nd derivative of -m**6/150 + m**5/25 - 8*m**3/15 + 8*m**2/5 + 2*m. Factor q(k).
-(k - 2)**3*(k + 2)/5
Let g(i) be the third derivative of i**6/1080 - i**5/180 + i**3/2 - 4*i**2. Let s(r) be the first derivative of g(r). Solve s(q) = 0 for q.
0, 2
Let d(p) be the second derivative of p**5/30 - p**4/9 - 16*p. Factor d(f).
2*f**2*(f - 2)/3
Suppose -y = 2*m + 1, -20 + 4 = 2*m + 4*y. Factor m + 2*b**2 + 4*b + b**2 - b**2.
2*(b + 1)**2
Let t(k) = -5*k**3 + 17*k**2 - 12*k - 17. Let h(a) = -2*a**3 + 6*a**2 - 4*a - 6. Let v(b) = 17*h(b) - 6*t(b). Find c, given that v(c) = 0.
-1, 0, 1
Let c(h) = -h + 1. Let v be c(-2). Determine p so that v*p**2 - 6*p + 1 - 6 + 8 = 0.
1
Solve -27/5*z**3 - 48/5*z + 0 - 72/5*z**2 - 3/5*z**4 = 0.
-4, -1, 0
Factor -4/7*j**4 - 4/7 - 4/7*j**5 + 8/7*j**2 + 8/7*j**3 - 4/7*j.
-4*(j - 1)**2*(j + 1)**3/7
Let m(u) be the second derivative of u**6/15 + 4*u**5/15 + 5*u**4/12 + u**3/3 + 7*u**2/2 - u. Let v(r) be the first derivative of m(r). Factor v(s).
2*(s + 1)*(2*s + 1)**2
Let j(n) be the third derivative of 0*n**6 - 5*n**2 + 0*n**3 + 1/210*n**7 + 1/12*n**4 + 0 - 1/20*n**5 + 0*n. Factor j(t).
t*(t - 1)**2*(t + 2)
Factor -n**5 + 3 - 7*n**2 - 4*n**2 - n**4 + 9*n**2 - 5*n + 6*n**3.
-(n - 1)**3*(n + 1)*(n + 3)
Let u(h) be the third derivative of -h**5/40 - 5*h**4/16 - 7*h**2. Factor u(d).
-3*d*(d + 5)/2
Suppose 5*l - 23 = -4*r, 4*r - 3*r + 4 = 2*l. Determine f, given that 1/2*f**r - f + 1/2 = 0.
1
Let v(f) = 8*f**3 + 34*f**2 + 37*f + 6. Let u(q) = 4*q**3 + 17*q**2 + 18*q + 3. Let t(x) = 5*u(x) - 2*v(x). Factor t(y).
(y + 1)*(y + 3)*(4*y + 1)
Let o(z) be the second derivative of 0*z**3 - 1/150*z**6 + 0 - 1/15*z**4 + 0*z**2 - 10*z + 1/25*z**5. Factor o(g).
-g**2*(g - 2)**2/5
Suppose 6*d - 3*i - 7 = 2*d, 2*d + 4*i = 20. Suppose 3*j - 5*y + 9 - 40 = 0, 2 = -d*j - 2*y. Let x**2 - 2*x**2 + 0*x + j*x - x**2 = 0. What is x?
0, 1
Let t(v) = v**3 - 4*v - 3. Let d be t(-2). Let c be (8/120)/((-1)/d). Find u, given that -1/5*u**2 + 1/5*u**4 + 0 - 1/5*u**3 + c*u**5 + 0*u = 0.
-1, 0, 1
Suppose -v = 2*v + 3*g + 12, 1 = -4*v - g. Let j be v/(2/(2 + 2)). Let -4*b**4 + j + 4*b**3 - 4*b - 4*b**4 + 6*b**4 = 0. What is b?
-1, 1
Suppose 0 = 3*l - f - 10, 5*l - 4 = 3*f + 10. Suppose 2*m + l*k + 16 = 0, 12 + 8 = -2*m - 5*k. Factor 0*c + 1/4*c**3 + m + 0*c**2.
c**3/4
Let y(h) be the third derivative of -h**8/840 + 27*h**2. Factor y(n).
-2*n**5/5
Suppose 2*z + 3*r = z + 17, -4*z + 5*r = 17. Factor -2*v**2 - 4*v**z + 7*v**2.
v**2
Let r be (-2)/(-20) + (-52)/(-130). Factor 1/4*o**2 - 1/4 - 1/2*o**3 + r*o.
-(o - 1)*(o + 1)*(2*o - 1)/4
Factor 4/13*d**2 + 0*d + 2/13*d**3 + 0 - 2/13*d**4.
-2*d**2*(d - 2)*(d + 1)/13
Let j be ((-3)/(-7))/((-30)/(-35)). Factor 0*u + 1/4*u**3 + 0 + j*u**2 - 3/4*u**4.
-u**2*(u - 1)*(3*u + 2)/4
Let s(p) be the first derivative of -3*p**4/4 - 3*p**3 + 6*p**2 - 22. Factor s(f).
-3*f*(f - 1)*(f + 4)
Let v(t) be the first derivative of t**9/13608 - t**8/3780 + t**6/810 - t**5/540 + t**3/3 + 2. Let j(y) be the third derivative of v(y). Factor j(g).
2*g*(g - 1)**3*(g + 1)/9
Solve -71*j + 2 + j**2 + 35*j + 33*j = 0 for j.
1, 2
Let i be 9/12 + (-10)/16. Let q(t) be the first derivative of 1/12*t**6 + 1 + 1/10*t**5 + 0*t + 0*t**2 - 1/6*t**3 - i*t**4. Factor q(m).
m**2*(m - 1)*(m + 1)**2/2
Let h(o) = -14*o - 10. Let s(y) = 5*y + 3. Let k(u) = 3*h(u) + 10*s(u). Let i be k(1). Let 8 - 2*w**2 - i = 0. What is w?
0
Let t(i) be the second derivative of -i**5/100 - i**4/15 - i**3/6 - i**2/5 - 26*i. Determine n, given that t(n) = 0.
-2, -1
Let b be (-11)/11 - (1 - -6). Let d be 0*(-2 - 12/b). Determine v, given that -4/3*v**2 - 56/3*v**4 + d + 0*v + 10*v**3 = 0.
0, 1/4, 2/7
Let i(h) be the first derivative of 3*h**5/20 - 9*h**4/8 + 3*h**3 - 3*h**2 - 4. Let i(w) = 0. Calculate w.
0, 2
Let z(j) be the third derivative of 0 - j**2 + 0*j + 0*j**3 + 0*j**4 + 1/150*j**5. Determine a, given that z(a) = 0.
0
Let j(i) = i**3 - i**2 - 1. Let f(s) = 2*s**4 + 7*s**3 - s**2 - 3. Let c(w) = 2*f(w) - 6*j(w). Solve c(o) = 0.
-1, 0
Suppose 0 = -0*m + 4*m - 8. Factor -3*b**4 + b**4 + b - 2*b**3 + 4*b**2 - 2*b**m + b.
-2*b*(b - 1)*(b + 1)**2
Factor -2/9*f**2 + 0*f**3 + 0 + 2/9*f**4 + 0*f.
2*f**2*(f - 1)*(f + 1)/9
Let a(l) be the first derivative of -3*l**5/10 + 3*l**4/8 + l**3/2 - 3*l**2/4 - 1. Suppose a(z) = 0. Calculate z.
-1, 0, 1
Let c(l) be the first derivative of -l**4/3 - 8*l**3/3 - 6*l**2 - 16*l/3 - 11. Factor c(d).
-4*(d + 1)**2*(d + 4)/3
Let z = -4 + 4. Let p(t) = 6*t**3 + t**2 + z*t - t - 7*t**3. Let c(m) = 4*m**3 + 10*m**2. Let w(y) = -c(y) + 2*p(y). Determine f so that w(f) = 0.
-1, -1/3, 0
Let x be 1*(-36)/(-8)*(-10)/(-15). Factor 1/4*r**x + r - r**2 + 0.
r*(r - 2)**2/4
Let b(y) be the second derivative of -2*y**7/21 + y**5/5 - 27*y. Let b(h) = 0. What is h?
-1, 0, 1
Suppose -q + 4*q - 9 = 0. Let m be ((-6)/28)/(q/(-16)). Suppose -2/7*j**2 - 16/7*j + 16/7*j**3 - 6/7*j**4 + m = 0. What is j?
-1, 2/3, 1, 2
Factor -1 - 30*z + 1 + 10*z**3 + 25*z**2 - 5*z**3.
5*z*(z - 1)*(z + 6)
Let z = 1012/5 - 202. Solve -z*b - 2/5*b**4 - 6/5*b**3 - 6/5*b**2 + 0 = 0.
-1, 0
Let z(s) = -2*s**3 + 11*s**2 - 12*s + 3. Let f be z(4). Factor 0 - 1/3*w**f + w**2 - 2/3*w.
-w*(w - 2)*(w - 1)/3
Let y(g) be the third derivative of g**6/300 + 7*g**5/300 - g**4/24 - 2*g**3/15 + 18*g**2. Factor y(f).
(f - 1)*(f + 4)*(2*f + 1)/5
Factor u**2 - u + 3*u - 4*u.
u*(u - 2)
Suppose -4*r + 4*b + 32 = 0, -4 = -8*r + 4*r - 3*b. Find v such that 2*v**2 - r*v**2 + v**2 = 0.
0
Let l(s) be the second derivative of s**4/42 + 2*s**3/21 + s**2/7 + 20*s. Solve l(p) = 0.
-1
Let g(c) = 5*c**2. Let b be g(-1). Let l(m) = m - 1. Let h(p) = -2*p**2 - 1 - 3*p + 6*p + 0 - 4. Let o(y) = b*l(y) - h(y). Factor o(w).
2*w*(w + 1)
Let c(l) be the first derivative of 8*l**6/15 + 68*l**5/25 + 28*l**4/5 + 88*l**3/15 + 16*l**2/5 + 4*l/5 + 12. Factor c(u).
4*(u + 1)**4*(4*u + 1)/5
Factor 12*z - 4*z**2 - 2*z**2 + 14*z**2 - 12*z**2.
-4*z*(z - 3)
Let o be 2*(-14)/4*(-9)/45. Let b(d) be the first derivative of 2 - 13/2*d**2 + 2*d + 9*d**3 + o*d**5 - 23/4*d**4. Solve b(w) = 0.
2/7, 1
Let z = -4/23 - -66/115. Suppose c = 2*c - 2. Determine j so that 14/5*j**c - 8/5*j**5 - 6*j**3 + 0 + 26/5*j**4 - z*j = 0.
0, 1/4, 1
Let z(v) be the first derivative of v**5 + 45*v**4/4 + 45*v**3 + 155*v**2/2 + 60*v + 72. Factor z(r).
5*(r + 1)**2*(r + 3)*(r + 4)
Let a(z) be the third derivative of z**5/330 - z**4/33 - 5*z**3/33 - 31*z**2. Let a(j) = 0. What is j?
-1, 5
Factor -139*i**2 + 137*i**2 + i**4 + 4 - 3.
(i - 1)**2*(i + 1)**2
Let b be 5 - 51*-2*2/(-60). Find g such that -2/5*g**3 - 8/5*g**2 - b*g + 0 = 0.
-2, 0
Let u(h) be the third derivative of 8*h**7/105 - h**6/6 - 7*h**5/15 + h**4/3 - 12*h**2. Determine k so that u(k) = 0.
-1, 0, 1/4, 2
Let a(m) be the first derivative of 3*m**2/2 - 22*m + 9. Let w be a(9). Determine c so that -1 - 25/4*c**2 - w*c = 0.
-2/5
Let l(q) = -q**4 - q**3 + q**2 - q - 1. Let r(s) = -5*s - 6*s - 9*s**4 + 2*s - 3*s**3 - 6 + 9*s**2. Let i = -30 + 36. Let v(g) = i*l(g) - r(g). Factor v(m).
3*m*(m - 1)**2*(m + 1)
Let q(t) = 20*t**2 - 1. Let b be q(1). Suppose 5*s = b + 1. Factor -5*d - 6*d**2 + 4*d**3 + s - d + 0*d.
2*(d - 2)*(d + 1)*(2*d - 1)
Let a(w) be the second derivative of 1/2*w**2 - 6*w - 1/3*w**3 - 1/30*w**6 + 0 + 0*w**4 + 1/10*w**5. Let a(j) = 0. What is j?
-1, 1
Let v(k) be the third derivative of k**7/42 + 13*k**6/120 + 3*k**5/20 - k**4/24 - k**3/3 + 30*k**2. Factor v(b).
(b + 1)**3*(5*b - 2)
Let i = 456 + -810. Let y = i - -2482/7. Factor 2*u + y + 10/7*u**2.
2*(u + 1)*(5*u + 2)/7
Let r(z) be the first derivative of z**3/5 + 9*z**2/5 + 3*z + 26. Solve r(m) = 0.
-5, -1
Factor 8/3*x - 8/3 - 2/3*x**2.
-2*(x - 2)**2/3
Let o(i) be the first derivative of i**5/5 - i**4/4 - 3*i**3 - 11*i**2/2 - 4*i - 12. Factor o(h).
(h - 4)*(h + 1)**3
Let 0 + 3/4*h**4 + 0*h**2 - 3/4*h**3 + 0*h = 0. Calculate h.
0, 1
Let m be (-77)/140 - 6/(-8). Let n(w) be the first derivative of -1/6*w**3 + m*w**5 + 0*w**2 + 0*w + 2 - 1/8*w**4. Solve n(x) = 0.
-1/2, 0, 1
Let z(q) = q**2 - 11*q + 27. Let w be z(3). Let x(f) be the third derivative of 1/420*f**6 + 0 - w*f**2 + 0*f - 1/210*f**5 + 0*f**3 + 0*f**4. Factor x(h).
2*h**2*(h - 1)/7
Factor 8/9*o**2 + 0 - 2/9*o.
2*o*(4*o - 1)/9
Let t = 33 - 31. Suppose t*b + 2*q + 7 = 17, 18 = 4*b + 3*q.