- 1)*(4*o + 1)
Let r(d) = -7*d**3 - 4*d**2 + 20*d - 12. Let s(x) = 20*x**3 + 12*x**2 - 60*x + 36. Let h(b) = 8*r(b) + 3*s(b). Factor h(j).
4*(j - 1)**2*(j + 3)
Suppose -1 = z - 3. Let b(y) = -y + 10. Let m be b(8). Let 6*f**2 + 0*f**2 - 4*f**z - m = 0. Calculate f.
-1, 1
Let s(d) = 12*d**5 - 8*d**4 + 22*d**3 - 18*d**2 + 12*d + 10. Let c(w) = -w**5 - w**3 + w**2 - w - 1. Let l(x) = 20*c(x) + 2*s(x). Factor l(n).
4*n*(n - 1)**4
Let x(f) be the second derivative of -1/54*f**4 - 4/27*f**3 + 6*f - 1/3*f**2 + 0. Factor x(b).
-2*(b + 1)*(b + 3)/9
Let d(h) be the first derivative of -4*h**3 - 12/5*h**5 - 2 + 0*h + 3/2*h**2 + 9/2*h**4 + 1/2*h**6. Find f, given that d(f) = 0.
0, 1
Let i(l) be the third derivative of l**6/600 - l**5/60 + l**4/15 - 2*l**3/15 - 6*l**2. Find h such that i(h) = 0.
1, 2
Let w(p) be the first derivative of -p**5/240 + p**4/96 + p**3/12 - 9*p**2/2 - 6. Let g(z) be the second derivative of w(z). Factor g(j).
-(j - 2)*(j + 1)/4
Suppose -3*l = -13*d + 11*d - 6, 0 = 3*d. Factor -27/7*g**l - 3/7*g**4 - 15/7*g**3 - 6/7 - 3*g.
-3*(g + 1)**3*(g + 2)/7
Let h(n) = -8*n**3 + 8*n + 5. Let g(l) = 9*l**3 - 9*l - 6. Let a(k) = -5*g(k) - 6*h(k). Find m such that a(m) = 0.
-1, 0, 1
Let q(c) be the second derivative of -c**5/70 + c**3/21 - 23*c. Factor q(x).
-2*x*(x - 1)*(x + 1)/7
Let s be (2 + -1)/(2/28). Let v be s/4 - (0 - -3). Factor 1/2*y**3 + 0 + 1/2*y**2 - 1/2*y - v*y**4.
-y*(y - 1)**2*(y + 1)/2
Factor 2/3*d**2 + 0*d - d**3 + 0 - 5/3*d**4.
-d**2*(d + 1)*(5*d - 2)/3
Let k(f) be the second derivative of f**7/21 - 17*f**6/60 + 2*f**5/5 + 13*f**4/24 - 5*f**3/3 + f**2 + f. Let k(j) = 0. Calculate j.
-1, 1/4, 1, 2
What is t in -18/7*t**4 + 0 + 0*t + 4/7*t**3 + 0*t**2 + 2*t**5 = 0?
0, 2/7, 1
Let w(l) be the third derivative of l**5/15 + l**4/3 - 2*l**3 + 5*l**2. Factor w(k).
4*(k - 1)*(k + 3)
Solve -2/3*p + 2/3*p**3 + 1/3*p**4 - 1/3*p**2 + 0 = 0 for p.
-2, -1, 0, 1
Let x(m) = 4*m**4 - 2. Let s(y) = 18*y**4 + 3*y**3 - 4*y**3 - 3 + y**5 + y**2 - 13*y**4. Let q(b) = -2*s(b) + 3*x(b). Suppose q(u) = 0. Calculate u.
-1, 0, 1
Let f = 25 - 28. Let v be (55/(-25) - -1)/f. Factor -v*m**2 + 6/5*m - 4/5.
-2*(m - 2)*(m - 1)/5
Let h(n) = -n + 16. Let g be h(14). Let u be 9*(0 + 1/3). Factor o - g*o**2 + u*o - 6*o.
-2*o*(o + 1)
Let h(q) be the second derivative of q**3/6 + 6*q**2 + 3*q. Let w be h(-9). Find r, given that -r**w - 2*r + 2*r - r**4 + r**5 + r**2 = 0.
-1, 0, 1
Let x(r) be the third derivative of 2*r**8/15 - 136*r**7/525 - 51*r**6/100 - 22*r**5/75 - r**4/15 + 21*r**2. Solve x(z) = 0.
-2/7, -1/4, 0, 2
Let v(s) = s**3 - 15*s**2 + 10*s. Let n(p) = -15*p**2 + 10*p. Let r(h) = 4*n(h) - 5*v(h). Factor r(x).
-5*x*(x - 2)*(x - 1)
Let k(s) = -12*s**3 - 27*s**2 - 24*s - 9. Let c(u) = 3*u**3 + 7*u**2 + 6*u + 2. Suppose v - 18 = 3*v. Let z(b) = v*c(b) - 2*k(b). Factor z(m).
-3*m*(m + 1)*(m + 2)
Let r(h) be the second derivative of 5*h**4/4 - h**3 - h. Find w such that r(w) = 0.
0, 2/5
Let g = 2371/34102 + -1/578. Let v = g - -106/177. Suppose 0*z + 0 + v*z**2 = 0. Calculate z.
0
Let v(d) be the third derivative of -d**7/280 - 3*d**6/160 - d**5/40 - d**2. Suppose v(w) = 0. Calculate w.
-2, -1, 0
Let t(m) be the first derivative of 2*m**3/9 + 2*m**2/3 + 7. Find h such that t(h) = 0.
-2, 0
Let m(x) = 2*x**3 + 2*x**2 - 1. Let g be m(1). Factor -3*n**g + 5*n**3 - n - n.
2*n*(n - 1)*(n + 1)
Let f(l) = -3*l**2 + 4*l + 11. Let m(n) = 2*n**2 - 3*n - 7. Let x(d) = -5*f(d) - 7*m(d). Solve x(w) = 0 for w.
-3, 2
Suppose 0 = -d - 3*c - 18, d = 6*d + 3*c + 30. Let r = 5 + d. Factor -2/5*o**3 - 2/5*o**r + 2/5*o + 2/5.
-2*(o - 1)*(o + 1)**2/5
Let i(j) = 5*j**5 - 20*j**3 - 10*j**2 + 10*j + 10. Let l(g) = 5*g**5 - 20*g**3 - 10*g**2 + 11*g + 10. Let w(z) = -4*i(z) + 5*l(z). What is s in w(s) = 0?
-1, 1, 2
Let l = -21 + 24. Factor 4*m**3 + 12*m**2 + 1 - l + 6 + 12*m.
4*(m + 1)**3
Suppose -18 = -c + 2*c + 3*w, 14 = -3*c - w. Let s = 3 + c. Let s + 0*n + 6/7*n**4 - 10/7*n**5 + 0*n**2 + 4/7*n**3 = 0. Calculate n.
-2/5, 0, 1
Suppose 3*w + 4 = -4*k, w = 2*w + 2*k + 2. Let u be 2/(-8) - 1/(-4). What is o in u*o**3 - 1/4*o**4 + w*o + 1/4*o**2 + 0 = 0?
-1, 0, 1
Let t be (1 - -2) + -21 + 20. Find i, given that 1/2*i + 0 - 1/4*i**3 + 1/4*i**t = 0.
-1, 0, 2
Suppose -4*c + 3 = -1. Let j(l) be the first derivative of -c + 1/10*l**5 + 1/6*l**3 + 0*l**2 + 0*l - 1/4*l**4. Factor j(o).
o**2*(o - 1)**2/2
Let j(r) = -r**2 + 9*r - 10. Let m be j(7). Suppose i - m = -3*i, 6 = 4*u - 2*i. What is h in 0 + 1/4*h + 1/4*h**3 + 1/2*h**u = 0?
-1, 0
Let w(q) be the second derivative of q**4/36 - 7*q. Factor w(z).
z**2/3
Suppose t + 1 = 5. Let h(o) be the second derivative of -1/126*o**7 - 1/10*o**5 + 2/45*o**6 - 1/18*o**3 + 1/9*o**t + 0 + 0*o**2 - o. Factor h(z).
-z*(z - 1)**4/3
Let l(f) be the first derivative of -4*f**5/5 - 13*f**4/2 - 10*f**3 + f**2 + 10*f - 23. Find m such that l(m) = 0.
-5, -1, 1/2
Let h = 209/24 + -67/8. Solve -5/3*k**4 + 1/3*k + 2/3*k**3 + 2*k**2 - h - k**5 = 0.
-1, 1/3, 1
Let t = 1 + 2. Suppose -9*l = -7*l - 6. Find v, given that v**l + 4*v**3 - 4*v**t - 4*v**3 = 0.
0
Let r = 4 + -7/2. Let g(x) be the first derivative of -1/4*x**2 - 3 - r*x + x**3 - 1/2*x**5 + 1/4*x**6 - 1/4*x**4. Factor g(d).
(d - 1)**3*(d + 1)*(3*d + 1)/2
Let t(a) be the first derivative of -2*a**5/35 + 4*a**4/7 - 4*a**3/7 - 40*a**2/7 - 50*a/7 + 24. Factor t(g).
-2*(g - 5)**2*(g + 1)**2/7
Let x(t) = 13*t**2 - 1. Let d be x(-1). Let s be (d/20)/((-3)/(-15)). Factor -1/5*k**2 + 1/5 - 1/5*k + 1/5*k**s.
(k - 1)**2*(k + 1)/5
Let w(o) be the first derivative of -o**4/12 - 2*o**3/9 + o**2/6 + 2*o/3 - 25. Factor w(j).
-(j - 1)*(j + 1)*(j + 2)/3
Let j(q) be the first derivative of -1/4*q**3 + 7 - 3/8*q**2 - 1/16*q**4 - 1/4*q. Factor j(w).
-(w + 1)**3/4
Let w(a) be the third derivative of -a**5/60 - 7*a**2. Let w(u) = 0. What is u?
0
Let u(y) be the third derivative of y**6/360 - y**5/40 + y**3/6 + 5*y**2. Let l(f) be the first derivative of u(f). Factor l(c).
c*(c - 3)
Suppose 2*v = 2*w + 10, 2*v + 0*w - 9 = 3*w. Let r be ((-4)/v)/((-18)/81). Factor 4/3*q**2 - r*q + 2/3.
(q - 2)*(4*q - 1)/3
Suppose -5 = -5*m - y, -3*y = -52*m + 50*m + 19. Factor 5/2*d + 1 + d**m.
(d + 2)*(2*d + 1)/2
Let d(z) = -25*z**4 + 47*z**3 - 9*z**2 - 17*z + 4. Let h(g) = 76*g**4 - 142*g**3 + 28*g**2 + 50*g - 12. Let t(m) = -8*d(m) - 3*h(m). Let t(b) = 0. What is b?
-1/2, 2/7, 1
Suppose -2*b + 4 + 0 = 0. Let u be (-18 - -13)*(-2)/20. Factor -u - d - 1/2*d**b.
-(d + 1)**2/2
Let w(c) be the first derivative of -3*c**4/16 + c**3/4 + 3*c**2/4 + 23. Factor w(o).
-3*o*(o - 2)*(o + 1)/4
Let s(b) = -14*b**3 - 24*b**2 - 3*b + 7. Let k(p) = -42*p**3 - 72*p**2 - 10*p + 20. Let y(u) = -3*k(u) + 8*s(u). Let y(m) = 0. Calculate m.
-1, 2/7
Let y be (-11 + 11)/13*2/2. Solve 6/7*v + 2/7*v**2 + y = 0 for v.
-3, 0
Let r be 38/(-57)*(-4)/(12/9). Find t such that -4/5*t - 6/5 + 8/5*t**3 + r*t**2 = 0.
-1, 3/4
Let t(f) be the third derivative of -f**6/720 + 11*f**5/360 - 35*f**4/144 + 25*f**3/36 - 5*f**2. Suppose t(a) = 0. What is a?
1, 5
Determine c, given that 0*c**2 - 1/2 - 1/4*c**3 + 3/4*c = 0.
-2, 1
Let s(o) = -o**2 - 1. Let j(c) = 9 + c - 3*c + 10*c**2 + 0*c. Let g(p) = 2*j(p) + 18*s(p). What is z in g(z) = 0?
0, 2
Let v(w) be the second derivative of -w**4/3 + 22*w. Factor v(h).
-4*h**2
Let j(k) be the third derivative of -3*k**2 + 1/30*k**6 + 0*k**4 + 0*k - 1/30*k**5 - 3/224*k**8 + 0*k**3 + 1/140*k**7 + 0. Factor j(p).
-p**2*(p + 1)*(3*p - 2)**2/2
Let l(y) = -y**3 + 2*y**2 + 5*y - 4. Let t = 5 - 2. Let h be l(t). Suppose -2*v**h + 2*v**2 + 3 - 2 - v**2 = 0. What is v?
-1, 1
Let y(i) be the second derivative of -i**5/5 + 2*i**3/3 - 9*i. Solve y(n) = 0 for n.
-1, 0, 1
Let j(m) = 9*m**3 + 9*m**2 - 12*m - 6. Let v(r) = -17*r**3 - 18*r**2 + 25*r + 13. Let h(a) = -13*j(a) - 6*v(a). Solve h(o) = 0 for o.
-1, 0, 2/5
Let t = -3 - -5. Let s(y) be the second derivative of 0 + 1/48*y**4 + 0*y**3 + 2*y - 1/8*y**t. Let s(c) = 0. What is c?
-1, 1
Let u(i) be the second derivative of -5*i**4/28 + 4*i**3/7 + 6*i**2/7 - 13*i. Let u(q) = 0. Calculate q.
-2/5, 2
Let z = -44 - -42. Let k be ((-27)/z)/(-9)*-2. Solve 0 - 2/3*g - 2/3*g**k - 4/3*g**2 = 0.
-1, 0
Let y(c) be the third derivative of -c**8/560 + c**7/126 - c**6/90 - c**4/4 + 6*c**2. Let w(n) be the second derivative of y(n)