 0 + 4/7*x**r + 2/7*x.
-2*x*(x - 1)**3*(x + 1)/7
Let g(y) = -3*y**2 - 3*y. Let w(s) = 2*s**2 + 2*s. Let l(p) = -6*g(p) - 7*w(p). Factor l(f).
4*f*(f + 1)
Let z(x) be the first derivative of -x**4 - 8*x**3/3 - 2*x**2 + 3. What is g in z(g) = 0?
-1, 0
Let s = 20 - 15. Let b(l) be the first derivative of 0*l**3 + 1/2*l**s + 0*l + 1/4*l**4 + 0*l**2 - 1. Factor b(o).
o**3*(5*o + 2)/2
Let x be 0 - (15/21 + -1). Let c = -114 - -116. Determine q so that x*q - 4/7 + 2/7*q**c = 0.
-2, 1
Solve -3*r**3 + 4*r**4 + 4*r**2 - r**3 - r**2 - 3*r**4 = 0 for r.
0, 1, 3
Factor 6*f**5 + f**4 - 3*f**5 - f**3 - 2*f**5 - f**2.
f**2*(f - 1)*(f + 1)**2
Let n(f) = 4*f + 14. Let o be n(-3). Factor 0 + 1/2*h**o + h.
h*(h + 2)/2
Let a be 3/(-2) - (-187)/22. Factor a*x + 5*x**3 - 4 - 9*x**3 - 3*x + 4*x**2.
-4*(x - 1)**2*(x + 1)
Let w(t) be the first derivative of -3 + 0*t**3 + 1/48*t**4 - 3*t + 1/40*t**5 + 1/120*t**6 + 0*t**2. Let n(l) be the first derivative of w(l). Factor n(q).
q**2*(q + 1)**2/4
Let u(c) be the first derivative of c**2/2 - 2*c - 1. Let p be u(5). Solve -4*d**4 + 4*d**4 + 3*d**4 - 4*d**4 - 3*d**2 + d + 3*d**p = 0 for d.
0, 1
Let o = -144 - -148. Let n(a) be the second derivative of -23/6*a**o + 0 + 9/5*a**5 + 2*a**2 + a**3 + 3*a. What is w in n(w) = 0?
-2/9, 1/2, 1
Suppose -18 = -7*g - 2*g. Factor 2/3*z**3 + 4/3 + 10/3*z + 8/3*z**g.
2*(z + 1)**2*(z + 2)/3
Let x be (0 + 6/5)/(122 + -120). Find f, given that 0 - 9/5*f**3 - x*f**4 + 3/5*f**2 + 3/5*f**5 + 6/5*f = 0.
-1, 0, 1, 2
Let d(i) = 4*i**5 + 4*i**4 - 4*i**3 - 12*i**2 + 8. Let p(w) = -w**5 + w**3 + w**2 - 1. Let y(f) = d(f) + 8*p(f). Suppose y(m) = 0. Calculate m.
-1, 0, 1
Suppose f = -f + 4. Suppose q - 12 = -f*q. Factor 0*w**2 - 4 + 2*w**4 - q*w**2 + 4 + 2*w**3.
2*w**2*(w - 1)*(w + 2)
Determine s so that 4/9*s + 0 - 2/9*s**2 + 2/3*s**4 - 8/9*s**3 = 0.
-2/3, 0, 1
Let g(u) be the third derivative of -u**6/480 - u**5/24 - 25*u**4/96 + 7*u**2 + 1. Determine r, given that g(r) = 0.
-5, 0
Let a = -13 + 17. Factor -18*u - 48*u**2 + 18*u**3 - 38*u**3 - 16*u**a - 24*u**3 - u**5 - u**5.
-2*u*(u + 1)**2*(u + 3)**2
Suppose 22 = 5*n + 7. Let i**2 - 6*i**n + 4*i**2 - 2*i**2 = 0. What is i?
0, 1/2
Let w(a) be the third derivative of -a**7/945 + a**6/108 - 7*a**5/270 + a**4/36 + 31*a**2. Factor w(s).
-2*s*(s - 3)*(s - 1)**2/9
Let l(m) be the first derivative of -m**3/12 + 5. Factor l(q).
-q**2/4
Let c be (6/6)/((-2)/(-8)). Let b(x) be the third derivative of 0*x + 0*x**c + 0 + 0*x**6 + 1/9*x**3 - 1/45*x**5 - 3*x**2 + 1/315*x**7. Factor b(d).
2*(d - 1)**2*(d + 1)**2/3
Let a(j) be the first derivative of 16*j**5/5 - 4*j**4 - 4*j**3 + 8*j**2 - 4*j - 13. Find h such that a(h) = 0.
-1, 1/2, 1
Let v(p) = -10*p**2 - 6*p - 5. Let y(b) be the first derivative of 11*b**3/3 + 5*b**2/2 + 6*b + 2. Let f(d) = -4*v(d) - 3*y(d). Factor f(a).
(a + 1)*(7*a + 2)
Factor -9/4 + 3/2*h - 3/2*h**3 + 1/4*h**4 + 2*h**2.
(h - 3)**2*(h - 1)*(h + 1)/4
Let g(y) be the second derivative of y**5/4 + 5*y**4/3 + 10*y**3/3 - 4*y. Suppose g(h) = 0. Calculate h.
-2, 0
Let f(p) = -5*p + 53. Let l be f(10). Let u(k) be the second derivative of 0*k**2 + 1/24*k**l - 1/80*k**5 + 0*k**4 + 3*k + 0. Factor u(q).
-q*(q - 1)*(q + 1)/4
Suppose -27*a - 3 + 84 = 0. Solve -2/5*f + 0 - 2/5*f**4 + 2/5*f**2 + 2/5*f**a = 0.
-1, 0, 1
Let p = -3 - -15. Let s be 26/6 - p/36. Determine h, given that -3/4*h**2 - 1/4*h**s + 0 + 1/4*h + 3/4*h**3 = 0.
0, 1
Factor 9/7*c**2 - 3/7*c - 9/7*c**3 + 0 + 3/7*c**4.
3*c*(c - 1)**3/7
Let c(i) = i**4 + 3*i**3 - 4*i**2 - 3*i. Let j(k) = 3*k**4 + 5*k**3 - 8*k**2 - 7*k. Let d(b) = -7*c(b) + 3*j(b). Factor d(v).
2*v**2*(v - 2)*(v - 1)
Let w = 83/70 + -9/10. Solve -2/7*h**4 - w*h**5 + 2/7*h**3 + 0*h + 0 + 2/7*h**2 = 0 for h.
-1, 0, 1
Let w = -7 - -10. What is f in 8*f**3 - f + 3*f**2 - 2*f**3 - 9*f**w + f**4 + 0*f = 0?
0, 1
Factor 14/3*l**4 + 50/3*l**2 + 8/3 - 38/3*l**3 - 2/3*l**5 - 32/3*l.
-2*(l - 2)**2*(l - 1)**3/3
Let g(d) = 7*d**3 + 3*d**2 - 3*d - 5. Let s(a) = -24*a - 11 + 6*a**2 + 17*a + a**3 + 14*a**3. Let w(i) = 13*g(i) - 6*s(i). Let w(h) = 0. Calculate h.
-1
Let -215*p**3 + 63*p**4 + 40 - 29*p - 3*p**4 - 151*p + 15*p**4 - 10*p**5 + 290*p**2 = 0. Calculate p.
1/2, 1, 2
Let i(k) = k**3 + k**2 - k - 1. Let q = 3 - 1. Let x(z) = -z**2 + 1. Let f(u) = q*i(u) - 2*x(u). Factor f(j).
2*(j - 1)*(j + 1)*(j + 2)
Let v be 9/5 - (-1)/5. What is n in -3*n**v - 2 - n + n**2 + 5*n = 0?
1
Let z = -10 - -3. Let a(x) = 5*x**3 - 5*x**2 - 4*x + 6. Let m(j) = -6*j**3 + 6*j**2 + 5*j - 7. Let y(n) = z*a(n) - 6*m(n). Solve y(l) = 0.
-1, 0, 2
Let p(m) = -m**5 + m**4 + m**3 + m + 1. Let u(c) = -8*c + 3 + 2*c**3 - 4*c**5 + 0*c**3 + c**4 + 11*c. Let j(b) = -6*p(b) + 2*u(b). Find g, given that j(g) = 0.
-1, 0
Let j(u) = -u**4 - u**2 + u - 1. Let l(x) = 16*x**4 + 4*x**3 + 18*x**2 - 22*x + 20. Let o(g) = 36*j(g) + 2*l(g). Factor o(d).
-4*(d - 1)**3*(d + 1)
Let d(p) be the second derivative of -p**10/15120 + p**9/3780 - p**7/630 + p**6/360 - p**4/2 - 5*p. Let n(j) be the third derivative of d(j). Factor n(a).
-2*a*(a - 1)**3*(a + 1)
Suppose 0 = -b - 5*b. Let 9*r**2 + 6 + 15*r + b*r + 0*r**2 = 0. What is r?
-1, -2/3
Let q(h) be the first derivative of h**4/54 + h**3/9 + 2*h**2/9 + h + 1. Let s(c) be the first derivative of q(c). Solve s(j) = 0 for j.
-2, -1
Suppose -40*p + 10 = -35*p. Let 0 + 9*l**p - 3*l**3 + 1/3*l**4 - 9*l = 0. Calculate l.
0, 3
Let h(x) be the first derivative of -x**6/1260 - x**5/420 + x**4/42 + 2*x**3/3 + 3. Let o(w) be the third derivative of h(w). Find s such that o(s) = 0.
-2, 1
Let v(z) be the third derivative of 0*z + 2*z**2 + 1/100*z**6 + 1/60*z**4 + 0*z**3 - 1/525*z**7 + 0 - 1/50*z**5. Suppose v(d) = 0. What is d?
0, 1
Let g = -18 - -19. Let i(x) be the first derivative of 1/12*x**4 + 1/3*x + g + 1/2*x**2 + 1/3*x**3. Let i(r) = 0. What is r?
-1
Let p(k) = 5*k**2 - 2*k. Let s(c) = -4*c**2 + c. Let t(x) = -3*p(x) - 4*s(x). Factor t(v).
v*(v + 2)
Let k = 1 + 12. Let i = -13 + k. Solve i*t**2 + 0 + 1/2*t**3 - 1/2*t = 0.
-1, 0, 1
Suppose 4*z - 5*z = 0. Factor -12*a - 5 + 12*a**2 + z*a**2 + 9 - 4*a**3.
-4*(a - 1)**3
Factor 2/9*t**2 - 2/9 + 0*t.
2*(t - 1)*(t + 1)/9
Let v(h) = -h**2 - 1. Let l(g) = -30*g**2 + 5*g - 25. Let p(y) = l(y) - 25*v(y). Find b, given that p(b) = 0.
0, 1
Let c(l) be the second derivative of -l**8/840 + l**7/140 - l**6/60 + l**5/60 - l**3/6 + 3*l. Let y(j) be the second derivative of c(j). Factor y(q).
-2*q*(q - 1)**3
Let g(r) be the first derivative of -4*r**3/3 + 12*r**2 - 43. Find v, given that g(v) = 0.
0, 6
Let r(z) = -6*z**3 - 18*z**2 - 30*z - 14. Let g(x) = -31*x**3 - 89*x**2 - 149*x - 69. Let i(j) = 2*g(j) - 11*r(j). Factor i(w).
4*(w + 1)*(w + 2)**2
Let m be (3/360)/(5/10). Let v(d) be the second derivative of 0*d**2 + 0*d**4 - 3*d + 1/18*d**3 + 0 - m*d**5. Factor v(l).
-l*(l - 1)*(l + 1)/3
Suppose 0 = -4*x + 3 + 13. Let j(d) be the third derivative of 0 + 0*d - 1/8*d**6 - 1/60*d**5 + 2/3*d**3 - d**2 + 1/2*d**x. Suppose j(s) = 0. What is s?
-2/3, -2/5, 1
Let v(h) be the first derivative of 0*h + h**2 - 1/3*h**3 - 1. Determine s so that v(s) = 0.
0, 2
Let x(v) be the second derivative of v**8/2240 - v**7/504 - v**6/180 + v**5/30 + v**4/4 + 2*v. Let r(k) be the third derivative of x(k). Solve r(j) = 0 for j.
-1, 2/3, 2
Let r(p) be the second derivative of p**5/10 - p**3 - 2*p**2 + 14*p. Factor r(q).
2*(q - 2)*(q + 1)**2
Let c(m) be the third derivative of -m**6/120 - 2*m**2. Factor c(s).
-s**3
Let b(t) = 5*t**3 + 8*t**2 + 7*t - 2. Let d(w) = -20*w**3 - 31*w**2 - 29*w + 9. Let k(o) = 9*b(o) + 2*d(o). Let k(q) = 0. Calculate q.
-1, 0
Suppose 2*v - 2 = -4*u, 0 = u - 2*u - 2. Suppose -v*l - 5*p = 0, 0*l = 5*l - 2*p - 21. Suppose -6/5*w**4 + 4/5*w**2 + 2/5 - 8/5*w + 8/5*w**l = 0. Calculate w.
-1, 1/3, 1
Let z(h) be the second derivative of -h**8/23520 + h**7/8820 - h**4/4 - h. Let o(g) be the third derivative of z(g). Factor o(b).
-2*b**2*(b - 1)/7
Let a(z) be the first derivative of -z**5/30 + z**4/6 + z**3 - 3*z**2/2 + 1. Let h(o) be the second derivative of a(o). Let h(m) = 0. Calculate m.
-1, 3
Factor 1/5*w**4 - w**3 - 4/5*w + 8/5*w**2 + 0.
w*(w - 2)**2*(w - 1)/5
Let c = -23 - -26. Suppose -w + 1 = x, -13 = -2*x - c*x - w. Find a, given that 8/5*a**x - 2/5 + 8/5*a - 2/5*a**4 - 12/5*a**2 = 0.
1
Let f(u) be the third d