 -474 - -474. Find i such that 0 + 0*i**2 + 4/5*i**3 - 2/5*i - 2/5*i**5 + k*i**4 = 0.
-1, 0, 1
Suppose -6*j - 5*w = -3*j - 77, -2*w = 4. Let t = j - 17. Factor -5 + 0 + 4 - 36*k**2 + t*k.
-(6*k - 1)**2
Let q be (6/180)/((-4)/6). Let v = 3/10 + q. Suppose 0 - v*p**3 + 1/2*p**2 - 1/4*p = 0. Calculate p.
0, 1
Suppose 5*h + 8 = 2*r, -3*r = -2*r - 4*h - 10. Let o = 9 + r. Find x such that -x + 5*x - x - 3*x**2 + o*x**4 - 3*x**3 = 0.
-1, 0, 1
Suppose -3/5*j**4 - 9/5*j**3 - 3/5*j - 9/5*j**2 + 0 = 0. Calculate j.
-1, 0
Let c(i) be the third derivative of -i**6/30 - 3*i**5/5 - 9*i**4/2 - 18*i**3 - 11*i**2. Factor c(b).
-4*(b + 3)**3
Let b = -104 + 106. Let n(j) be the first derivative of j - b + 1/3*j**3 - j**2. Factor n(s).
(s - 1)**2
Let a(v) be the third derivative of v**8/112 + 3*v**7/70 + 3*v**6/40 + v**5/20 - 8*v**2. Factor a(l).
3*l**2*(l + 1)**3
Let g(q) be the third derivative of 1/5*q**3 + 0*q - 1/200*q**6 - 3/100*q**5 + 1/40*q**4 + 1/350*q**7 - 6*q**2 + 0. Let g(l) = 0. What is l?
-1, 1, 2
Let z(i) be the third derivative of 0*i + 1/735*i**7 + 0*i**3 + 0*i**4 - i**2 + 0 - 1/140*i**6 + 1/105*i**5. Factor z(s).
2*s**2*(s - 2)*(s - 1)/7
Let h be 6*(2/(-3))/(-2). Solve -4*g**h - 2*g - g**3 + 0*g**2 - g**3 = 0 for g.
-1, 0
Suppose 55*h - 36 - 74 = 0. Factor 0*b**h + 0*b**3 + 2/7*b**5 - 2/7*b**4 + 0*b + 0.
2*b**4*(b - 1)/7
Find t such that 0 - 2/13*t**5 - 200/13*t**3 + 0*t - 40/13*t**4 + 0*t**2 = 0.
-10, 0
Let u(o) be the third derivative of -5*o**8/336 + 5*o**7/42 - o**6/6 - 32*o**2. Factor u(c).
-5*c**3*(c - 4)*(c - 1)
Let r(c) be the first derivative of c**7/420 - c**3 - 4. Let p(g) be the third derivative of r(g). Find h such that p(h) = 0.
0
Let m(u) be the second derivative of -u**5/20 - u**4/3 + 8*u. Factor m(i).
-i**2*(i + 4)
Determine d so that 1/2*d**4 - 1/4*d**3 - 1/4*d**5 + 0 + 0*d + 0*d**2 = 0.
0, 1
Let c = -4 + 6. Let h be (22/4 + -4)/(3/4). Factor 0*r**4 - 2*r**2 + 2*r**4 + h*r**5 + 2*r - 2*r**3 - c*r.
2*r**2*(r - 1)*(r + 1)**2
Factor 24/7*u**4 - 30/7*u**3 - 6/7*u**5 + 12/7*u**2 + 0*u + 0.
-6*u**2*(u - 2)*(u - 1)**2/7
Suppose -10 = -5*r - 2*g + 112, r = -4*g + 28. Let l be -3*2*(-2)/r. Factor 1/4*u**4 - 1/2*u**3 + 0*u**2 - 1/4 + l*u.
(u - 1)**3*(u + 1)/4
Let f(w) be the second derivative of w**4/12 + w**3/2 - 2*w**2 - 3*w. Let i be f(-5). Factor -5*s**3 - 3*s**4 + 4*s**2 - i*s**2 + 0*s**2 + 0*s**3.
-s**2*(s + 1)*(3*s + 2)
Let n(k) be the third derivative of 1/90*k**5 + 1/126*k**7 + 4*k**2 + 0*k**4 + 0*k + 0*k**3 - 7/360*k**6 + 0. Find w, given that n(w) = 0.
0, 2/5, 1
Let w(x) be the first derivative of x**4/3 - 8*x**3/9 - 2*x**2/3 + 8*x/3 - 17. Factor w(d).
4*(d - 2)*(d - 1)*(d + 1)/3
Let -4/5*t + 4/5*t**2 + 0 = 0. What is t?
0, 1
Let i(x) = 2*x**4 - 6*x**3 - 4*x. Let o(p) = -3*p**4 + 7*p**3 + 5*p. Let z(g) = 5*i(g) + 4*o(g). Solve z(b) = 0 for b.
-1, 0
Let y(x) be the second derivative of -x**7/21 - x**6/15 + 3*x**5/10 + x**4/6 - 2*x**3/3 - 13*x + 1. Suppose y(a) = 0. What is a?
-2, -1, 0, 1
Determine r so that -3/5 - 6/5*r - 3/5*r**2 = 0.
-1
Let c(j) be the third derivative of 0 - 1/18*j**3 + 1/360*j**5 + 1/1260*j**7 - 1/240*j**6 + 0*j - 3*j**2 + 1/48*j**4. Suppose c(n) = 0. Calculate n.
-1, 1, 2
Suppose -2*s + 6 = 0, 2*a + 6 = 5*s - s. Factor -3*p - 18*p**2 - 15*p**3 + 5*p**a - 12*p**5 - 27*p**3 - 2*p**3 - 36*p**4.
-3*p*(p + 1)**2*(2*p + 1)**2
Let p = -3 - -7. Let c(k) be the second derivative of -4*k**2 + 2*k - 1/6*k**p + 0 + 4/3*k**3. Let c(j) = 0. What is j?
2
Let x = -39473 + 354703/9. Let c = x + 62. Find y such that 10/9*y**4 + 0 + 0*y**2 + c*y**3 + 0*y = 0.
-2/5, 0
Let x be ((-26)/(-195))/((-1)/(-6)). Solve 2/5*l + 0 - x*l**2 = 0 for l.
0, 1/2
Let b(o) = -4*o**2 + 6*o - 30*o**3 - 5*o**2 + 3*o**2 - 18*o**4 + 8. Let x(a) = -6*a**4 - 10*a**3 - 2*a**2 + 2*a + 3. Let z(n) = 3*b(n) - 8*x(n). Factor z(d).
-2*d*(d + 1)**2*(3*d - 1)
Let p(m) = -m**3 - 5*m**2 - 2*m - 5. Let b be p(-5). Factor -2*r**3 + 2*r + 2*r**2 + 0*r**b - 4*r - 1 - r**4 + 3*r + r**5.
(r - 1)**3*(r + 1)**2
Let d(z) be the second derivative of -z**8/3360 - z**7/1260 + z**6/360 + z**5/60 + z**4/6 - 4*z. Let s(f) be the third derivative of d(f). Factor s(q).
-2*(q - 1)*(q + 1)**2
Let c(q) = 1. Let w(d) = d**2 + 5*d + 8. Let r(l) = 4*c(l) - w(l). Solve r(y) = 0 for y.
-4, -1
Let p(g) be the first derivative of -g**6/180 + 5*g**2/2 + 4. Let u(m) be the second derivative of p(m). Factor u(z).
-2*z**3/3
Let u be -1*1/(-1)*3. Factor -s - 4*s**2 + 2*s**3 + 2*s**4 + s**2 + 2 - s**4 - s**u.
(s - 1)**2*(s + 1)*(s + 2)
Let d(t) be the second derivative of t**6/30 - t**5/40 - t**4/3 + t**3/3 - 6*t. Solve d(a) = 0.
-2, 0, 1/2, 2
Let l(o) = 2*o**5 + 11*o**4 + 5*o**3 + 7*o**2 - 11*o. Let h(n) = n**4 + n**3 + n**2 - n. Let s(c) = 22*h(c) - 2*l(c). Factor s(z).
-4*z**2*(z - 2)*(z + 1)**2
Let s(f) be the second derivative of -f**4/12 - 13*f**3/24 - 3*f**2/8 - 9*f. Factor s(u).
-(u + 3)*(4*u + 1)/4
Let a(o) be the first derivative of o**9/7560 - o**8/2100 + o**6/450 - o**5/300 + o**3 + 5. Let y(p) be the third derivative of a(p). Factor y(s).
2*s*(s - 1)**3*(s + 1)/5
Suppose 5*o = -9 - 1. Let y be 2/2 + o/6. Factor 0*j**2 - y*j**4 + 4/3*j + 2/3 - 4/3*j**3.
-2*(j - 1)*(j + 1)**3/3
Let l be 47/(-2) + 3/6. Let w = 33 + l. Factor -6*s + 6*s**3 + w*s**4 + 3 + s**2 - 15*s**2 + 1.
2*(s - 1)*(s + 1)**2*(5*s - 2)
Let h(y) be the third derivative of -y**8/1344 - y**7/105 - 11*y**6/240 - y**5/10 - 3*y**4/32 - 7*y**2. Determine g, given that h(g) = 0.
-3, -1, 0
Let r = 21 - 18. Factor -4 + 8*d**2 - 13*d**5 + 9*d**5 - 3*d**r - 4*d + 11*d**3 - 4*d**4.
-4*(d - 1)**2*(d + 1)**3
Let i(l) be the third derivative of -l**6/200 + 3*l**2. Factor i(b).
-3*b**3/5
Let n(k) be the second derivative of 0*k**2 - 2/27*k**3 + 0 + 8*k - 1/54*k**4 + 1/90*k**5. Factor n(h).
2*h*(h - 2)*(h + 1)/9
Suppose -2*f + 3*f = 3*w - 19, -3*w - 3*f = -3. Suppose -2*o = -5*t - w, -4*o = -7*o + 3*t + 3. Factor 2/3*b**4 + 0 - 1/3*b**3 + o*b**2 + 0*b.
b**3*(2*b - 1)/3
Let p be -33 + 1 + (-8)/(-4). Let j be (-7)/(-15) - 6/p. Let 2/3 - 2/3*k**2 + j*k - 2/3*k**3 = 0. Calculate k.
-1, 1
Let a(r) = r**3 + 6*r**3 - 5*r**3. Let g(b) = -7*b**3 - 2*b**2 - b. Let c(v) = -6*a(v) - 2*g(v). Let c(x) = 0. Calculate x.
-1, 0
Let i(y) be the third derivative of y**7/105 + y**6/30 + y**5/30 + 19*y**2. Factor i(a).
2*a**2*(a + 1)**2
Suppose -4*w + 0 + 16 = 0. Factor -w - 4*b**2 - 12 + 4*b + 12*b.
-4*(b - 2)**2
Let u(x) be the second derivative of x**5/330 - x**4/22 + 3*x**3/11 + x**2/2 - 2*x. Let v(i) be the first derivative of u(i). Factor v(w).
2*(w - 3)**2/11
Let r(d) be the third derivative of -d**7/1680 - d**6/480 - 7*d**4/24 - 3*d**2. Let s(z) be the second derivative of r(z). Determine c so that s(c) = 0.
-1, 0
Suppose 4*w + 16 = q, 3*q + 10 = 4*w + 34. Suppose 5*b = -4*r - 10, 4*b + 8 = -r + q*r. Factor 0 - 1/2*k**5 + 0*k + 0*k**4 + 0*k**2 + r*k**3.
-k**5/2
Let d(n) be the first derivative of 8 + 1/8*n**2 + 0*n - 1/12*n**3. Factor d(z).
-z*(z - 1)/4
Let b = 89 - 89. Let j(m) be the second derivative of -2/3*m**3 - m**2 + b - 1/6*m**4 + m. Factor j(p).
-2*(p + 1)**2
Factor -1/4*l**2 - 1/2*l**3 - 1/4*l**4 + 0*l + 0.
-l**2*(l + 1)**2/4
Let k = 17/20 - 9/20. Let q be (16/(-20) - -1) + 3. Solve k + 32/5*t**2 + q*t = 0.
-1/4
Let r = 39 + -19. Let 4*h**4 + 16*h**3 - 12*h + 3*h + 17*h + r*h**2 = 0. Calculate h.
-2, -1, 0
Let s(f) = 4*f**3 + 9*f**2 + 8*f - 3. Let y(j) be the second derivative of -j**4/12 - j**2/2 + 3*j. Let x(u) = -s(u) + 3*y(u). Find l, given that x(l) = 0.
-2, -1, 0
Factor -2397 + 2397 - 4*y - 2*y**2.
-2*y*(y + 2)
Let f(t) be the second derivative of -5*t**4/3 + 22*t**3/3 - 4*t**2 + 30*t. Determine p, given that f(p) = 0.
1/5, 2
Let k be ((-2)/4 - -2)/(468/26). Let j(b) be the first derivative of k*b**2 - 1/9*b**3 + 1/24*b**4 + 0*b - 3. Solve j(m) = 0 for m.
0, 1
Let y(b) be the first derivative of 6 + 2/9*b**3 - 1/3*b**4 + 0*b + 0*b**2 + 2/15*b**5. Factor y(t).
2*t**2*(t - 1)**2/3
Let t = -684/7 - -98. Factor t*r**3 + 0 + 2/7*r**2 + 0*r.
2*r**2*(r + 1)/7
Let m(r) = -r**3 + 4*r**2 + r - 2. Let g(s) = 2*s**3 - 9*s**2 - 3*s + 5. Let o(z) = 2*g(z) + 5*m(z). Factor o(i).
-i*(i - 1)**2
Let u(s) be the first derivative of -4*s**5/5 - s**4 + 4*s**3/3 + 2*s**2 + 7. Factor u(n).
-4*n*(n - 1)*(n + 1)**2
Let x be 2*(1 + -2 - -2). Let r(