 + m**6/30 + 9*m. Determine h so that q(h) = 0.
-1, 0
Let q(p) be the third derivative of -4*p**5/15 - 5*p**4/2 + 8*p**3/3 - 14*p**2. Factor q(y).
-4*(y + 4)*(4*y - 1)
Let b = 1 - -9. Factor 3*j**2 - 2*j + 26*j**3 + 4*j**2 + b*j**4 + 1 - 5 + 11*j**2.
2*(j + 1)**3*(5*j - 2)
Let t(q) be the second derivative of -q**6/150 + 3*q**5/100 - q**4/20 + q**3/30 + 3*q. Suppose t(w) = 0. What is w?
0, 1
Suppose 2*y - 37 = -5*z, 0 = 2*y - 5*y + z + 47. Suppose -2*w = -0*w - y. Factor -1 + w*x**3 + 2*x**2 - 1 - 7*x - x.
2*(x - 1)*(x + 1)*(4*x + 1)
Let s be -5 + 2 + (-39)/(-9). Let h(u) be the first derivative of -1 + 8/3*u + 2/9*u**3 - s*u**2. Factor h(n).
2*(n - 2)**2/3
Let n = 10 + -7. Suppose -2*c + n*t + t = -20, -2*t - 8 = 0. Factor 4*g**2 - 2*g**2 + c*g - g**2.
g*(g + 2)
Factor -4*q**2 - 4*q - 8*q**3 + 2*q**5 + 4*q + 6*q + 4.
2*(q - 2)*(q - 1)*(q + 1)*