+ 0*k + 0*k**5 - 1/60*k**6 - 3*k**2. Factor g(h).
2*h**3*(h - 1)
Suppose -l + 3 = 2*b, -5*b = -l + 9 + 1. Suppose 5*m + 2*g = 6 + 3, l*m - g - 18 = 0. Factor 16/7*j**4 + 2*j**m + 4/7*j**2 + 0 + 0*j + 6/7*j**5.
2*j**2*(j + 1)**2*(3*j + 2)/7
Suppose 0 = 3*u - 8 - 1. Suppose -2*r - 4 = -36. Find x, given that -r*x**3 + 3 + 14*x**2 - 6*x + 1 - u + 15*x**4 - 6*x**4 - 2*x**5 = 0.
1/2, 1
Let n(g) be the second derivative of 5*g**4/12 - 5*g**3 + 25*g**2/2 + 19*g. Factor n(l).
5*(l - 5)*(l - 1)
Let z(p) be the first derivative of p**4/5 - 2*p**2/5 + 2. Determine o, given that z(o) = 0.
-1, 0, 1
Let t = 359/7 - 51. Let f(y) be the second derivative of -1/7*y**2 + 0 - 3/14*y**4 - t*y**3 - 2/35*y**5 - 2*y. Find g, given that f(g) = 0.
-1, -1/4
Let g(b) be the second derivative of -b**6/900 + b**4/60 - b**3/6 - b. Let z(v) be the second derivative of g(v). Factor z(x).
-2*(x - 1)*(x + 1)/5
Let v(p) be the third derivative of -1/105*p**7 - 13/300*p**6 + 0 + 0*p + 2*p**2 + 0*p**3 - 2/75*p**5 + 1/15*p**4. Suppose v(w) = 0. Calculate w.
-2, -1, 0, 2/5
Let q be (-4)/10 - 16/(-15). Let f(n) be the first derivative of -q*n**5 + 2 - 2/3*n - 20/9*n**3 + 1/9*n**6 + 5/3*n**2 + 5/3*n**4. Factor f(h).
2*(h - 1)**5/3
Suppose 0 = -o + 1 + 1. Let v(w) be the first derivative of -7/2*w**6 + o - 33/4*w**4 + 2*w**2 + 0*w - 10*w**5 + 0*w**3. Suppose v(r) = 0. Calculate r.
-1, -2/3, 0, 2/7
Suppose 3 + 7 = 5*w. Find j, given that j**3 + j**3 + 0*j**2 - j**3 - 2*j**w + 3*j**4 = 0.
-1, 0, 2/3
Let t(s) be the second derivative of 3*s**5/10 - s**4/4 - s. Determine l, given that t(l) = 0.
0, 1/2
Let c = -18 + 17. Let b = 5/3 + c. Factor 0 - b*g**4 + 2/3*g**2 + 0*g**3 + 0*g.
-2*g**2*(g - 1)*(g + 1)/3
Let o(f) be the second derivative of f**7/105 - f**5/15 + f**3/3 - 3*f**2 + 8*f. Let q(c) be the first derivative of o(c). Suppose q(d) = 0. What is d?
-1, 1
Factor -5/2*g**2 + g + 0.
-g*(5*g - 2)/2
Let q = 5/11 - -40/33. Let g = -190 + 193. Determine x so that -q*x**2 - 1/3*x**g - 4/3 - 8/3*x = 0.
-2, -1
Suppose -m = -2*m + 3. Let c(h) be the second derivative of -1/12*h**4 + 0*h**2 + 0 + h - 1/6*h**m + 1/20*h**5 + 1/30*h**6. Factor c(x).
x*(x - 1)*(x + 1)**2
Let d(g) = 5*g**2 - 1. Let o be d(1). Suppose -4*r = -o - 4. Find h such that 7*h**2 + 2*h**r + 2*h + 8*h**3 - h**2 = 0.
-1/2, 0
Let g(z) be the third derivative of -z**6/300 + z**5/50 - 4*z**3/15 - 19*z**2. Factor g(f).
-2*(f - 2)**2*(f + 1)/5
Suppose 2 = 5*a - 4*a. Let k be ((-20)/11 - -1) + 1. Suppose -k*y + 2/11*y**3 + 0 + 0*y**a = 0. Calculate y.
-1, 0, 1
Let c(w) be the second derivative of 0*w**2 + 1/135*w**6 + 0*w**3 + 1/54*w**4 + 0 + 1/45*w**5 - 3*w. Factor c(x).
2*x**2*(x + 1)**2/9
Let f be 0/(-4) + -2 - (-153)/68. Let p = 113/234 - -2/117. Factor -1/4*k**2 + p - f*k.
-(k - 1)*(k + 2)/4
Suppose 16/3*r**2 + 100/3*r**5 + 0 + 0*r + 32*r**3 + 60*r**4 = 0. What is r?
-1, -2/5, 0
Suppose 5*o - 15/2*o**2 + 25/2*o**5 - 35/2*o**3 + 0 + 15/2*o**4 = 0. Calculate o.
-1, 0, 2/5, 1
Let c = -1381 - -1383. Solve 0*f**c + 0 + 0*f - 1/2*f**3 = 0 for f.
0
Let w(j) be the third derivative of j**10/252000 - j**8/16800 + j**6/1200 - j**5/60 - 5*j**2. Let v(t) be the third derivative of w(t). Factor v(d).
3*(d - 1)**2*(d + 1)**2/5
Factor o**2 - o**3 - 33*o**4 + 34*o**4 - o**3.
o**2*(o - 1)**2
Let d(m) be the first derivative of -m**3 - 9*m**2/2 - 6*m + 18. Suppose d(k) = 0. What is k?
-2, -1
Suppose j + 2*j = 9. Let n(g) be the second derivative of -1/60*g**6 + 0*g**j - g - 1/84*g**7 + 1/40*g**5 + 1/24*g**4 + 0 + 0*g**2. Factor n(b).
-b**2*(b - 1)*(b + 1)**2/2
Let f(m) be the first derivative of -m**4/3 - 2*m**3/3 - m**2/3 + 9. Factor f(l).
-2*l*(l + 1)*(2*l + 1)/3
Let i(d) be the third derivative of -d**5/210 + 5*d**4/84 - 4*d**3/21 + d**2. Factor i(b).
-2*(b - 4)*(b - 1)/7
Let i = 3 + -5. Let b be i/7 + (-32)/(-14). Factor 4*j + j**b - 4*j + 2*j**3 + j**4.
j**2*(j + 1)**2
Suppose -4*w + 3*u = -19, -3*w + 5*u + 4 + 13 = 0. Factor 2/3*k**3 + 0 + 0*k - 2/3*k**5 + 2/3*k**w - 2/3*k**2.
-2*k**2*(k - 1)**2*(k + 1)/3
Let n = -19 - -25. Let h(t) be the third derivative of 1/336*t**8 - 3*t**2 + 0*t**3 + 0 + 1/210*t**7 - 1/60*t**5 + 0*t**4 + 0*t - 1/120*t**n. Factor h(q).
q**2*(q - 1)*(q + 1)**2
Let v(u) = u**2 + u - 7. Let m be v(-4). Factor 0*p**4 + 2/3*p**m + 0 + 0*p**2 - 4/3*p**3 + 2/3*p.
2*p*(p - 1)**2*(p + 1)**2/3
Suppose -2*r + 5*r = 0. Determine t so that 3*t**2 - t**2 + r*t**2 - 2*t = 0.
0, 1
Let l(a) be the first derivative of a**4/4 - 4*a**3/3 + 3*a**2/2 + 2*a - 7. Let r be l(2). Suppose r - 2/3*i**2 - 2/3*i = 0. Calculate i.
-1, 0
Let s(n) = 6*n**3 + 11*n**2 - n - 1. Let p(r) = -3*r**3 - 6*r**2. Let m(o) = -5*p(o) - 3*s(o). Factor m(j).
-3*(j - 1)*(j + 1)**2
Let t = 383 - 379. Suppose 5*u + 9 = -3*v - 11, 3*u + 12 = 3*v. Determine d, given that -2/3*d**5 - 8/3*d**2 - 8/3*d**4 - 2/3*d + v - t*d**3 = 0.
-1, 0
Find p, given that 4/3 - 2/3*p - 16/3*p**2 - 10/3*p**3 = 0.
-1, 2/5
Suppose 0 = -6*k + k - 25. Let f be ((-2)/k)/((-49)/(-35)). Factor -2/7 + 2/7*x**3 + 2/7*x**2 - f*x.
2*(x - 1)*(x + 1)**2/7
Let d(q) be the first derivative of -q**5/10 + q**3/3 - 2*q + 1. Let n(u) be the first derivative of d(u). Factor n(r).
-2*r*(r - 1)*(r + 1)
Let o be 0 + (-1)/(-3) + 80/(-960). Suppose 1 + o*m**2 - m = 0. Calculate m.
2
Let x(t) be the second derivative of t**5/30 - t**4/3 + 4*t**3/3 - t**2/2 + t. Let j(f) be the first derivative of x(f). Solve j(a) = 0.
2
Let j(h) = 3*h**3 - 3*h**2 + 8*h - 2. Let f(q) = -7*q**3 + 5*q**2 - 16*q + 3. Let o(t) = -2*f(t) - 5*j(t). Factor o(z).
-(z - 2)**2*(z - 1)
Let a(s) be the first derivative of s**3/6 + 13*s**2/4 + 6*s - 7. Determine v, given that a(v) = 0.
-12, -1
Let y be 4 + -2 + (-16)/9. Suppose -10*s + 6 = -7*s. Solve y*a**s + 4/9 - 2/3*a = 0.
1, 2
Let o = 16 + -10. Solve 2*m**4 + o*m**3 + 3*m**3 + 2*m**2 - m**3 - 4*m**3 = 0.
-1, 0
Let a = 8 + -4. Let j(x) = -8*x**3 + 13*x**2 - 10*x - 3. Let z(d) = 15*d**3 - 25*d**2 + 19*d + 5. Let c(b) = a*z(b) + 7*j(b). Factor c(r).
(r - 1)**2*(4*r - 1)
Let g(u) be the third derivative of 0*u + u**2 + 0 - 1/6*u**3 + 1/24*u**4 - 1/240*u**5. Factor g(j).
-(j - 2)**2/4
Let z(y) = y**5 - 6*y**4 - 4*y**2 + 3. Let g(v) = -2*v**5 + 11*v**4 - v**3 + 7*v**2 - 5. Let a(n) = -3*g(n) - 5*z(n). Find f such that a(f) = 0.
0, 1
Find i such that 20 - 5*i**3 + 15*i**2 - 10*i - 18 - 2 = 0.
0, 1, 2
Suppose 5*n = 3*n + 4. Let -2*h**2 + 3*h**2 + h**n - h - h**3 = 0. What is h?
0, 1
Let f(q) = 6*q**3 + 10*q**2 + 26*q - 10. Let a(o) = o**3 + 2*o**2 + 5*o - 2. Let u = 2 - -1. Let t(c) = u*f(c) - 16*a(c). Determine i so that t(i) = 0.
-1, 1
Let g(s) be the third derivative of 0 - 4/15*s**5 + 0*s - 1/30*s**6 + 5*s**2 - 4/3*s**3 - 5/6*s**4. Suppose g(w) = 0. Calculate w.
-2, -1
Let m(i) be the second derivative of i**7/2520 - i**6/540 - i**5/360 + i**4/36 + i**3/3 + 4*i. Let u(d) be the second derivative of m(d). Factor u(p).
(p - 2)*(p - 1)*(p + 1)/3
Let q be (-8)/6*(-21)/(-14). Let a(t) = -t**2 - 3*t - 2. Let u be a(q). Factor 0 + u*n**2 + 2/7*n - 2/7*n**3.
-2*n*(n - 1)*(n + 1)/7
Let m(q) be the first derivative of q**4/4 + q**3/3 - q**2/2 - q + 4. Factor m(a).
(a - 1)*(a + 1)**2
Suppose 2*c = -3*v + 18, -3*c + v - 7 = -3*v. Let b be (-2)/(-24) - c/(-12). Let 2/3*j - 1/3*j**5 + 0 + j**3 - 5/3*j**2 + b*j**4 = 0. Calculate j.
-2, 0, 1
Let d(j) = j**3 + 4*j**2 - 6*j. Let b be (-6)/4*56/(-21). Let h(r) = -11*r**2 + 11*r - b*r + 7*r**2 - 2*r**3. Let v(t) = 3*d(t) + 2*h(t). What is q in v(q) = 0?
0, 2
Let b(d) = d**2 - 6*d + 17. Let o be b(7). Let i be ((-4)/18)/(o/(-36)). Factor 2/3*f + 0 + i*f**2.
f*(f + 2)/3
Let z(n) be the first derivative of n**7/525 + n**6/150 + n**5/150 - n**2 + 1. Let w(b) be the second derivative of z(b). Factor w(a).
2*a**2*(a + 1)**2/5
Let r(w) be the second derivative of w**5/70 - w**4/42 - 5*w**3/21 - 3*w**2/7 - 3*w. Factor r(u).
2*(u - 3)*(u + 1)**2/7
Let y(p) = p**2 + p + 1. Let a(n) = 2*n**2 + 7*n + 8. Let u(i) = -a(i) + 3*y(i). Solve u(k) = 0.
-1, 5
Suppose -3*u = -2*h - 10 - 4, u - 1 = -3*h. Factor 5*b**4 - 5*b**u - 8*b - 2*b**4 + 6*b**3.
-2*b*(b - 2)**2*(b + 1)
Let j(v) = v. Let h be j(0). Factor 2*c**2 - c - 4 + h*c - c.
2*(c - 2)*(c + 1)
Let z(v) be the third derivative of v**8/252 - v**7/63 + v**6/60 + v**5/90 - v**4/36 - 6*v**2. Factor z(j).
2*j*(j - 1)**3*(2*j 