(d) be the third derivative of p(d). Factor v(j).
3*(j - 1)*(j + 3)/2
Suppose 2*d = 3*v + 2*v - 49, -2*v - 2 = d. Let x be 62/18 + d + 9. Factor 4/9*g**2 - 14/9*g**3 - x + 14/9*g.
-2*(g - 1)*(g + 1)*(7*g - 2)/9
Let m(h) be the first derivative of -2*h**5/75 + 2*h**4/15 - 2*h**3/15 - 4*h**2/15 + 8*h/15 - 19. Suppose m(k) = 0. What is k?
-1, 1, 2
Let p = -1/19 - -41/57. Solve p*b**5 - 2/3 + 2/3*b + 4/3*b**2 - 2/3*b**4 - 4/3*b**3 = 0.
-1, 1
Let a(m) be the first derivative of -2*m**5/35 + 1. Suppose a(z) = 0. Calculate z.
0
Let w(y) be the first derivative of -y**7/4200 - y**6/1800 - 5*y**3/3 - 6. Let g(m) be the third derivative of w(m). Find s such that g(s) = 0.
-1, 0
Let d(l) = -l**2 - 6*l + 7. Let b be d(-7). Let w be (3 + b + -3)/3. Factor 0*j**2 + 0 - 1/2*j**4 + w*j + 1/2*j**3.
-j**3*(j - 1)/2
Let a(p) be the first derivative of -p**6/6 + 7*p**5/5 - 19*p**4/4 + 25*p**3/3 - 8*p**2 + 4*p - 27. Factor a(o).
-(o - 2)**2*(o - 1)**3
Let n(g) be the second derivative of -g**4/54 - 2*g**3/27 - g**2/9 + 6*g. Suppose n(o) = 0. What is o?
-1
Let b be ((-27)/(-18))/((-6)/(-8)). Let d be 1 + 1 - 10/6. Factor -u + d*u**b + 2/3.
(u - 2)*(u - 1)/3
Suppose 5*i - 4*p + 5 = p, 2*i - 4*p + 6 = 0. Determine u so that -4*u + i + 9*u + 3*u**2 + u**2 = 0.
-1, -1/4
Let y(i) be the second derivative of 0 + 93/20*i**5 - 3*i + 7/12*i**7 - 17/6*i**4 + 0*i**2 - 35/12*i**6 + 2/3*i**3. Determine o so that y(o) = 0.
0, 2/7, 1, 2
Let n(y) = 10*y**3 + 8*y**2 + 6*y. Let d(k) = k**4 - 31*k**3 - 23*k**2 - 19*k. Let z(j) = 4*d(j) + 14*n(j). Find i such that z(i) = 0.
-2, -1, 0
Let c(v) be the second derivative of 1/42*v**7 + 0*v**3 - 1/20*v**5 + 1/30*v**6 - 1/12*v**4 + 0*v**2 + 0 + 4*v. Find i, given that c(i) = 0.
-1, 0, 1
Let t = 51 + -51. Let 0 + 1/2*m**3 + 0*m**4 - 1/2*m**5 + 0*m + t*m**2 = 0. What is m?
-1, 0, 1
Let h(v) be the second derivative of 1/21*v**4 - 8/7*v**2 - 2*v + 1/70*v**5 + 0 - 4/21*v**3. Solve h(d) = 0 for d.
-2, 2
Let a(f) be the first derivative of f**5/390 - f**4/78 - f**3/13 - 2*f**2 + 2. Let y(g) be the second derivative of a(g). Factor y(d).
2*(d - 3)*(d + 1)/13
Let i(t) be the third derivative of t**7/105 + 7*t**6/60 + 3*t**5/5 + 5*t**4/3 + 8*t**3/3 + 43*t**2. Factor i(w).
2*(w + 1)*(w + 2)**3
Let x be (-6)/(-9)*(6 + 0). Suppose -x*k = 0, 0 = -3*i + k + 2*k. Factor 0*c**2 + i + 2/3*c - 2/3*c**3.
-2*c*(c - 1)*(c + 1)/3
Let b be (1 - -226)*(-2)/(-140). Let a = -3/70 + b. Factor 6/5*v**2 - a*v + 8/5.
2*(v - 2)*(3*v - 2)/5
Let u(r) be the first derivative of r**4/24 - r**3/6 + r**2/4 + r - 2. Let t(n) be the first derivative of u(n). Determine q so that t(q) = 0.
1
Suppose -109*k = -100*k - 36. Factor 49/3*i**k + 4/3 - 12*i - 42*i**3 + 109/3*i**2.
(i - 1)**2*(7*i - 2)**2/3
Let c be 5/(-140)*146/(-5). Let a = c - 9/14. Solve 2/5 - 2/5*t**2 - 2/5*t + a*t**3 = 0.
-1, 1
Suppose -q + 6*q = 30. Suppose 7*i - q = 4*i. Factor 3*g**2 - 2*g**2 + 3*g**i + 2 - 9*g + 0.
(g - 2)*(4*g - 1)
Let x(u) = -u**2 - u + 1. Let v(z) = z**2 + 7*z - 9. Let y(h) = 2*v(h) - 2*x(h). Factor y(r).
4*(r - 1)*(r + 5)
Let 128/9 + 2/9*v**2 + 32/9*v = 0. What is v?
-8
Let c(p) be the second derivative of p**4/132 - 2*p**2/11 - 44*p. Factor c(x).
(x - 2)*(x + 2)/11
Let x(a) be the first derivative of a**8/1680 + a**7/420 + a**6/360 + 5*a**3/3 - 4. Let l(w) be the third derivative of x(w). Factor l(t).
t**2*(t + 1)**2
Let h(g) be the second derivative of g**7/2520 - g**4/4 + 2*g. Let c(y) be the third derivative of h(y). Factor c(d).
d**2
What is u in -8*u**2 + 4*u + 4*u**4 + 20*u**5 + 4*u**4 + 0*u**4 - 24*u**5 = 0?
-1, 0, 1
Let l(k) = -k**2 - 3*k. Let b be l(-2). Determine o so that -5*o - 37*o**3 + 24*o**b + 28*o**3 - 7*o = 0.
0, 2/3, 2
Let y(j) be the third derivative of -j**9/5040 - j**8/1120 + j**7/840 + j**6/120 - j**4/24 + 2*j**2. Let s(t) be the second derivative of y(t). Factor s(h).
-3*h*(h - 1)*(h + 1)*(h + 2)
Let d(c) = -c**2 - 3*c. Let n be d(-2). Factor -n*o - 1 - 1/4*o**3 - 5/4*o**2.
-(o + 1)*(o + 2)**2/4
Let q(s) = 3*s**2 + 22*s + 24. Let t(c) = c**2 - 2*c + 1. Let n(o) = q(o) + t(o). What is r in n(r) = 0?
-5/2
Let u be (-1)/((-35)/15 + 2). Let w be (-1 - (-1 - u)) + -1. Determine c, given that 4/5*c - w*c**2 + 0 = 0.
0, 2/5
Let d(p) be the second derivative of -p**6/60 - 3*p**5/40 + p**3/3 + p. Suppose d(c) = 0. Calculate c.
-2, 0, 1
Let n(h) be the first derivative of -2*h**3/15 + 2*h/5 + 32. Factor n(x).
-2*(x - 1)*(x + 1)/5
Let -20*j**2 - 23550 + 15*j**3 + 23550 + 5*j = 0. Calculate j.
0, 1/3, 1
Let g(o) be the third derivative of o**7/4200 - o**5/600 + o**3/2 - 2*o**2. Let l(b) be the first derivative of g(b). Find q such that l(q) = 0.
-1, 0, 1
Suppose -5*c + 0*n = n - 8, -5*n = -5*c + 20. Solve w**5 - 2*w**2 + 3*w**4 + 3*w - 2*w**3 - 1 - 3 + 3 - c*w**5 = 0.
-1, 1
Let f(z) = z**4 - z**3 + z**2 - z - 1. Let d(s) = s**2 + 8*s**2 + 4*s**2 - 3*s**2 - 6*s**3 - 5 - 4*s. Let c(h) = -3*d(h) + 15*f(h). Factor c(u).
3*u*(u - 1)*(u + 1)*(5*u + 1)
Determine t so that 0 - 2/5*t + 1/5*t**2 = 0.
0, 2
Factor 0 - 1 - 2*u - 10*u**2 + 9*u**2.
-(u + 1)**2
Let o(r) be the first derivative of 4*r + 0*r**3 - 3*r**2 + 4 + 1/2*r**4. What is c in o(c) = 0?
-2, 1
Let h be 4/(5/((-5)/(-2))). Factor 1 - 2*g**4 + 4*g**3 - 1 - 2*g**h.
-2*g**2*(g - 1)**2
Let n(i) be the third derivative of 0 - 2*i**2 + 0*i + 1/9*i**4 - 1/90*i**5 - 4/9*i**3. Let n(f) = 0. Calculate f.
2
Suppose -3*f = -5*q + 13, 3*f = -2*f + 3*q - 11. Let c = 1 + f. Factor -1/4*t**2 + 1/4*t + c.
-t*(t - 1)/4
Let i(q) be the first derivative of 0*q - 2/9*q**3 + 1/3*q**2 + 3. Find o, given that i(o) = 0.
0, 1
Let r = 9 - 4. Suppose m + 3*c = 17, -3*c + 2*c = -5*m + r. Factor -2 + m*w - 1/2*w**2.
-(w - 2)**2/2
Let m(z) be the second derivative of -z**6/3 + z**5/4 + 5*z**4/6 - 5*z**3/6 + 9*z. Factor m(r).
-5*r*(r - 1)*(r + 1)*(2*r - 1)
Let t(d) be the second derivative of 5/42*d**4 + 0 + 1/70*d**5 + 1/3*d**3 + 3/7*d**2 - 2*d. Factor t(a).
2*(a + 1)**2*(a + 3)/7
Suppose 4*v - 6 = -5*f, -2*v - 3 = -4*f + 7. Factor -8*b**4 + 3*b**2 + 2*b**f - 7*b + 2 + b**2 + 3*b**5 + 0*b**2 + 4*b**3.
(b - 1)**3*(b + 1)*(3*b - 2)
Let v(r) be the third derivative of r**6/240 - r**5/40 + r**4/24 - 4*r**2. Suppose v(d) = 0. Calculate d.
0, 1, 2
Suppose 10*v + 5 = 5*v + 4*r, -3*r + 21 = 2*v. Factor -5*q + 3*q + q + q**v.
q*(q - 1)*(q + 1)
Let 0 - 2/3*x + 0*x**2 - 2/3*x**5 + 0*x**4 + 4/3*x**3 = 0. Calculate x.
-1, 0, 1
Let a be 1/4 + 8/(-32). Let r(n) be the third derivative of 1/180*n**5 + 2/9*n**3 - 1/18*n**4 + a + 0*n - 2*n**2. Suppose r(w) = 0. What is w?
2
Suppose 5*b + 25 = -2*f, 5*f - 2*f = -b - 5. Find l such that 0 + 1/2*l + f*l**4 + 1/2*l**5 + 0*l**2 - l**3 = 0.
-1, 0, 1
Let o be (-5)/15*(0 - (-2)/(-10)). Let z(b) be the third derivative of 0*b - 4/15*b**3 + o*b**4 - 3*b**2 - 1/150*b**5 + 0. Factor z(y).
-2*(y - 2)**2/5
Let n = -656 + 1969/3. Factor -n + 2/3*f - 1/3*f**2.
-(f - 1)**2/3
Let i(d) be the third derivative of 3*d**5/20 + d**4/8 - 6*d**2. Factor i(g).
3*g*(3*g + 1)
Let m(x) be the second derivative of -x**7/14 + 3*x**6/5 - 39*x**5/20 + 3*x**4 - 2*x**3 + 15*x + 2. What is t in m(t) = 0?
0, 1, 2
Let t(l) be the first derivative of 1/10*l**4 - 3 + 1/5*l**2 + 0*l - 4/15*l**3. Factor t(f).
2*f*(f - 1)**2/5
Let f(b) be the third derivative of -b**8/840 + 2*b**7/525 - b**6/300 - 22*b**2. Factor f(g).
-2*g**3*(g - 1)**2/5
Let b = 7 - 5. Let k = -5 + b. Let m(v) = -1. Let j(t) = 2*t**2 - 2*t + 3. Let n(f) = k*m(f) - j(f). Factor n(r).
-2*r*(r - 1)
Let u = -107 + 110. Let i(c) be the third derivative of -1/270*c**5 + 2/27*c**u + 0 + 0*c - 1/108*c**4 + 3*c**2. Factor i(q).
-2*(q - 1)*(q + 2)/9
Let z(u) = u**2 - u. Let b(d) = -d**3 - 2*d**2 + 2*d + 1. Suppose -4*n = -35 + 15. Let s(p) = n*z(p) + b(p). Let s(j) = 0. Calculate j.
1
Let n(h) = -h**2 + 11*h - 4. Let v be n(11). Let w be (v/10)/(1/(-5)). Factor 1/4*z + 1/4*z**3 + 1/2*z**w + 0.
z*(z + 1)**2/4
Factor -1/7*j + 2/7*j**3 + 0 + 0*j**2 + 0*j**4 - 1/7*j**5.
-j*(j - 1)**2*(j + 1)**2/7
Let y(g) be the first derivative of -g**6/60 + g**5/30 - g**2/2 + 2. Let o(a) be the second derivative of y(a). Factor o(l).
-2*l**2*(l - 1)
Let j be (-108)/(-63)*(-28)/(-30). Factor j*h**3 - 8/5*h - 4/5 + 4/5*h**4 + 0*h**2.
4*(h - 1)*(h + 1)**3/5
Let 5*c**3 - 3*c**2 - c**4 - 2*c**4 + c**3 = 0. Calculate c.
0, 1
Let