)*(4*p - 1)/3
Let t(x) be the third derivative of -x**8/168 + 2*x**7/35 - x**6/5 + x**5/3 - x**4/4 + 18*x**2. Factor t(a).
-2*a*(a - 3)*(a - 1)**3
Let o(d) be the third derivative of d**7/1260 + d**6/90 + d**5/15 - d**4/8 - 3*d**2. Let y(b) be the second derivative of o(b). Factor y(t).
2*(t + 2)**2
Let a(n) be the second derivative of 5/18*n**4 + 0 + 1/3*n**3 + 2*n - 2/3*n**2. Factor a(w).
2*(w + 1)*(5*w - 2)/3
Let j(y) be the first derivative of -3*y**4/28 - 3*y**3 - 63*y**2/2 - 147*y - 12. Factor j(q).
-3*(q + 7)**3/7
Let g = -223 + 325. Let r = -508/5 + g. Factor -2/5*q**2 - 2/5*q**3 + 0 + 2/5*q**4 + r*q.
2*q*(q - 1)**2*(q + 1)/5
Suppose -3*j + 5 - 17 = 0. Let i = j - -6. Factor -p + 0*p**3 - p**3 + i*p.
-p*(p - 1)*(p + 1)
Let h be (-5)/2*2/(-10). Let z = 36 + -33. What is y in 2*y**z + 0 + h*y**4 + y + 5/2*y**2 = 0?
-2, -1, 0
Determine q, given that -8/11*q - 2/11*q**5 - 2/11*q**4 - 8/11 + 10/11*q**2 + 10/11*q**3 = 0.
-2, -1, 1, 2
Suppose 2*o = 25 - 21. Factor -8*v + 2*v**3 + 3*v**4 + v**5 - o*v**2 - 1 + 7*v - 2*v.
(v - 1)*(v + 1)**4
Let m(l) = 3*l + 5*l - 3*l. Let t be m(1). Factor -1 + k**2 - 1 + k**3 - t*k**2 + 5*k.
(k - 2)*(k - 1)**2
Let g(k) = -12*k**2 + 0*k**3 - 2*k - 10*k**4 + k + k**3 + 11. Let s(c) = -c**4 - c**2 + 1. Let t = 56 - 34. Let n(v) = t*s(v) - 2*g(v). Factor n(q).
-2*q*(q - 1)*(q + 1)**2
Let j be 142/9 + (-2)/(-9). Let f = j + -29/2. Factor f*q + 1/2*q**2 + 1.
(q + 1)*(q + 2)/2
Let c(g) be the second derivative of -9*g**5/100 - g**4/10 + 3*g**3/10 + 3*g**2/5 + 5*g + 1. Find w, given that c(w) = 0.
-1, -2/3, 1
Let k be ((-183)/(-15))/((-20)/25). Let b = -15 - k. Factor -1 - b*x**2 + x.
-(x - 2)**2/4
Let r(t) be the first derivative of 2 - 1/5*t**4 - 4/15*t**3 + 0*t + 0*t**2. Factor r(d).
-4*d**2*(d + 1)/5
Let q(d) be the first derivative of -9*d**3/2 - d**2/2 + 15. Determine t, given that q(t) = 0.
-2/27, 0
Let g(s) be the first derivative of s**3/4 + 3*s**2/8 + 5. Solve g(j) = 0 for j.
-1, 0
Let u = 7 + -6. Let v = 1 - u. Determine a so that 2*a**2 + a - 3*a**2 + v*a = 0.
0, 1
Let r(j) be the first derivative of -j**5/180 - j**4/18 - 2*j**3/9 + j**2/2 + 1. Let a(s) be the second derivative of r(s). Solve a(w) = 0.
-2
Let t(v) be the second derivative of -2*v**7/105 - 2*v**6/25 - 3*v**5/25 - v**4/15 - 58*v. Solve t(k) = 0.
-1, 0
Suppose 8*w - 3*w - 10 = 0. Let d = 5/2 - w. Solve -1/4 + d*y - 1/4*y**2 = 0.
1
Let b(l) be the second derivative of -l**5/20 - 2*l**4/9 - 7*l**3/18 - l**2/3 - 15*l. Factor b(w).
-(w + 1)**2*(3*w + 2)/3
Let g(v) = 11*v**5 - 11*v**4 - 16*v**3 + 10*v**2 + 5*v - 11. Let c(z) = -z**5 + z**4 + z**3 + 1. Let m(q) = -6*c(q) - g(q). Factor m(a).
-5*(a - 1)**3*(a + 1)**2
Suppose 2*w - 4*w + 4 = 0. Factor -8/11 + 0*x - 2/11*x**3 + 6/11*x**w.
-2*(x - 2)**2*(x + 1)/11
Let a(d) be the second derivative of -d**6/10 - 9*d**5/20 - 3*d**4/4 - d**3/2 + 16*d. Factor a(l).
-3*l*(l + 1)**3
Let g be 0*(2 - 3/2). Factor 1/2*k + k**2 + 1/2*k**3 + g.
k*(k + 1)**2/2
Let t(a) be the second derivative of -3/20*a**5 + 0*a**2 + 0*a**3 + 0 + 4*a + 0*a**4. Determine o, given that t(o) = 0.
0
Solve 3*y**5 - 15*y**3 + 12 - 28*y**4 - 36*y**4 + 96*y**4 - 15*y**2 - 29*y**4 + 12*y = 0.
-2, -1, 1, 2
Let s = -9 + 10. Let o be (s*3)/(252/48). Factor 8/7*v**3 - 10/7*v**2 - 2/7*v**4 + o*v + 0.
-2*v*(v - 2)*(v - 1)**2/7
Let r(p) be the first derivative of 2*p**5/5 + p**4 - 2*p**2 - 2*p - 8. Factor r(s).
2*(s - 1)*(s + 1)**3
Let g(h) be the second derivative of 4/15*h**6 + 1/3*h**3 + 2/3*h**4 + 0 + 0*h**2 - h + 1/21*h**7 + 3/5*h**5. Factor g(p).
2*p*(p + 1)**4
Suppose -6 - 2 = -2*o. Let i(h) = h**3 - 2*h**2 + h + 4. Let j(v) = v**3 - 3*v**2 + v + 5. Let f(n) = o*j(n) - 5*i(n). Factor f(k).
-k*(k + 1)**2
Let o(r) be the second derivative of -r**4/36 + 4*r**3/9 - 8*r**2/3 + 3*r. What is y in o(y) = 0?
4
Factor -45/2*f**3 - 35/2*f**2 - 5*f - 25/2*f**4 + 0 - 5/2*f**5.
-5*f*(f + 1)**3*(f + 2)/2
Suppose y = 7*y. Factor -2/3 + y*q + 2/3*q**2.
2*(q - 1)*(q + 1)/3
Find j such that -5*j**3 + 2*j**3 + 0*j**3 + j**3 - 4*j - 6*j**2 = 0.
-2, -1, 0
Let i(y) be the third derivative of y**5/80 + y**4/8 + y**3/2 + 30*y**2 + 2. What is f in i(f) = 0?
-2
Suppose 27*a - 97 = -16. Factor -12/5*s**2 - 8/5*s - 2/5*s**4 - 2/5 - 8/5*s**a.
-2*(s + 1)**4/5
Let j(h) be the third derivative of h**6/10 - 2*h**5/15 - h**4/6 + 13*h**2. Factor j(p).
4*p*(p - 1)*(3*p + 1)
Solve 5/3*r + 1/3*r**5 + 10/3*r**3 + 10/3*r**2 + 5/3*r**4 + 1/3 = 0 for r.
-1
Factor 4*w - 6*w - 18*w + 15 + 0*w + 5*w**2.
5*(w - 3)*(w - 1)
Let i be (-13)/(-4) + -4 + (-116)/(-112). Factor -2/7*a**3 + 2/7*a + 2/7*a**2 - i.
-2*(a - 1)**2*(a + 1)/7
Let l be (0 + -2)/(-2) + 1. Let z(p) be the first derivative of -l - 2/5*p - 2/15*p**3 + 2/5*p**2. Determine x, given that z(x) = 0.
1
Let z = -4933/5 - -990. Factor 16/5*p**2 + 0 + z*p**3 + 4/5*p + p**4.
p*(p + 1)*(p + 2)*(5*p + 2)/5
Let t(f) = -f**3 - 16*f**2 - 14*f + 18. Let d be t(-15). Let l(p) be the first derivative of 1/15*p**5 + 2 - 1/9*p**d + 0*p**4 + 0*p**2 + 0*p. Factor l(r).
r**2*(r - 1)*(r + 1)/3
Let w(n) = n**2 + 2*n. Let x(q) = -1. Let y = 8 + -7. Let r(m) = y*x(m) - w(m). Determine f so that r(f) = 0.
-1
Let v(d) = -76*d**5 + 12*d**4 + 164*d**3 - 44*d**2 - 120*d. Let q(u) = 7*u**5 - u**4 - 15*u**3 + 4*u**2 + 11*u. Let i(x) = -32*q(x) - 3*v(x). Factor i(h).
4*h*(h - 2)*(h - 1)*(h + 1)**2
Let c(s) be the first derivative of -s**4/32 + s**3/8 + s**2/4 + 10. What is o in c(o) = 0?
-1, 0, 4
Let w(h) be the first derivative of -1/9*h**2 + 1/18*h**4 + 2/27*h**3 + 0*h + 5 - 2/45*h**5. Factor w(x).
-2*x*(x - 1)**2*(x + 1)/9
Let b(g) be the first derivative of -g**6/60 - 3*g**5/50 - g**4/20 + 36. Solve b(o) = 0.
-2, -1, 0
Let p(m) be the second derivative of m**4/12 - 7*m**3/6 + 7*m**2/2 + 3*m. Let z be p(6). Factor -1/2*y**2 - 1/2*y + z.
-(y - 1)*(y + 2)/2
Let i(a) = a**2 + a. Let x(s) = 6*s**2 + 7*s + 4. Let u(r) = 21*i(r) - 3*x(r). Factor u(p).
3*(p - 2)*(p + 2)
Factor -2/3*i - 8/9 + 2/9*i**2.
2*(i - 4)*(i + 1)/9
Let u(n) be the first derivative of -5*n**3/3 - 30*n**2 - 55*n + 51. Solve u(b) = 0.
-11, -1
Factor -d**3 - 8*d + 7 + 0*d**2 - 5*d**2 - 11.
-(d + 1)*(d + 2)**2
Suppose -z + 5*z - 80 = 0. Let t be 52/z + (-3)/5. Let -a**t + 0 + 11*a**4 - 21/2*a**5 + 1/2*a**3 + 0*a = 0. What is a?
-2/7, 0, 1/3, 1
Let h(w) be the first derivative of -w**5/10 + 3*w**4/8 + 3*w**3/2 + 5*w**2/4 - 20. Factor h(x).
-x*(x - 5)*(x + 1)**2/2
Let k(d) be the third derivative of -d**8/1512 - d**7/945 + d**6/180 + d**5/54 + d**4/54 - 8*d**2. Factor k(m).
-2*m*(m - 2)*(m + 1)**3/9
Let y(x) be the second derivative of -2*x**7/21 + 4*x**6/15 - 2*x**4/3 + 2*x**3/3 - 10*x. What is a in y(a) = 0?
-1, 0, 1
Let o = -29/50 + 1693/850. Determine q so that 10/17*q**2 + 8/17 - o*q = 0.
2/5, 2
Let x be (16/(-6))/2*25/(-500). Let q(a) be the third derivative of 3*a**2 - x*a**5 + 0*a**4 + 0 + 0*a + 1/60*a**6 + 0*a**3. Factor q(g).
2*g**2*(g - 2)
Let b(y) be the second derivative of 1/180*y**5 + y**2 + 0*y**3 + 0 + 0*y**4 + y + 1/360*y**6. Let l(p) be the first derivative of b(p). Solve l(m) = 0 for m.
-1, 0
Suppose -13 = 5*k + 7. Let t be k/12 - (-1)/3. Solve -2/7*j**4 - 6/7*j**2 + t + 6/7*j**3 + 2/7*j = 0 for j.
0, 1
Let g(o) be the third derivative of o**8/1600 + 3*o**7/1400 + o**6/600 - o**4/24 - o**2. Let s(c) be the second derivative of g(c). Suppose s(b) = 0. What is b?
-1, -2/7, 0
Let m(k) be the second derivative of 5*k**4/32 - k**3/16 + 11*k. Factor m(i).
3*i*(5*i - 1)/8
Let u be 40/25 + 4/10. Factor 0*q**2 + 4*q - 17*q**3 - 2*q**u - 14*q**5 - 13*q**3 - 38*q**4.
-2*q*(q + 1)**3*(7*q - 2)
Let q(h) be the second derivative of -1/14*h**5 + 0*h**2 - 1/14*h**4 - h + 0 + 2/21*h**3. Find t such that q(t) = 0.
-1, 0, 2/5
Let q(i) be the third derivative of 1/80*i**6 + 0 - 1/30*i**5 - 6*i**2 + 0*i**3 + 1/48*i**4 + 0*i. Determine o, given that q(o) = 0.
0, 1/3, 1
Suppose 2*j - 4 = -0. Let n(o) = o**2 - 2*o + 3. Let q be n(j). Find s such that -2/3*s**2 + 0 + 0*s + 4/3*s**q - 2/3*s**4 = 0.
0, 1
Let h(j) be the second derivative of -j**7/8820 - j**6/840 - j**5/210 + j**4/4 + j. Let q(a) be the third derivative of h(a). Factor q(g).
-2*(g + 1)*(g + 2)/7
Let u(i) = i**3 - 7*i**2 - 31*i + 12. Let b be u(10). Let -3/7*c**b + 3/7*c**3 + 0 - 3/7*c + 3/7*c**4 = 0. What is c?
-1, 0, 1
Suppose -1/