 derivative of 0*z**2 + 0*z**3 + 1/6*z**7 - z + 3/20*z**5 + 1/6*z**n - 2/5*z**6 + 0. Factor r(q).
q**2*(q - 1)**2*(7*q + 2)
Suppose 2*q = 4 + 4. Let s(n) be the third derivative of 1/18*n**q + 0*n + 1/90*n**5 - n**2 + 1/9*n**3 + 0. Factor s(b).
2*(b + 1)**2/3
Suppose 3/7*o**2 + 0 + 6/7*o = 0. Calculate o.
-2, 0
Factor 3*a**2 + 1 + 1 + a**3 - 1 + 3*a.
(a + 1)**3
Let s be (-2)/7 + 2/7. Let z(j) be the third derivative of 1/180*j**5 + 0 + 2*j**2 + s*j**4 - 1/18*j**3 + 0*j. Factor z(l).
(l - 1)*(l + 1)/3
Let m(o) = -o**2 + o + 1. Let p(y) = 6*y**2 + 10*y - 26. Let g(s) = -10*m(s) - p(s). What is j in g(j) = 0?
1, 4
Let w = 449 - 49391/110. Let b = 433/770 - w. Factor 4/7*q**2 + 2/7*q**3 - b - 2/7*q.
2*(q - 1)*(q + 1)*(q + 2)/7
Let m(o) = -o**3 - 7*o**2 + 0*o**3 + 2*o**2. Let b be m(-5). Factor b*g + 2/3*g**2 + 0.
2*g**2/3
Let j(a) be the second derivative of -4*a**7/315 + a**6/30 - a**5/30 + a**4/72 - 3*a**2/2 + 3*a. Let q(o) be the first derivative of j(o). Factor q(y).
-y*(2*y - 1)**3/3
Suppose p - 6 + 0 = 0. Suppose -4*f + p = -f. Solve -7*d - f + 0*d**3 - 5*d**3 - d**4 + 0*d**4 - 9*d**2 = 0.
-2, -1
Let h(v) = v. Let b(g) = 2*g**2 - 30*g + 18. Let y(w) = -2*b(w) - 36*h(w). Factor y(m).
-4*(m - 3)**2
Let g(w) = 5*w**3 - 5*w**2 - 2*w. Let k(l) = -24*l + 16*l**3 + 17*l - 3*l**2 - 13*l**2. Let o(j) = 7*g(j) - 2*k(j). Factor o(n).
3*n**2*(n - 1)
Let b = 13 - 13. Let i(m) be the third derivative of -1/180*m**5 + b*m**4 + m**2 + 0 + 0*m + 1/18*m**3. What is x in i(x) = 0?
-1, 1
Let u(k) = 5*k**2 + 13*k + 10. Let w(f) = -21*f**2 - 51*f - 39. Let h(q) = 9*u(q) + 2*w(q). Factor h(n).
3*(n + 1)*(n + 4)
Let d(f) be the third derivative of 1/315*f**7 + 1/180*f**6 + 0*f**3 + 0 + 0*f**5 + 0*f - 4*f**2 + 0*f**4. Factor d(z).
2*z**3*(z + 1)/3
Let o be (-5 + -1)*(-2)/4. Determine j, given that 0*j - 4*j + 4*j**o - 2*j + 6*j**4 - 6*j**2 + 2*j = 0.
-1, -2/3, 0, 1
Factor 3/4*r**2 + 0 + 3/4*r.
3*r*(r + 1)/4
Let k be -1 - -3*(-7)/(-15). Factor -1/5*w**2 - k*w - 1/5.
-(w + 1)**2/5
Factor -3/5*x**2 - 9/5 - 12/5*x.
-3*(x + 1)*(x + 3)/5
Let c(m) be the second derivative of m**8/3360 + m**7/630 + m**4/4 + 2*m. Let w(d) be the third derivative of c(d). Solve w(x) = 0.
-2, 0
Factor 236 + 52*i + 2*i**2 + 80 + 22.
2*(i + 13)**2
Solve -22*m**2 + 4*m**4 - 12*m**2 + 4*m**4 - 4*m**3 + 4*m + 26*m**2 = 0 for m.
-1, 0, 1/2, 1
Let f(j) = -j**3 - 7*j**2 - 5*j + 8. Let w(h) = -6*h. Let o be w(1). Let r be f(o). Factor g**4 + 1/2*g - g**r - 1/2*g**5 + 0*g**3 + 0.
-g*(g - 1)**3*(g + 1)/2
Let d be 2 + (1 - (6 + -2)). Let q be 11*(-3)/(-27) + d. Find k such that -q*k**3 + 2/9*k**2 + 0*k + 0 = 0.
0, 1
Let g(t) be the third derivative of t**7/70 - 23*t**6/280 + t**5/7 - t**4/14 + 10*t**2. What is s in g(s) = 0?
0, 2/7, 1, 2
Factor 35*t**2 - 12 + 0 + 20*t + 9*t**2 + 12*t**3.
4*(t + 1)*(t + 3)*(3*t - 1)
Find s, given that 15/4*s - 3/2 + 3/4*s**3 - 3*s**2 = 0.
1, 2
Let u(i) be the third derivative of 0 - 1/20*i**5 - 3/70*i**7 + 0*i - 1/112*i**8 - 3/40*i**6 + 4*i**2 + 0*i**4 + 0*i**3. Suppose u(g) = 0. What is g?
-1, 0
Factor 0*d + 3/8*d**3 + 0 - 3/8*d**2.
3*d**2*(d - 1)/8
Let p(b) be the second derivative of -b**6/10 + 3*b**5/10 + 3*b**4/4 - 4*b**3 + 6*b**2 - 2*b - 19. Factor p(x).
-3*(x - 2)*(x - 1)**2*(x + 2)
Factor 0*r + r**4 + 1/3*r**5 + 0 + 1/3*r**2 + r**3.
r**2*(r + 1)**3/3
Suppose n - 5*n = 2*f - 36, 3*f = -n + 14. Factor 2*i**2 + n*i**3 + 0 - 7*i**3 + 0.
i**2*(i + 2)
Let t(r) = -2*r**3 + 1. Let j be t(-1). Factor -3/2*o**2 + 3/2*o**j + 0 + 0*o.
3*o**2*(o - 1)/2
Let w(a) be the third derivative of a**7/2730 - a**6/780 + a**4/156 + a**3/3 + 5*a**2. Let v(x) be the first derivative of w(x). Let v(r) = 0. What is r?
-1/2, 1
Let u(t) be the second derivative of t**8/1512 - t**6/135 + t**5/135 + t**4/36 - 2*t**3/27 - t**2 + 2*t. Let s(h) be the first derivative of u(h). Factor s(y).
2*(y - 1)**3*(y + 1)*(y + 2)/9
Let q = 25 - 25. Let d(k) be the third derivative of -1/210*k**7 + 2*k**2 - 1/60*k**5 + 0*k + q + 0*k**3 + 0*k**4 + 1/60*k**6. Suppose d(h) = 0. Calculate h.
0, 1
Factor 4/3*m**3 + 0 - 1/3*m**4 - 5/3*m**2 + 2/3*m.
-m*(m - 2)*(m - 1)**2/3
Suppose 0 = 8*q - 16 - 16. Let f(r) be the third derivative of 0*r**3 + 0*r + 2*r**2 + 0 + 1/24*r**q + 1/60*r**5. Find o, given that f(o) = 0.
-1, 0
Factor 2/5*c**2 - 2/5*c - 2/5 + 2/5*c**3.
2*(c - 1)*(c + 1)**2/5
Factor -18/5*i - 3/5 - 27/5*i**2.
-3*(3*i + 1)**2/5
Let a(z) be the second derivative of z**7/2940 + z**6/420 + z**5/210 + z**3/3 + z. Let k(o) be the second derivative of a(o). Factor k(y).
2*y*(y + 1)*(y + 2)/7
Let s be 8/12*(-6)/(-2). Factor -v - v**2 + s*v + v.
-v*(v - 2)
Let t(g) = -45*g**2 + 30*g + 5. Let f(d) = -67*d**2 + 45*d + 7. Let l(w) = -5*f(w) + 7*t(w). Factor l(k).
5*k*(4*k - 3)
Let n(i) be the third derivative of -i**5/210 + i**4/42 + 2*i**2. Suppose n(g) = 0. What is g?
0, 2
Let h be -2*(-4)/36*3. Solve 2/3*u**2 - h*u + 0 = 0.
0, 1
Let n(y) = -2*y - 6. Let z be n(-4). Suppose 2*i**2 + z*i**3 - i**2 + 0*i**4 + i**4 = 0. What is i?
-1, 0
Let x(w) be the first derivative of 0*w**4 + 0*w**2 + 0*w + 0*w**3 + 1/15*w**5 + 2. Factor x(d).
d**4/3
Let y(s) = 10*s**3 + 16*s**2 + 2*s. Suppose -2*w + 3 = -1. Suppose -3 = -g + 6. Let a(k) = -40*k**3 - 65*k**2 - 7*k. Let u(x) = g*y(x) + w*a(x). Factor u(t).
2*t*(t + 1)*(5*t + 2)
Let f = -22 - -22. Let l(w) be the second derivative of 1/30*w**5 + 0*w**3 + 0 + 1/36*w**4 - w + f*w**2 + 1/90*w**6. Factor l(m).
m**2*(m + 1)**2/3
Let u be 3 + -13 - 3 - -1. Let g be (-14)/u + (-12)/18. Factor 1/4*t**2 + g*t + 1/4.
(t + 1)**2/4
Suppose -3*f - 4 = -4*f. Let d(w) be the first derivative of 1 + 1/10*w**f + 2/15*w**3 + 0*w**2 + 0*w. What is j in d(j) = 0?
-1, 0
Let p(l) = l**4 - 4*l**3 - 3*l**2 - 2*l + 2. Let v(u) = -u**4 + u**3 + u**2 + u - 1. Let z(h) = -3*p(h) - 6*v(h). Factor z(g).
3*g**2*(g + 1)**2
Let h(s) be the second derivative of s**8/1512 - s**7/945 - s**6/540 + s**5/270 - 2*s**2 + s. Let u(r) be the first derivative of h(r). Solve u(d) = 0.
-1, 0, 1
Let i(n) = n**3 + 15*n**2 - 2*n - 28. Let s be i(-15). Let l(d) be the first derivative of 2*d - 2/3*d**3 + 1 - d**s + 1/2*d**4. Suppose l(t) = 0. What is t?
-1, 1
Let g(a) be the third derivative of 5*a**8/112 - 8*a**7/21 + 5*a**6/8 + a**5/2 - 5*a**4/3 - 21*a**2. Let g(v) = 0. Calculate v.
-2/3, 0, 1, 4
Let u(s) be the third derivative of -s**7/1365 - s**6/260 - s**5/130 - s**4/156 + 11*s**2. Find x, given that u(x) = 0.
-1, 0
Let g be (-4 - -7)*2/6. Let w be ((-11)/(-11))/(g/4). What is d in 16/3*d**2 + d + 4/3*d**w - 2/3 + 5*d**3 = 0?
-2, -1, 1/4
Let w be (-35)/(-10)*12/35. Factor -2/5*v + 2/5*v**4 + 2/5*v**3 - w*v**2 + 4/5.
2*(v - 1)**2*(v + 1)*(v + 2)/5
Factor -1/10*b**2 + 3/10*b - 1/5.
-(b - 2)*(b - 1)/10
Let s(r) be the first derivative of -2*r**5/5 + r**4 - 2*r**3/3 - 7. Suppose s(l) = 0. Calculate l.
0, 1
Let r(a) = a. Let u(b) = 18*b**2 - 9*b + 2. Let z(o) = 3*r(o) - u(o). Suppose z(m) = 0. What is m?
1/3
Let d(q) be the first derivative of 3/10*q**5 - 1/8*q**6 + 0*q**4 + 0*q + 3/8*q**2 - 3 - 1/2*q**3. Factor d(u).
-3*u*(u - 1)**3*(u + 1)/4
Let j be 171/12 + 2/(-8). Suppose 4*c = -3*c + j. Let 0 + 2/3*i + 0*i**4 + 0*i**c + 2/3*i**5 - 4/3*i**3 = 0. Calculate i.
-1, 0, 1
Let 10/11*x - 6/11 - 4/11*x**2 = 0. What is x?
1, 3/2
Find h such that 54*h - 2*h**3 + 15*h**2 + 9*h**2 + 16 + 12 = 0.
-1, 14
Let m(l) be the second derivative of l**8/6720 + l**7/1680 + l**6/1440 + l**3/6 + 3*l. Let t(n) be the second derivative of m(n). Suppose t(b) = 0. Calculate b.
-1, 0
Let x(d) = d**2 - 4*d - 14. Let u be x(7). Let s = u + -6. Factor s - 3/4*l**2 - 1/4*l**3 + 0*l.
-(l - 1)*(l + 2)**2/4
Find i such that 53*i**2 - 34*i - 10*i + 8 + 36*i**3 - 5*i**2 = 0.
-2, 1/3
Let b(k) be the second derivative of -k**6/36 - k**5/10 - k**4/8 - k**3/18 - k - 31. Determine r so that b(r) = 0.
-1, -2/5, 0
Let g = -665 - -2663/4. Factor 3/2*k**2 + g + 3/8*k**3 + 15/8*k.
3*(k + 1)**2*(k + 2)/8
Factor 28*c**3 - 5*c**4 + 8*c**4 - 31*c**3.
3*c**3*(c - 1)
Let 6912/5 + 144/5*m**2 + 4/5*m**3 + 1728/5*m = 0. What is m?
-12
Let d = 128/35 + 22/7. Find h such that -28/5*h**5 - d*h - 106/5*h**2 - 106/5*h**4 - 4/5 - 154/5*h**3 = 0.
-1, -1/2, -2/7
Factor -5*r**2 + 5 + 6*r**2 - 4 - 34*r + 32*r.
(r - 1)**2
Let a(i) be the third derivative of 0 + 0*i + 1/540*i**6 + 5*i**2 + 0*i**