 i(l) be the third derivative of r(l). What is x in i(x) = 0?
-2, 0
Suppose -8*q + 7*q + 6 = 0. Let h(w) be the second derivative of -1/15*w**q + 0 + 0*w**2 - w + 0*w**5 + 0*w**4 + 0*w**3 + 1/21*w**7. Factor h(o).
2*o**4*(o - 1)
Let b(m) = -2*m. Let j be b(1). Let f be j/4*8/(-14). Solve -f*g - 8/7*g**4 + 0*g**3 + 6/7*g**2 + 0 = 0 for g.
-1, 0, 1/2
Let u(h) be the third derivative of -h**8/672 - h**7/210 + h**6/48 + h**5/12 - h**4/12 - 2*h**3/3 - 10*h**2. Find a such that u(a) = 0.
-2, -1, 1, 2
Let b(z) be the third derivative of z**11/1995840 + z**10/302400 - z**8/30240 + 3*z**5/20 - 10*z**2. Let g(s) be the third derivative of b(s). Factor g(y).
y**2*(y - 1)*(y + 2)**2/6
Suppose 3*g + 22 - 79 = 0. Suppose 4*d - g + 11 = 0. Factor -3 - 3/2*y**d - 9/2*y.
-3*(y + 1)*(y + 2)/2
Let o(t) be the third derivative of t**6/210 - 2*t**5/105 + t**4/42 + 22*t**2. Factor o(k).
4*k*(k - 1)**2/7
Let w(m) be the first derivative of 0*m**3 + 4/5*m**5 + 1 + m**2 - 3/2*m**4 + 0*m. Factor w(v).
2*v*(v - 1)**2*(2*v + 1)
Let m be -20*(-10)/8*(-5)/(-25). Let r(a) be the second derivative of 0 + 0*a**2 + 0*a**3 + 1/12*a**4 + 1/20*a**m - 2*a. Solve r(s) = 0 for s.
-1, 0
Let n(g) be the first derivative of g**3/4 + 3*g**2/2 + 9*g/4 - 20. Factor n(s).
3*(s + 1)*(s + 3)/4
Let x(d) be the second derivative of d**7/42 + d**6/15 + d**5/20 - 3*d. Determine t, given that x(t) = 0.
-1, 0
Let h(g) be the third derivative of 0 + 1/1620*g**6 + 0*g - 1/6*g**3 - g**2 + 1/108*g**4 - 1/270*g**5. Let k(m) be the first derivative of h(m). Factor k(d).
2*(d - 1)**2/9
Let k(f) be the third derivative of -13*f**6/60 + f**5/2 - f**4/6 + 2*f**2 + 3*f. Factor k(y).
-2*y*(y - 1)*(13*y - 2)
Let h(c) = 3*c - 15. Let u be h(5). Factor u - 1/5*l + 0*l**2 + 1/5*l**3.
l*(l - 1)*(l + 1)/5
Let y(f) = f**3 - f**2 + f. Let x be y(0). Factor 0 + 1/2*c**5 - 1/2*c**4 + 1/2*c**2 - 1/2*c**3 + x*c.
c**2*(c - 1)**2*(c + 1)/2
Determine y so that -1/9*y**3 - 8/3*y - 16/9 - y**2 = 0.
-4, -1
Let y(j) be the first derivative of 1/9*j**3 + 2/3*j**2 + j - 4. Factor y(c).
(c + 1)*(c + 3)/3
Determine o so that o**3 + 3*o**4 - 21*o**5 + 22*o**5 - 3*o**2 + 0*o**2 - 2*o + 0*o = 0.
-2, -1, 0, 1
Let x = 3004/7535 - -2/1507. Factor -8/5*f - x*f**2 - 8/5.
-2*(f + 2)**2/5
Let f(r) = -r**3 - 32*r**2 - 32*r - 28. Let x be f(-31). Let b(j) be the first derivative of 0*j**2 - 1/3*j + 1/9*j**3 - x. Factor b(p).
(p - 1)*(p + 1)/3
Let p(h) = -h**3 - 6*h**2 + 3. Let t be p(-6). Suppose -i - 2*i - 14 = 4*x, -3*i = -t*x - 21. Determine r so that -3*r**2 + 2*r**2 + 2*r - r**2 - r**i + 1 = 0.
-1/3, 1
Let u be (1/(-2))/(3/(-72)). Suppose -u = -2*k - k. What is d in d - d**3 + 1/2 + 3/2*d**k - 2*d**2 = 0?
-1, -1/3, 1
Let v be ((4/6)/(15/(-18)))/(-4). Factor -2/5*x + 0 - v*x**2.
-x*(x + 2)/5
Suppose 5*l - 191 = -831. Let s be l/(-24) - 1/3. Find f such that 1/3*f**s - 1/3*f**2 + 0 - 1/3*f**3 + 1/3*f**4 + 0*f = 0.
-1, 0, 1
Let a(b) be the third derivative of -b**7/70 - b**6/20 + b**4/4 + b**3/2 + 5*b**2. Suppose a(l) = 0. Calculate l.
-1, 1
Let z = -8 + 12. Factor 17*w**4 + 48*w**3 + 1 + 1 + 44*w**2 + 15*w + w**z + w.
2*(w + 1)**2*(3*w + 1)**2
Let i(m) be the second derivative of -m**6/150 + m**5/50 + m**4/15 - m**3/15 - 3*m**2/10 - 7*m. Suppose i(t) = 0. Calculate t.
-1, 1, 3
Let c = -142 + 146. Let l(d) be the third derivative of -1/42*d**c + 0*d**3 + 4*d**2 - 1/210*d**5 + 0*d + 0. Suppose l(x) = 0. Calculate x.
-2, 0
Let r(t) = -5*t**2 + 6*t - 7. Suppose 3*l + 3 = 6*l. Let i(g) = l + g**2 + 4*g - 2*g - 3*g. Let s(h) = 6*i(h) + r(h). Suppose s(a) = 0. Calculate a.
-1, 1
Let w(k) = -2*k - 4. Let f be w(-6). Let g be (6/4)/(4/f). Factor o**4 - 2*o**4 - o**5 - o**4 + 3*o**g - 4*o**3.
-o**3*(o + 1)**2
Let p(s) = -s**3 + 7*s**2 - 7*s + 5. Let j be p(6). Let h be 6 + j + (-4 - -2). Solve 3 - 3*z**2 + 0*z - 3 + h*z = 0 for z.
0, 1
Let q be ((-2784)/10)/4 - 0. Let s = q - -70. Solve s*i**2 + 0*i + 0 + 0*i**3 - 2/5*i**4 = 0 for i.
-1, 0, 1
Let w(i) be the first derivative of i**5/30 - i**3/9 + 2*i + 6. Let f(t) be the first derivative of w(t). Factor f(n).
2*n*(n - 1)*(n + 1)/3
Let q be ((-1)/((-6)/(-9)))/(-9). Let h = -3/19 + 28/57. Factor -q*z**2 + h*z - 1/6*z**3 + 0.
-z*(z - 1)*(z + 2)/6
Let k be 4 - (1 - 0)/(-1). Factor 8*p**4 - 10*p**k - p**3 - 2*p**4 + 10*p**4 - p**3 - 4*p**2.
-2*p**2*(p - 1)**2*(5*p + 2)
Let a(g) be the second derivative of -g**5/270 - g**4/54 - g**3/27 - g**2/2 + 4*g. Let l(q) be the first derivative of a(q). Factor l(i).
-2*(i + 1)**2/9
Factor -3/5*v**5 + 3/5*v**2 - 9/5*v**3 + 9/5*v**4 + 0*v + 0.
-3*v**2*(v - 1)**3/5
Let g(p) be the first derivative of 10*p**6/9 + 37*p**5/15 + p**4 - 7*p**3/9 - p**2/3 - 8. Determine h so that g(h) = 0.
-1, -1/4, 0, 2/5
Suppose -2*g + 2 = 0, 0 = -5*j - 2*g - 0*g + 17. Suppose 2*l - j*l = -3. Determine u, given that -2*u**2 + 0 - 4 + l - 2*u + 5*u = 0.
1/2, 1
Let s(x) = -11*x**2 - 5*x - 5. Let w(v) = 5*v**2 + 2*v + 2. Let c(h) = 2*s(h) + 5*w(h). Factor c(o).
3*o**2
Suppose 0 = 4*y + 3*w - 4, -3*w + w = 3*y - 4. Factor 0 - 1/2*d - 1/4*d**2 + 1/4*d**y + 1/2*d**3.
d*(d - 1)*(d + 1)*(d + 2)/4
Let j(v) be the second derivative of -v + 0 - v**2 + 1/240*v**5 - 1/24*v**3 + 0*v**4. Let n(f) be the first derivative of j(f). Factor n(z).
(z - 1)*(z + 1)/4
Let i(j) be the third derivative of 0 + 0*j - 2*j**4 - 32/3*j**3 - 1/5*j**5 - 8*j**2 - 1/120*j**6. Factor i(u).
-(u + 4)**3
Determine p, given that 3/4*p + 0 - 1/4*p**2 = 0.
0, 3
Let n(m) be the second derivative of m**8/20160 - m**7/3780 - m**6/2160 + m**5/180 - m**4/4 + m. Let q(z) be the third derivative of n(z). Factor q(i).
(i - 2)*(i - 1)*(i + 1)/3
Suppose d + 4 = -0*n + 3*n, -2*n + 20 = -5*d. Let h be (5 + -21)*(-3)/10. Suppose 6/5*r**3 + 14/5*r**5 - h*r**4 + 0 + 4/5*r**2 + n*r = 0. Calculate r.
-2/7, 0, 1
Suppose 3*m - 4 = -2*n + 6, 5*n - 11 = -4*m. Suppose 0 = -4*z + 16, -3*r + 0*z = -2*z - m. Factor -3*u**2 + 5*u**2 - u - r + 3*u - 4*u.
2*(u - 2)*(u + 1)
Suppose 2*x + 7*x = 27. Let u be (-6)/18 - 22/(-30). Factor -2/5*r**x - u*r**2 + 2/5*r + 2/5.
-2*(r - 1)*(r + 1)**2/5
Let b(s) be the first derivative of s**6/180 - s**3 - 3. Let h(d) be the third derivative of b(d). Factor h(a).
2*a**2
Let r be 1/((-2)/8*-2). Find x such that r*x - 3/2*x**2 + 2 = 0.
-2/3, 2
Let l = 13 + -10. Factor -6*h + 0*h**4 + 6*h**l + 3 - 3*h**4 + 0.
-3*(h - 1)**3*(h + 1)
Let c be 2/12 + (-3)/21. Let v(a) be the second derivative of 0*a**2 + a + 0*a**3 + c*a**4 + 0. Factor v(s).
2*s**2/7
Let q(s) be the second derivative of s**5/10 + 8*s**4/3 + 29*s**3/3 + 14*s**2 - 4*s + 8. Suppose q(t) = 0. Calculate t.
-14, -1
Suppose 0 + 3/5*h**2 - 6/5*h = 0. What is h?
0, 2
Let u(l) be the first derivative of -4*l**5/15 - l**4/3 + 4*l**3/9 + 2*l**2/3 + 14. What is c in u(c) = 0?
-1, 0, 1
Let h be (2 + 58/(-28))*-4. Let o(v) be the first derivative of 1 + h*v + 2/7*v**2 + 2/21*v**3. Determine p, given that o(p) = 0.
-1
Let d = -88 - -92. Let c(y) be the second derivative of 0*y**2 + 0 + 1/10*y**5 - 2*y + 1/6*y**6 - 1/3*y**3 - 5/12*y**d. Find f, given that c(f) = 0.
-1, -2/5, 0, 1
Let v(f) = -f**2 - 7*f + 3. Let r(d) = -d**3 + 8*d**2 - 7*d + 1. Let h be r(7). Let k(a) = -2 + 3 - 4*a + h. Let m(p) = 5*k(p) - 2*v(p). Factor m(n).
2*(n - 2)*(n - 1)
What is a in 3*a**2 - 3*a**2 - a**2 + 2*a**2 = 0?
0
Let c(z) be the third derivative of z**8/6720 - z**7/1680 + z**6/1440 + z**3/3 - 3*z**2. Let x(t) be the first derivative of c(t). Solve x(u) = 0 for u.
0, 1
Let y(q) be the third derivative of -q**5/30 - 13*q**4/48 - q**3/4 - 16*q**2. Factor y(g).
-(g + 3)*(4*g + 1)/2
Let r be ((-512)/120)/(-2) - 2/1. Let j(f) be the first derivative of -1/3*f**2 - 2/9*f**3 - 2 + 0*f + r*f**5 + 1/6*f**4. Solve j(i) = 0 for i.
-1, 0, 1
Find y, given that 0*y**2 + 1506*y - 14*y**2 + 2*y**4 + 4*y**3 - 1498*y = 0.
-4, 0, 1
Let v(n) = -3*n**4 - 6*n**3 + 6*n**2 + 3*n. Let p(j) = -9*j**4 - 17*j**3 + 17*j**2 + 9*j. Let m = 22 - 19. Let k(u) = m*p(u) - 8*v(u). Factor k(z).
-3*z*(z - 1)*(z + 1)**2
Factor 0*o - 2/5 + 2/5*o**2.
2*(o - 1)*(o + 1)/5
Let b(g) be the third derivative of -g**6/420 + g**5/140 + g**4/56 - g**3/21 + 4*g**2. Factor b(p).
-(p - 2)*(p + 1)*(2*p - 1)/7
Let h(x) be the first derivative of 1/3*x**3 + 1/2*x**2 - 2*x + 2. Factor h(j).
(j - 1)*(j + 2)
Let g = 1777/4 + -4459/12. Let j = g + -72. 