+ 1)
Let b be 85/(-528) - (-22)/121. Let r(u) be the third derivative of -1/240*u**6 + 0 + 0*u**3 - u**2 + 0*u - 1/120*u**5 + b*u**4 + 1/420*u**7. Factor r(q).
q*(q - 1)**2*(q + 1)/2
Let j(y) be the second derivative of y**5/30 + y**4/6 + y**3/3 - y**2 + 4*y. Let z(d) be the first derivative of j(d). Suppose z(h) = 0. Calculate h.
-1
Factor -45*r**2 - 15*r**4 - 21*r + 70*r**2 + 35*r**2 + 5*r**3 + r.
-5*r*(r - 2)*(r + 2)*(3*r - 1)
Let n(v) be the third derivative of 1/60*v**5 + 0*v + 1/120*v**6 + 0 + 0*v**4 + 0*v**3 - 4*v**2. Find k such that n(k) = 0.
-1, 0
Let c be 6/(-15) - ((-78)/40)/3. Factor 1/4*w**2 + c*w - 1/2.
(w - 1)*(w + 2)/4
Let k(v) be the second derivative of v**5/120 - v**4/24 + v**3/12 - 3*v**2/2 - 2*v. Let z(u) be the first derivative of k(u). Determine p so that z(p) = 0.
1
Let b be (-6)/54*((3 - 3) + -3). Let o(i) be the second derivative of b*i**4 + 0 + 1/2*i**2 + 4*i - 2/3*i**3. Find s such that o(s) = 0.
1/2
Suppose 395/2*u**4 - 87*u**3 - 175/4*u**5 + 8*u + 0 - 14*u**2 = 0. What is u?
-2/7, 0, 2/5, 4
Let g be (-2)/8*8/(-18). Let n(p) be the first derivative of g*p**3 + 1/3*p - 1/3*p**2 + 3. Factor n(z).
(z - 1)**2/3
Let t(b) = -14*b**3 + 2*b**2 + 10*b - 2. Let f(q) = -29*q**3 + 5*q**2 + 20*q - 3. Let u(m) = 4*f(m) - 7*t(m). Factor u(v).
-2*(v - 1)*(3*v + 1)**2
Let h(j) be the first derivative of 4*j**5/5 + 26. Factor h(r).
4*r**4
Let q(u) be the third derivative of 0 + 0*u**3 - 1/60*u**5 + 1/12*u**4 + 3*u**2 + 0*u. Find d such that q(d) = 0.
0, 2
Let q be 4 - (0/2 + 2). Factor 2*c**2 + 2*c - 3*c + 4*c**3 - c**4 - q*c**3 - 4 - c**5 + 3.
-(c - 1)**2*(c + 1)**3
Let j(x) = 10*x**4 + 36*x**3 + 4*x**2 - 16*x - 5. Let n(s) = -4*s**4 - s**2 - 7*s**3 + s + 2*s + 2*s**4 + 1. Let h(q) = -4*j(q) - 22*n(q). Factor h(r).
2*(r + 1)**3*(2*r - 1)
Let m(j) be the first derivative of -2 - 3*j**2 - 4*j**4 + 14/3*j**3 + j + 9/5*j**5 - 1/3*j**6. Find n such that m(n) = 0.
1/2, 1
Factor -9/7*k - 6/7 - 3/7*k**2.
-3*(k + 1)*(k + 2)/7
Let s(y) be the third derivative of 1/168*y**8 + 1/60*y**6 + 0*y - 1/45*y**7 + 1/30*y**5 - 3*y**2 + 0 + 0*y**3 - 1/18*y**4. Factor s(i).
2*i*(i - 1)**3*(3*i + 2)/3
Suppose 3*g = -c + 8, 4*c = -c - 2*g + 14. Factor 2*d**c - d - d**3 - d**2 - 3*d**2.
-d*(d + 1)**2
Let k = -3126 - -15766/5. Let a = -27 + k. Solve -y - a - 4/5*y**2 = 0 for y.
-1, -1/4
Let m(p) be the first derivative of p**5/3 + 2*p**4/3 + p**3/3 - 7. Factor m(o).
o**2*(o + 1)*(5*o + 3)/3
Let a(d) be the second derivative of d**7/56 - d**6/20 - 3*d**5/80 + d**4/8 + 5*d. Solve a(x) = 0 for x.
-1, 0, 1, 2
Let y(r) be the third derivative of -r**5/4 + 7*r**4/24 - 2*r**2. Let u(j) = 4*j**2 - 2*j. Let i(n) = -22*u(n) - 6*y(n). Factor i(p).
2*p*(p + 1)
Let v(z) be the first derivative of -2*z**3/21 - 2*z**2/7 + 23. Solve v(g) = 0 for g.
-2, 0
Factor -8*u - 3*u**2 + u**4 - 4 + 2*u**3 + 6*u - 6*u.
(u - 2)*(u + 1)**2*(u + 2)
Let p(x) = 2*x - 6. Let l(q) = 3*q - 11. Let o(b) = -3*l(b) + 5*p(b). Let c be o(0). Factor 0*t + 2/7*t**c + 0 + 8*t**4 - 4/7*t**2.
2*t**2*(4*t - 1)*(7*t + 2)/7
Let k = -505 + 505. Let -2/7*g**2 - 6/7*g + k = 0. Calculate g.
-3, 0
Let s(z) be the first derivative of 2*z**3/3 + 6*z**2 + 18*z - 22. Factor s(j).
2*(j + 3)**2
Suppose -12 = 2*q - 18. Let s(y) be the first derivative of 1/12*y**4 - 2/3*y**q + 2*y**2 - 8/3*y - 1. Factor s(h).
(h - 2)**3/3
Let s(c) be the first derivative of -c**6/10 - 3*c**5/25 + 3*c**4/20 + c**3/5 - 12. Suppose s(x) = 0. Calculate x.
-1, 0, 1
Determine z, given that 2/5*z + 0*z**3 + 4/5*z**4 + 0 - 2/5*z**5 - 4/5*z**2 = 0.
-1, 0, 1
Suppose 15 - 13 - 30*l + 43 + 9*l**2 - 4*l**2 = 0. Calculate l.
3
Let l(w) = -w**3 - 3*w**2 - w. Let k be l(-2). Let p = 0 - k. Factor -1 - o**2 - 2*o + 6 - p - 4.
-(o + 1)**2
Let o(b) be the second derivative of -b**6/75 + b**4/5 - 8*b**3/15 + 3*b**2/5 - 8*b. Factor o(j).
-2*(j - 1)**3*(j + 3)/5
Let v be (-18 - -18)/(1 - 0). Let j(k) be the third derivative of -1/18*k**4 - 1/90*k**5 + 3*k**2 + 0*k + 1/315*k**7 + 1/90*k**6 + v + 0*k**3. Factor j(l).
2*l*(l - 1)*(l + 1)*(l + 2)/3
Suppose 0 = -3*q - 12, 5*p + 3*q = q - 8. Suppose 3*m - g = p, 3*g + g = -m. What is w in 2/3*w + 4/3*w**2 + m + 2/3*w**3 = 0?
-1, 0
Let j(z) = 3*z**3 + 1. Let c be j(1). Let p(u) be the first derivative of -5/12*u**3 - 1/8*u**c + 2 - 1/2*u**2 - 1/4*u. Solve p(b) = 0 for b.
-1, -1/2
Let x(f) be the second derivative of 7/90*f**6 + 1/9*f**3 - 7/36*f**4 - 1/30*f**5 + 0*f**2 + 2*f + 0. Factor x(r).
r*(r - 1)*(r + 1)*(7*r - 2)/3
Let w(t) be the first derivative of t**3/9 - t/3 - 4. Factor w(n).
(n - 1)*(n + 1)/3
Let m(l) = -l**3 - 8*l**2 - 3. Let f be m(-8). Let z(a) = 5*a**5 + a**4 + 2*a**3. Let t(o) = 14*o**5 + 3*o**4 + 5*o**3. Let n(x) = f*t(x) + 8*z(x). Factor n(d).
-d**3*(d + 1)*(2*d - 1)
Let c(i) be the third derivative of -3*i**7/35 + i**6/10 + 11*i**5/30 - i**4/3 - 4*i**3/3 + 9*i**2. What is t in c(t) = 0?
-2/3, 1
Suppose z - 3 = n + 2, 0 = -4*n + 16. Let r = z - 7. Solve -r*s**3 - 4/3*s**2 - 1/3*s + 0 - 4/3*s**4 - 1/3*s**5 = 0.
-1, 0
Solve -4/9 - 20/9*v**4 - 40/9*v**2 + 20/9*v + 4/9*v**5 + 40/9*v**3 = 0.
1
Let p(r) = r**3 - 4*r**2 + 2*r - 6. Let m be p(4). Let d be 0/((m - 3)/1). Factor o**3 + 3*o**2 - 3 + 4 + 3*o + d*o.
(o + 1)**3
Let a(j) be the third derivative of 0*j - 1/75*j**5 + 0*j**4 + 1/120*j**8 + 1/100*j**6 + 0 + 4/175*j**7 - 4*j**2 + 0*j**3. Factor a(u).
2*u**2*(u + 1)**2*(7*u - 2)/5
Suppose -3*d - 1 = -10. Factor 3*y - y**4 + y - 3*y - 3*y**2 + 3*y**d.
-y*(y - 1)**3
Let y(o) be the second derivative of -o**9/9072 - o**8/2520 - o**7/2520 + o**3/2 - 2*o. Let m(j) be the second derivative of y(j). Factor m(f).
-f**3*(f + 1)**2/3
Let v(n) = -n**3 + n**2 + n + 1. Let y(u) = 2*u**5 - 8*u**4 + 5*u**3 + u**2 + 5*u + 5. Let g(p) = -5*v(p) + y(p). Solve g(i) = 0.
0, 1, 2
Let h(a) be the second derivative of 3/10*a**3 + 0 - 3/25*a**5 - 3/5*a**2 + 1/10*a**4 + 1/70*a**7 - 6*a + 0*a**6. Factor h(s).
3*(s - 1)**3*(s + 1)*(s + 2)/5
Let i(t) = t**2 - t - 7. Let x be i(4). Let u(j) be the second derivative of 0 + 0*j**4 + 0*j**3 + 2*j + 1/60*j**x + 0*j**2. Suppose u(r) = 0. Calculate r.
0
Let s(n) be the first derivative of -n**8/2800 - n**7/420 - n**6/450 + n**5/75 - 2*n**3/3 + 4. Let y(i) be the third derivative of s(i). Factor y(k).
-k*(k + 2)**2*(3*k - 2)/5
Find u, given that -2/3*u**3 + 0 + 2/3*u**2 + 2/3*u - 2/3*u**4 = 0.
-1, 0, 1
Let m(h) be the third derivative of -h**5/210 + h**4/42 - h**3/21 - 13*h**2. Let m(k) = 0. What is k?
1
Let f(v) be the second derivative of -v**6/105 - 3*v**5/70 + 4*v**3/21 + 18*v. Suppose f(d) = 0. What is d?
-2, 0, 1
Let w(r) be the second derivative of -r**6/30 - r**5/5 - 5*r**4/12 - r**3/3 - 11*r. Factor w(t).
-t*(t + 1)**2*(t + 2)
Let y(d) be the first derivative of d**8/168 - d**7/35 + d**6/30 + d**5/15 - d**4/4 + d**3/3 - d**2 + 1. Let k(c) be the second derivative of y(c). Factor k(u).
2*(u - 1)**4*(u + 1)
Factor 9*p**2 - 5*p**4 - 3*p**4 + 5*p**4 + 9*p**2 + 15*p**3.
-3*p**2*(p - 6)*(p + 1)
Suppose -2*b + 9 = b. Suppose 20 = -b*w + 7*w. Let x(p) = 20*p**2 - 12*p - 3. Let a(j) = 10*j**2 - 6*j - 1. Let t(n) = w*a(n) - 3*x(n). Factor t(r).
-2*(r - 1)*(5*r + 2)
Let a(k) be the second derivative of -3*k**5/140 + 15*k**4/28 - 75*k**3/14 + 375*k**2/14 + 17*k. Factor a(j).
-3*(j - 5)**3/7
Let g(v) be the second derivative of v**4/24 - v**3/2 + 5*v**2/4 - 2*v + 35. Factor g(o).
(o - 5)*(o - 1)/2
Let h be 1045/(-210) - -3 - -2. Let g(i) be the second derivative of -2*i - 1/105*i**6 + h*i**4 + 0*i**3 + 0*i**2 + 0*i**5 + 0. Factor g(q).
-2*q**2*(q - 1)*(q + 1)/7
Let d(l) be the second derivative of -l**9/6048 + l**8/2016 - l**7/5040 - l**6/2160 + l**3/2 - 2*l. Let m(y) be the second derivative of d(y). Factor m(p).
-p**2*(p - 1)**2*(3*p + 1)/6
Let w be (2/(-4))/(7/(-70)). Let f be w*-2*(-8)/60. Suppose -y**2 - 1/3*y**4 - 4/3*y + 4/3 + f*y**3 = 0. What is y?
-1, 1, 2
Suppose -4*l + 20 = w + 4, -l = -4*w - 4. Let y(o) be the third derivative of o**2 + 0*o - 1/30*o**4 + 1/150*o**5 + 1/15*o**3 + w. Factor y(i).
2*(i - 1)**2/5
Suppose 0 = 5*t + 4*x - 30, -8 = -3*t - 3*x + 13. Factor 4*n**t - 2/3*n**3 - 6*n + 0.
-2*n*(n - 3)**2/3
Let w be (-69)/21 + 3 + (-46)/(-14). Let x(p) be the second derivative of 0 + 0*p**2 - p - 1/12*p**4 + 0*p**w. Determine i so that x(i) = 0.
0
Let p(d) be the s