4*i**2 = 0. Calculate i.
4
Let g(a) be the first derivative of -a**5/210 - a**4/84 + a**2 - 2. Let u(i) be the second derivative of g(i). Factor u(x).
-2*x*(x + 1)/7
Let g(x) = -x**5 + 10*x**4 - 19*x**3 + 8*x**2 - 2*x. Let t(u) = -u**5 + 10*u**4 - 20*u**3 + 8*u**2 - 3*u. Let h(b) = -3*g(b) + 2*t(b). Factor h(f).
f**2*(f - 8)*(f - 1)**2
Solve -r - 3/5*r**2 + 2/5 = 0 for r.
-2, 1/3
Find s, given that 14*s**5 - 18*s**5 - 8*s**4 - 4*s**3 - 4 + 4 = 0.
-1, 0
Find r such that -7/3*r + 1 + 5/3*r**2 - 1/3*r**3 = 0.
1, 3
Factor -3 - 3*r**2 - 9 + 7*r + 10*r - 2*r.
-3*(r - 4)*(r - 1)
Let n = -12 - -13. Let j(u) be the first derivative of 0*u + n + 2/21*u**3 - 1/14*u**4 + 0*u**2. Factor j(w).
-2*w**2*(w - 1)/7
Let a(p) be the third derivative of p**6/180 + p**5/20 + p**4/6 + p**3/2 + 7*p**2. Let h(j) be the first derivative of a(j). Factor h(q).
2*(q + 1)*(q + 2)
Let p(t) = -7*t**4 - 17*t**3 - 35*t**2 - 19*t + 3. Let w(o) = -20*o**4 - 52*o**3 - 104*o**2 - 56*o + 8. Let n(q) = 8*p(q) - 3*w(q). Find d, given that n(d) = 0.
-2, -1, 0
Suppose 0 = 5*f - f. Let h be (-1)/(f + (-2)/4). Factor -2 + 5*z + 2*z**h - 7*z - 2.
2*(z - 2)*(z + 1)
Let b = -12 - -15. Let z(s) be the first derivative of s**2 + s - 1/3*s**3 - b - 1/2*s**4. Factor z(q).
-(q - 1)*(q + 1)*(2*q + 1)
Let l(g) be the second derivative of g**9/68040 - g**7/5670 + g**5/540 - g**4/4 + 2*g. Let h(x) be the third derivative of l(x). Let h(d) = 0. Calculate d.
-1, 1
Let m(s) be the third derivative of -s**7/420 + s**6/5 - 36*s**5/5 + 144*s**4 - 1728*s**3 - 5*s**2. Factor m(o).
-(o - 12)**4/2
Solve -w**2 - 4*w**2 + 48*w + 20*w**2 + 12 - 75*w**3 = 0 for w.
-2/5, 1
Let q = -3 + 2. Let v = q + 3. Solve 2/7 + 32/7*j**v - 16/7*j = 0.
1/4
Let l(c) be the first derivative of -c**3/12 - c**2 - 7*c/4 + 35. What is o in l(o) = 0?
-7, -1
Let l = 3/28 - -1/7. Determine f so that 0*f**3 - l*f**4 + 3/4*f**2 + 0 + 1/2*f = 0.
-1, 0, 2
Find v such that -2/13*v**2 + 4/13*v - 2/13 = 0.
1
Let q be (4/(-5))/(2/(-10)). Suppose -4*s = v - 14, 0 = 5*s + 5*v - 20 - 5. What is p in -2*p**3 + 2*p**3 - 2*p + 0*p**4 - q*p**s + p**4 + 5*p**2 = 0?
0, 1, 2
Suppose 9 = 40*f - 37*f. Let v(t) be the second derivative of -2*t + 3/4*t**f - 11/24*t**4 + 1/2*t**2 + 0. Factor v(z).
-(z - 1)*(11*z + 2)/2
Let n(a) be the second derivative of a**6/40 - a**5/20 - a**4/4 + a**2 + a. Let t(b) be the first derivative of n(b). Determine c, given that t(c) = 0.
-1, 0, 2
Let i(g) be the first derivative of 2*g**3/21 - g**2/7 - 4*g/7 + 3. Let i(v) = 0. Calculate v.
-1, 2
Let q(b) = b**3 - b**2. Let w(f) = -f**3 + f**2. Let y(j) = 2*q(j) + w(j). Factor y(p).
p**2*(p - 1)
Let j be (-2)/15 - 468/4590. Let v = 25/34 + j. Suppose -3/4*m + v + 1/4*m**2 = 0. Calculate m.
1, 2
Let t(b) be the second derivative of -b**7/231 + b**6/33 - 9*b**5/110 + 7*b**4/66 - 2*b**3/33 - 7*b. Suppose t(o) = 0. What is o?
0, 1, 2
Let t(a) be the third derivative of -a**7/350 + 10*a**2. Factor t(i).
-3*i**4/5
Let p(o) = -o**2 + 10*o - 6. Let h be p(9). Let g be (-1)/(-1)*h/1. Factor 0*c - 6/7*c**g + 2/7*c**2 - 2/7*c**5 + 6/7*c**4 + 0.
-2*c**2*(c - 1)**3/7
Let i(j) be the second derivative of -j**7/3360 - j**6/720 - j**5/480 + j**3/2 - 4*j. Let o(k) be the second derivative of i(k). Let o(w) = 0. Calculate w.
-1, 0
Let b = 5 - -7. Factor t**3 - 3*t**4 - 11*t + 0*t**2 - 2 + 7*t**4 - b*t**2.
(t - 2)*(t + 1)**2*(4*t + 1)
Let k(p) be the first derivative of p**4/30 - p**2/5 - 4*p/15 + 24. Factor k(m).
2*(m - 2)*(m + 1)**2/15
What is n in 0 + 0*n - 24/5*n**2 - 42*n**4 + 156/5*n**3 - 147/5*n**5 = 0?
-2, 0, 2/7
Let d(x) = -3*x - 4. Let a be d(-3). Suppose 0 = 3*w + w + l - 16, -a*w - l = -19. Suppose 8/9*h**2 - 10/9*h - 2/9*h**w + 4/9 = 0. What is h?
1, 2
Let q = 100 - 4601/46. Let v = 12/23 + q. Factor v*l**3 - 1/2*l + 1/2*l**2 - 1/2.
(l - 1)*(l + 1)**2/2
Let m(l) be the second derivative of 1/12*l**3 - 1/12*l**2 + 1/120*l**5 - 1/24*l**4 + 0 + 5*l. Factor m(h).
(h - 1)**3/6
Let o = 10 + -7. Suppose 0*n - n - 5 = 0, 3*f = -o*n - 9. Factor 4*j**3 + 3*j**5 - f*j**3 - 6*j**5 - j**4.
-j**3*(j + 1)*(3*j - 2)
Let h(j) be the first derivative of j**3/18 - j**2/2 + 3*j/2 - 53. Factor h(t).
(t - 3)**2/6
Let c = 1154/5 + -230. Let m be 4/14*(-378)/(-36). Factor 6/5*h**5 + 6/5*h**m + 0 + 14/5*h**4 - 6/5*h**2 - c*h.
2*h*(h + 1)**3*(3*h - 2)/5
Let d(z) be the first derivative of z**5/15 - z**4/6 + z**2/3 - z/3 + 6. Factor d(m).
(m - 1)**3*(m + 1)/3
Let x = -5 + 3. Let k be x/6 + (-18)/(-27). Factor 0 + 0*p - 1/3*p**3 + k*p**2.
-p**2*(p - 1)/3
Suppose 4 - 26 = -b. Suppose -f - f + 4 = -2*r, -5*f + b = -r. Find i such that -i**3 + 3*i**3 + 3*i**2 - f*i**3 + 0*i**2 = 0.
0, 1
Factor 0 - 1/7*b + 1/7*b**2.
b*(b - 1)/7
Let g(w) = 5*w**5 + 4*w**4 - 6*w**3 - 3*w - 4. Let l(h) = -6*h**5 - 5*h**4 + 7*h**3 + 4*h + 5. Let u(n) = 5*g(n) + 4*l(n). Factor u(i).
i*(i - 1)**2*(i + 1)**2
Let a(j) = j**3 - 11*j**2 + 10*j. Let m be a(10). Let m - 2/5*w**2 - 2/5*w = 0. Calculate w.
-1, 0
Factor n**2 + 4*n + 0*n**2 + 0*n - 2*n.
n*(n + 2)
Let v = 3 - 2. Suppose 0 = u - 3 + v. Factor -2/5*d - 2/5*d**4 - 2/5*d**5 + 4/5*d**3 + 4/5*d**u - 2/5.
-2*(d - 1)**2*(d + 1)**3/5
Let k(g) = 16*g**3 - 9*g**2 + 15*g - 11. Let u(o) = 3*o**3 - 2*o**2 + 3*o - 2. Let d(b) = -4*k(b) + 22*u(b). Factor d(q).
2*q*(q - 3)*(q - 1)
Let x(g) be the second derivative of g**7/700 - g**6/90 + 3*g**5/100 - g**4/30 - 5*g**3/6 - 6*g. Let q(z) be the second derivative of x(z). Factor q(w).
2*(w - 2)*(w - 1)*(3*w - 1)/5
Let o be (1 - 6) + (-1548)/(-288). Determine a so that o*a**3 + 0 + 3/8*a**4 + 0*a - 3/4*a**2 = 0.
-2, 0, 1
Suppose -36 = -10*n + 4*n. Suppose 0 = 5*a - n - 4. What is j in 1/2*j**a + 0 + j = 0?
-2, 0
Let d(w) be the first derivative of w**4/21 - 2*w**2/7 + 2*w - 4. Let t(k) be the first derivative of d(k). Factor t(v).
4*(v - 1)*(v + 1)/7
Let x(u) = -u**2 - 13*u + 17. Let f be x(-14). Suppose -5*q + 4 = -f*d + 3, -4*d + 5*q = -2. Factor 3/2*k**2 + 2*k**d - 9/2*k + 1.
(k - 1)*(k + 2)*(4*k - 1)/2
Determine i so that 8*i**2 - 22/3*i + 4/3 + 6*i**3 = 0.
-2, 1/3
Suppose -9*i - 30*i = -5*i. Factor i + 147/5*r**4 - 231/5*r**3 - 12/5*r + 96/5*r**2.
3*r*(r - 1)*(7*r - 2)**2/5
Let d be -2 - (-8 + (3 - 0)). Suppose 3*a - n + 0*n - 5 = 0, 2*n = -d*a + 8. Factor 0 - 8/5*b**a + 8/5*b + 2/5*b**3.
2*b*(b - 2)**2/5
Let a(t) be the second derivative of -t**6/360 + t**5/60 - t**4/24 + t**3/3 - t. Let q(m) be the second derivative of a(m). Suppose q(v) = 0. What is v?
1
Let x = 9 - 7. Factor 2*y**2 + 0*y**2 - 2*y**2 - 3*y**x.
-3*y**2
Let l(v) be the third derivative of -1/24*v**3 + 2*v**2 + 0 + 0*v + 1/48*v**4 + 1/80*v**5. Find i, given that l(i) = 0.
-1, 1/3
Let w(c) = -2*c**2 + 2*c + 1. Let h(z) = 1. Let g(f) = 6*h(f) + 2*w(f). Let g(i) = 0. What is i?
-1, 2
Let l be (288/40 - 7)/((-2)/(-20)). Factor 1/6*a**3 + 4/3 + a**l + 2*a.
(a + 2)**3/6
Let w(v) = -26*v**4 + 41*v**3 + 11*v**2 - 30*v + 15. Let z = 21 + -10. Let r(l) = 5*l**4 - 8*l**3 - 2*l**2 + 6*l - 3. Let x(c) = z*r(c) + 2*w(c). Factor x(a).
3*(a - 1)**3*(a + 1)
Let p be 2/1 - (-6)/(6 - 3). Factor 0*v + 6/5*v**2 - 3/5 + 0*v**3 - 3/5*v**p.
-3*(v - 1)**2*(v + 1)**2/5
Suppose -21 = h - 2*h. Factor -18*d - 6 - 3*d**2 - d**2 + d**2 - h.
-3*(d + 3)**2
Let x = 1 - -3. Let n be (-182)/(-5) - x/10. Factor -3*g**3 - 15*g**2 - 15*g**2 + 28*g**3 - 8 - n*g.
(g - 2)*(5*g + 2)**2
Suppose 0 = -3*c + 9. Suppose 5*d + k + 6 = c, 12 = 2*d - 4*k. What is b in 1/5*b**3 + 2/5*b**2 + 0 + d*b = 0?
-2, 0
Let n be 9/(-3)*(-5)/(180/16). Factor 4/3 - n*p**3 + 14/3*p**2 - 14/3*p.
-2*(p - 2)*(p - 1)*(2*p - 1)/3
Let n(t) be the first derivative of 8 - 1/15*t**3 + 4/5*t**2 - 3/20*t**4 - 4/5*t. Determine x, given that n(x) = 0.
-2, 2/3, 1
Let o be 2/7 - 585/(-35). Let x be o/(-34) - (-13)/18. Factor -2/9*j + x*j**3 + 2/9*j**4 - 2/9*j**2 + 0.
2*j*(j - 1)*(j + 1)**2/9
Factor -20*g + 12 - 32 + 36*g - 45*g**2 + 44*g.
-5*(3*g - 2)**2
Let y(j) be the third derivative of j**8/4704 - 2*j**7/2205 - j**6/630 + j**4/8 - 3*j**2. Let c(g) be the second derivative of y(g). Factor c(q).
2*q*(q - 2)*(5*q + 2)/7
Let f(s) = s**3 + 10*s**2 + 9*s. Suppose -l = -3*l - 18. Let m be f(l). Determine z so that 0*z**2 + 0 + 0*z**3 - 1/2*z**5 - 1/2*z**4 + m*z = 0.
-1, 0
Let j(r) = 20*r**3 + 35*r**2 + 10*r - 5. Let i(o) = 20*o**3 + 34*o**2 + 8*o - 6. Let q(y) 