 209/12. Let s(k) be the first derivative of -d*k**2 - 1 - k + 1/3*k**3 + 7/8*k**4. Factor s(f).
(f - 1)*(f + 1)*(7*f + 2)/2
Let h(b) = -66*b**2 - 9*b + 15. Let j(u) = -13*u**2 - 2*u + 3. Let i(p) = 4*h(p) - 21*j(p). Factor i(r).
3*(r + 1)*(3*r - 1)
Let g be 2/(-5) - 8/(-20). Suppose g = -2*z + 4*z. Factor 0 + z*v - 1/2*v**3 + 1/2*v**4 + 0*v**2.
v**3*(v - 1)/2
Let i be ((-6)/30)/(2/(-5)). Let y(s) be the first derivative of -2 - 2/15*s**5 + 0*s - 1/3*s**2 - i*s**4 - 2/3*s**3. Factor y(n).
-2*n*(n + 1)**3/3
Let i(y) be the second derivative of y**5/4 + 5*y**4/4 - y. Let i(g) = 0. Calculate g.
-3, 0
Let b(m) = -3*m**2 - 2*m - 6. Let h(r) = -7*r**2 - 3*r - 13. Let f(q) = 10*b(q) - 4*h(q). Factor f(p).
-2*(p + 2)**2
Let n be ((-192)/84)/((54/(-28))/3). Factor -2/9*l**2 - n + 16/9*l.
-2*(l - 4)**2/9
Let g(c) be the second derivative of -5*c**4/12 - 10*c**3/3 - 15*c**2/2 + 5*c. Factor g(v).
-5*(v + 1)*(v + 3)
Let j = 48 + -31. Let o = j - 14. Find r, given that -4/5*r**2 + 2/5*r**o + 0 + 2/5*r = 0.
0, 1
Let m(w) be the first derivative of -3*w**4/4 - 2*w**3 - 3*w**2/2 - 7. Factor m(i).
-3*i*(i + 1)**2
Let t(m) be the first derivative of -3*m**4/8 - 3*m**3/2 + 6*m + 18. Factor t(y).
-3*(y - 1)*(y + 2)**2/2
Let c(k) be the third derivative of -k**7/595 - k**6/1020 + k**5/170 + k**4/204 + 5*k**2. Let c(b) = 0. Calculate b.
-1, -1/3, 0, 1
Let z = -5 - -2. Let u be (z/2)/((-3)/6). Factor j**2 - 2*j + 4*j - u*j.
j*(j - 1)
Let y(c) be the first derivative of -c**7/4620 - c**3 - 1. Let u(n) be the third derivative of y(n). Solve u(v) = 0.
0
Let y(c) be the third derivative of -c**6/420 + c**4/84 + 10*c**2. Factor y(h).
-2*h*(h - 1)*(h + 1)/7
Suppose -b + 4*x + 5 = 3*x, b + 3*x + 3 = 0. Let g(n) be the second derivative of -1/10*n**5 - 1/6*n**4 + 0*n**2 + 3*n + 1/15*n**6 + 0 + 1/3*n**b. Factor g(f).
2*f*(f - 1)**2*(f + 1)
Factor -2/7*a**2 + 0*a + 2/7*a**5 + 0 - 2/7*a**3 + 2/7*a**4.
2*a**2*(a - 1)*(a + 1)**2/7
Let w = 234 + -234. Factor -3/2*z**5 + w + 9/2*z**4 + 0*z**2 - 3*z**3 + 0*z.
-3*z**3*(z - 2)*(z - 1)/2
Suppose -3*d + 0 = -3. Let m(f) be the first derivative of d + 2/9*f**3 + 2/3*f + 2/3*f**2. Factor m(j).
2*(j + 1)**2/3
Let 2/5*h**2 + 6/5 - 8/5*h = 0. Calculate h.
1, 3
Let v(b) be the first derivative of -b**3/18 + b/6 - 35. Factor v(c).
-(c - 1)*(c + 1)/6
Let l = 4 - 2. Suppose 4*y**l - 17*y + 11*y - y**2 = 0. Calculate y.
0, 2
Suppose 0 = 2*d + 3*d - 10. Suppose -4*v = v. Find h such that v*h**3 + h**3 + h**5 - h**2 + h**4 - 4*h**3 + d*h**3 = 0.
-1, 0, 1
Let h = -3 + -1. Let i be (-18)/(-4) + 2/h. Factor -13*m + m + 0*m**4 - m**4 - 24*m**2 - 2*m**i - 15*m**3.
-3*m*(m + 1)*(m + 2)**2
Factor 0 + 10/3*p + 4*p**2.
2*p*(6*p + 5)/3
Let h(p) = p**5 + p**4 - p**3 - p - 1. Let u(v) = 6*v**5 + 24*v**4 - 26*v**3 - 124*v**2 - 80*v - 8. Let g(i) = -8*h(i) - u(i). Suppose g(a) = 0. What is a?
-2, -1, -2/7, 2
Let q(j) = 2*j**3 + 38*j**2 - 40*j + 3. Let h be q(-20). What is g in -h*g**3 - 3/2*g - 3/4 + 21/4*g**2 = 0?
-1/4, 1
Suppose -5*j = -17 - 53. What is k in -4*k**3 - 6*k - 14*k**2 + 10*k + j*k**4 + 0*k = 0?
-1, 0, 2/7, 1
Factor 4/11*y - 2/11 - 2/11*y**2.
-2*(y - 1)**2/11
Let f be (-1)/2*-10*1. Suppose -s = 3, 2*c - 4*c = f*s - 21. Factor c*z + 2 + 81/2*z**2.
(9*z + 2)**2/2
Let k(z) = z**3 + z. Let m(t) = 12*t**4 + 21*t**3 - 9*t**2 - 9*t - 3. Let b(p) = 6*k(p) - m(p). Solve b(u) = 0 for u.
-1, -1/4, 1
Suppose -d - 1 + 6 = 0. Suppose 7*y - d*y = 0. Factor y + 3/4*c**2 + 3/4*c**3 - 3/4*c - 3/4*c**4.
-3*c*(c - 1)**2*(c + 1)/4
Let h(q) = q**2 - 5*q - 3. Let n be h(5). Let s be (n/2)/(1/(-2)). Factor -3*t**2 + t + 2*t**2 + s*t**2 + 3*t.
2*t*(t + 2)
Let u(y) be the first derivative of 0*y**2 - 1/8*y**4 - 1/6*y**3 + 5 + 0*y. What is q in u(q) = 0?
-1, 0
Let h(d) = -6*d + 1. Let v be h(-1). Suppose b - x - 3 = 0, -v = -2*b - 0*x + 3*x. Factor -2 - b*m - m**2 + 1 + 0*m.
-(m + 1)**2
Factor -302*n**3 - 15*n**4 + n + 10*n**2 - n + 297*n**3.
-5*n**2*(n + 1)*(3*n - 2)
Let t be 42/27 - (-2)/(-9). Let d(y) be the first derivative of -2/3*y + 8/3*y**2 + 32/15*y**5 + 1 - 10/3*y**3 - t*y**4. What is u in d(u) = 0?
-1, 1/4, 1
Let w be 2/16 - (-6 + 99/24). Solve -1/2*y**4 + y**w + 0*y + 0*y**3 - 1/2 = 0.
-1, 1
Solve 3 - 59*l**2 - 12*l**3 + 12*l**2 + 5*l + 1 = 0.
-4, -1/4, 1/3
Let s(f) be the third derivative of -f**8/224 + 3*f**6/80 + f**5/20 - 7*f**2. Factor s(q).
-3*q**2*(q - 2)*(q + 1)**2/2
Let o(c) = -10*c**4 - 12*c**3 + 4*c**2 + 10*c + 6. Let s(z) = -41*z**4 - 48*z**3 + 16*z**2 + 39*z + 25. Let i(g) = -9*o(g) + 2*s(g). Factor i(m).
4*(m - 1)*(m + 1)**2*(2*m + 1)
Let d = -749 + 751. Let -2*r - 4 - 1/4*r**d = 0. Calculate r.
-4
Let s(t) be the third derivative of -t**5/54 - 13*t**4/108 + 2*t**3/9 - 5*t**2. What is u in s(u) = 0?
-3, 2/5
Let z(t) be the second derivative of -t**5/5 - t**4/12 - t**3/6 + 3*t**2/2 - 3*t. Let o(d) = -7*d**3 - d**2 - 2*d + 5. Let j(v) = -3*o(v) + 5*z(v). Factor j(r).
r*(r - 1)**2
Let q(x) be the first derivative of x**5/270 - x**4/54 + 5*x**2/2 - 3. Let y(c) be the second derivative of q(c). Determine f so that y(f) = 0.
0, 2
Let j(o) be the second derivative of 3*o + 7/12*o**4 + 0 + 2*o**2 - 8/3*o**3. Factor j(k).
(k - 2)*(7*k - 2)
Let x(h) be the first derivative of h**5/30 - h**3/3 - h**2 - 3. Let j(i) be the second derivative of x(i). Factor j(p).
2*(p - 1)*(p + 1)
Let p be 40/(-6)*((-265)/25 - 7). Solve -72*h**2 - 4/3 + p*h**3 - 128/3*h**4 + 50/3*h = 0 for h.
1/4, 2
Let -4*r + 2/5*r**2 + 10 = 0. Calculate r.
5
Let g(z) be the third derivative of 0 + z**2 + 0*z**3 + 0*z + 0*z**7 + 1/20*z**6 - 1/112*z**8 + 0*z**5 - 1/8*z**4. Let g(b) = 0. Calculate b.
-1, 0, 1
Let c = 811/18 - 45. Let a(k) be the third derivative of 1/180*k**5 - 1/36*k**4 + k**2 + 0*k + c*k**3 + 0. Let a(w) = 0. Calculate w.
1
Let i = 13 - 5. Let g = i + -6. Suppose u**4 - 4 + 4*u**g + 2 - 5*u**4 + 2*u**4 = 0. What is u?
-1, 1
Let s be 8/(-6)*(-5652)/24. Let h = 2204/7 - s. Find f such that 0 - h*f**2 + 2/7*f = 0.
0, 1/3
Let k be 0/(4 - (-1 - -3)). Factor -1/3*g**3 + 2/3*g + k + 1/3*g**2.
-g*(g - 2)*(g + 1)/3
Let r(k) be the second derivative of k**6/270 + k**5/72 + k**4/72 + k**3/6 + 3*k. Let p(q) be the second derivative of r(q). Determine w so that p(w) = 0.
-1, -1/4
Let w(p) = p**3 + 6*p + 3 - 2*p**2 - 6*p**2 + 6. Let k be w(7). Factor 7*d**2 - 4*d**2 - 2*d**k - d**4.
-d**2*(d - 1)*(d + 1)
Factor 4*x**2 + 2*x + 0 + 5/2*x**3 + 1/2*x**4.
x*(x + 1)*(x + 2)**2/2
Factor 4 + 4*r**3 - 4 + 8*r + 45*r**2 - 33*r**2.
4*r*(r + 1)*(r + 2)
Let -4 - 3*s**2 - 4*s + 5 - 5 + 3 = 0. What is s?
-1, -1/3
Let s(m) be the third derivative of -1/105*m**7 - 1/30*m**5 + 0*m + 0 + 0*m**4 + 0*m**3 - 1/30*m**6 - m**2. Determine c so that s(c) = 0.
-1, 0
Let u(s) = -7*s**3 - 10*s**2 - 4*s + 8. Let p(c) = c**3 + c**2. Let i(x) = -24*p(x) - 3*u(x). Factor i(h).
-3*(h - 2)**2*(h + 2)
Let c(z) = -z - 5. Let g be c(-5). Factor h**2 + 0 + g*h**3 + 1 - 3*h - h**3 + 2*h**2.
-(h - 1)**3
Let f(k) be the third derivative of k**7/1260 - k**6/144 + k**5/45 - k**4/36 - 9*k**2. Suppose f(u) = 0. What is u?
0, 1, 2
Suppose 3*o = o + 4. Let s(p) be the first derivative of -3 + 4/3*p**o - 2/15*p**5 - 4/3*p**3 + 2/3*p**4 - 2/3*p. Find a, given that s(a) = 0.
1
Suppose 3*g = 9*g. Let v be (-6 - g)*(-1)/3. Factor -1/2*w + 1/4*w**3 + 0 - 1/4*w**v.
w*(w - 2)*(w + 1)/4
Let x(i) be the third derivative of 4*i**2 - 1/210*i**5 + 0*i + 1/42*i**4 - 1/21*i**3 + 0. Find u such that x(u) = 0.
1
Let i(z) be the first derivative of -1/10*z**2 + 0*z**3 + 3 + 0*z + 1/20*z**4. Let i(d) = 0. Calculate d.
-1, 0, 1
Let z be ((-16)/(-10))/(4/20). Factor -33 + 33 - 4*f**2 - z*f.
-4*f*(f + 2)
Factor 6/13*j - 4/13 - 2/13*j**2.
-2*(j - 2)*(j - 1)/13
Let b(g) = -26*g**2 + 19*g - 44. Let a(u) = -9*u**2 + 6*u - 15. Let x(t) = 17*a(t) - 6*b(t). Find z such that x(z) = 0.
1, 3
Let l(i) be the first derivative of -i**4/4 + i**2/2 - 4. Solve l(a) = 0.
-1, 0, 1
Factor -2/7 - 13/7*u**2 + 15/7*u.
-(u - 1)*(13*u - 2)/7
Let s = 33 + -31. Suppose 38 = 4*d - 2*w, -4*w = d - 3*w - 5. Factor 6*y - 3*y**s + y**2 - d + 6*y - 10.
-2*(y - 3)**2
Let o(w) be the first derivative of -27 - 3*w + 2*w**2 + 26 - w**3 + w**2. Factor o(a).
-3*(a - 1)**2
Let a(x) be the second derivative of 0*x**3 + 0 + 3*x + 0*x**2 - 1/8*x**4 + 3/40*x**5. Factor a(w).
3*w**2*(w - 1)/2
Let s