6/45 - l**5/15 + 20*l. Find w, given that f(w) = 0.
0, 1
Let x(l) be the second derivative of l**5/30 - l**4/6 - 2*l + 41. What is a in x(a) = 0?
0, 3
Let c(r) be the first derivative of 5/2*r**3 - 6*r + 6*r**2 + 2. Factor c(f).
3*(f + 2)*(5*f - 2)/2
Let j(i) be the first derivative of -2*i**3/33 + i**2/11 + 11. Find l, given that j(l) = 0.
0, 1
Let z(r) = 6*r**2 - 4*r - 6. Let b(w) = -13*w**2 + 8*w + 11. Let n(u) = 2*b(u) + 5*z(u). Find k, given that n(k) = 0.
-1, 2
Let j(v) be the first derivative of 4 - 2/15*v**5 + 0*v + 1/6*v**4 + 2/9*v**3 - 1/3*v**2. Factor j(d).
-2*d*(d - 1)**2*(d + 1)/3
Let f(k) = k. Let p(o) = -6*o**2 + 14*o - 2. Let j(y) = y**3 + 10*y**2 - y - 4. Let q be j(-10). Let w(c) = q*f(c) - p(c). Suppose w(r) = 0. Calculate r.
1/3, 1
Let x be 2 - 2/(-4)*0. Let u(n) = -2*n**x - n - n**2 + n**2 + 1 + n**2. Let j(g) = 2*g**2 + 6*g - 5. Let s(b) = j(b) + 3*u(b). Factor s(f).
-(f - 2)*(f - 1)
Let r be 50/20*1*(-2)/(-10). Factor 0*o + 2 - 3/2*o**2 - r*o**3.
-(o - 1)*(o + 2)**2/2
Suppose w - 1 = -2. Let i = 4 - w. Factor 2*f**i + 3*f - 6*f**2 + 12*f**3 - f - 7*f**4 - 2*f**2 - f**4.
2*f*(f - 1)**4
Find p such that -9*p - 5 - 2*p + 8*p**2 + 7 + p = 0.
1/4, 1
Let o be (-2)/(-10) - 21/5. Let v be (-4)/o*(1 + 2). Determine n, given that 2/5*n - 2/5 - 2/5*n**v + 2/5*n**2 = 0.
-1, 1
Let s = -1510 + 1510. Factor -2/5*x**4 + 0*x**3 + s + 2/5*x**2 + 1/5*x - 1/5*x**5.
-x*(x - 1)*(x + 1)**3/5
Let 1 + 2*q**2 + 0*q**2 + 2 - 5 = 0. What is q?
-1, 1
Let o(i) be the first derivative of 4*i**4/3 - 8*i**3/3 + 3*i**2/2 - i/3 + 4. What is c in o(c) = 0?
1/4, 1
Let p = -557 + 6129/11. What is b in -4/11 + p*b**2 - 2/11*b = 0?
-1, 2
Let o(l) be the second derivative of 2*l**7/63 - 2*l**5/15 + 2*l**3/9 + 14*l. Factor o(d).
4*d*(d - 1)**2*(d + 1)**2/3
Let a(x) be the third derivative of x**6/240 + x**5/40 - x**3/3 - 9*x**2. Factor a(r).
(r - 1)*(r + 2)**2/2
Let h = 20 - 26. Let b be 44/66*h/(-10). Find m, given that -b*m**2 - 4/5*m + 2/5*m**3 + 0 = 0.
-1, 0, 2
Let p(m) = 40*m**5 - 64*m**4 + 16*m**3 + 8*m**2 + 4. Let h(b) = -b**5 + b**3 - 1. Let o(l) = 4*h(l) + p(l). Factor o(a).
4*a**2*(a - 1)**2*(9*a + 2)
Let n(t) = -13*t**3 - 7*t**2 - 6*t - 4. Let x(z) = -14*z**3 - 6*z**2 - 7*z - 5. Let y(w) = 5*n(w) - 4*x(w). Factor y(p).
-p*(p + 1)*(9*p + 2)
Suppose 5*k + 8 = -3*y, 2*y - 28 = -y + 4*k. Suppose 0 = y*w - 10 - 2. Factor 5/3*s - 5/3*s**w - 2/3 + 2/3*s**2.
-(s - 1)*(s + 1)*(5*s - 2)/3
Factor -1 - 5*g**2 - 16*g + 1 - 203*g**2 - 1764*g**5 - 2184*g**4 - 1012*g**3.
-4*g*(3*g + 1)**2*(7*g + 2)**2
Let b(a) = -2*a**4 - 4*a**2 - 4*a + 4. Let k(r) = -2*r**4 - 5*r**2 - 5*r + 5. Let i(g) = -5*b(g) + 4*k(g). What is u in i(u) = 0?
0
Let q(r) be the first derivative of 81*r**4/4 + 54*r**3 + 54*r**2 + 24*r + 8. Factor q(m).
3*(3*m + 2)**3
Let b be (1/(-6))/(13/(-13)). Find p such that -2/3*p**2 + 0 - 2/3*p**3 - b*p**4 + 0*p = 0.
-2, 0
Factor -23*i**2 + 6*i**2 + 4*i**2 + 12*i - 18 + 11*i**2.
-2*(i - 3)**2
Let a(r) be the third derivative of -r**5/60 + 13*r**4/24 - 3*r**3/2 - r**2. Let l be a(12). Determine t, given that 1/6*t**l + 5/6*t**2 + 2/3 + 4/3*t = 0.
-2, -1
Let k(r) be the first derivative of -4/3*r**3 - 1/30*r**5 + 1/2*r**2 + 1/3*r**4 - 4 + 0*r. Let h(l) be the second derivative of k(l). Factor h(c).
-2*(c - 2)**2
Let -12 + 12*d + 3*d**4 - d**2 + 119*d**3 - 131*d**3 + 10*d**2 = 0. What is d?
-1, 1, 2
Let h(q) be the second derivative of -q**7/252 - q**6/60 + q**4/18 - 13*q. Factor h(g).
-g**2*(g - 1)*(g + 2)**2/6
Let p = -6 - -8. Factor 4*v**4 + v**5 - 2*v + 4*v - 3*v**5 - 4*v**p.
-2*v*(v - 1)**3*(v + 1)
Let b(r) = -8*r**2 - 64*r + 72. Let y(h) = -h**2 - 7*h + 8. Let j(w) = -3*b(w) + 28*y(w). Solve j(s) = 0.
-2, 1
Let c(x) be the second derivative of x**8/112 + x**7/70 - x**6/40 - x**5/20 + x**2 - x. Let h(q) be the first derivative of c(q). Solve h(z) = 0.
-1, 0, 1
Find v, given that -4*v + 9 + 14*v**2 - 13*v**2 - 2*v = 0.
3
Let p(l) = -31*l**4 + 21*l**3 - 4*l**2. Let d(b) = -10*b**4 + 7*b**3 - b**2. Let z(c) = 14*d(c) - 4*p(c). Factor z(v).
-2*v**2*(v - 1)*(8*v + 1)
Let m(u) be the third derivative of 0*u + 0 + 4/15*u**3 - 1/30*u**5 + 2/15*u**4 + u**2. Solve m(s) = 0.
-2/5, 2
Let w(a) = -a - 5. Let m be w(5). Let s = 12 + m. Factor 0 + 2/3*h + 1/3*h**s.
h*(h + 2)/3
Let b(o) = 2*o**2 - 5*o + 7. Let v(p) = -2*p**2 + 5*p - 6. Let g(c) = 3*b(c) + 4*v(c). Factor g(a).
-(a - 1)*(2*a - 3)
Suppose 2*y - 17 = -5*g, 0*g - 4*y = -g - 1. Factor 5*q**2 + q**4 + 3*q**g + 0*q**3 + 0*q**3 + q**3 + 2*q.
q*(q + 1)**2*(q + 2)
Suppose v + 3 = 7. Suppose i + 2*n + 8 = -0*n, -3 = -v*i - n. Factor 2/9*j**i + 0 + 2/9*j.
2*j*(j + 1)/9
Let g be 1 - (1 - 2/2). Let v be g*4 - 4/2. Factor -2*a**2 + 2*a**2 + 2*a**2 - v*a.
2*a*(a - 1)
Let d(f) = f**4 - 2*f**3 - 4*f**2 + 8*f - 3. Let g(a) = -a**4 + 2*a**3 + 4*a**2 - 9*a + 4. Let j(n) = -7*d(n) - 6*g(n). Find b, given that j(b) = 0.
-1, 1, 3
Factor -2/7*s**4 - 8/7 + 6/7*s**2 + 8/7*s - 4/7*s**3.
-2*(s - 1)**2*(s + 2)**2/7
Let k(t) be the first derivative of -t**4/42 + 2*t**3/21 - t**2/7 - 3*t - 5. Let j(g) be the first derivative of k(g). What is r in j(r) = 0?
1
Let c be -12*(33/(-9) + 3). Suppose -b - 3*b = -c. Factor b*m - 2/3*m**2 - 4/3.
-2*(m - 2)*(m - 1)/3
Let p = -18 + 21. Let y(f) be the third derivative of 0*f + 1/75*f**5 + 1/300*f**6 + 0 + 0*f**4 - 1/525*f**7 + f**2 + 0*f**p. Let y(b) = 0. What is b?
-1, 0, 2
Let r(v) = -25*v**4 - 105*v**3 - 121*v**2 - 31*v - 11. Let m(y) = -26*y**4 - 106*y**3 - 120*y**2 - 32*y - 10. Let c(u) = -7*m(u) + 6*r(u). Factor c(p).
2*(p + 1)*(p + 2)*(4*p + 1)**2
Let b(g) be the second derivative of g**5/10 - g**4/6 - 2*g**3/3 - 5*g. Factor b(x).
2*x*(x - 2)*(x + 1)
Suppose -5*g - 5*s = -114 + 44, 0 = -4*g - 2*s + 56. Suppose 4 - g = -5*v. Factor 6/5*k - 4/5 - 2/5*k**v.
-2*(k - 2)*(k - 1)/5
Let b(z) be the first derivative of -2/27*z**3 + 1 + 2/9*z**2 - 2/9*z. Solve b(j) = 0 for j.
1
Let l(q) be the second derivative of q**4/4 - q**3/2 + 18*q. Factor l(y).
3*y*(y - 1)
Let q be (7*1)/(0 + 1). Let r be ((-1)/9)/(q/(-42)). Factor r*m**2 + 2/3*m**3 - 2/3*m - 2/3*m**4 + 0.
-2*m*(m - 1)**2*(m + 1)/3
Suppose -26 = 13*p - 26*p. Solve -1/2*y + y**3 - y**p + 1/2 + 1/2*y**4 - 1/2*y**5 = 0.
-1, 1
Let b(s) = s**2 - 2*s. Let l be b(3). Factor -2*n + 3*n**2 - 3*n**3 + 3*n**l - n**3.
-n*(n - 2)*(n - 1)
Let r be (4/(-5))/(3 + (-66)/15). Let 0*s**4 - 8/7*s**3 + 2/7*s**5 + 4/7 + 6/7*s - r*s**2 = 0. Calculate s.
-1, 1, 2
Suppose 0 = 43*n - 41*n. Factor n*f - 8/5*f**3 + 2/5*f**2 + 0 + 6/5*f**4.
2*f**2*(f - 1)*(3*f - 1)/5
Let b(o) be the third derivative of o**10/378000 + o**9/75600 + o**8/50400 - o**5/60 + 4*o**2. Let g(f) be the third derivative of b(f). Factor g(q).
2*q**2*(q + 1)**2/5
Let p be 5/(30/(-12) + 5). Let x(b) be the first derivative of 2/27*b**3 - 3 + 1/9*b**p + 0*b. Factor x(j).
2*j*(j + 1)/9
Solve -174*a**4 - 4*a**3 - 4*a**2 + 2*a + 178*a**4 + 2*a = 0.
-1, 0, 1
Factor -5*t**3 - 18*t**4 + 14*t**5 + 0*t**4 + 9*t**3.
2*t**3*(t - 1)*(7*t - 2)
Let z(y) = -y**3 + 4. Let o(g) = g - 3. Let j be o(3). Let r be z(j). Find p, given that 3*p**5 + p**4 + 3*p - p**r - 6*p**3 + 0*p**4 = 0.
-1, 0, 1
Let c(f) = -f - 2. Let j be c(-4). Factor j*z**4 - 14 + 14.
2*z**4
Suppose 0 = -4*p + 8. Factor 2/5*v**3 + 0*v - 4/5*v**p + 0.
2*v**2*(v - 2)/5
Factor 2/7*k**4 + 2/21*k**5 + 0*k**2 - 8/21*k**3 + 0 + 0*k.
2*k**3*(k - 1)*(k + 4)/21
Suppose 0 + 0*v - 3/7*v**3 - 6/7*v**2 = 0. Calculate v.
-2, 0
Let f(v) be the first derivative of v**4/12 - 2*v**3/9 - v**2/6 + 2*v/3 + 1. Factor f(j).
(j - 2)*(j - 1)*(j + 1)/3
Let g(z) be the third derivative of -z**9/68040 + z**8/30240 - z**4/8 - z**2. Let d(j) be the second derivative of g(j). Factor d(l).
-2*l**3*(l - 1)/9
Let p(k) be the second derivative of -k**4/78 + 4*k**2/13 - 2*k. Factor p(d).
-2*(d - 2)*(d + 2)/13
Let n be (10 + -18 + 10)*(2 + -1). Factor -4/3 + 1/3*m**3 + 0*m + m**n.
(m - 1)*(m + 2)**2/3
Let f(w) be the second derivative of -w**7/7560 - w**6/2160 - w**4/3 + 5*w. Let t(x) be the third derivative of f(x). Factor t(b).
-b*(b + 1)/3
Let x(b) be the first derivative of -b**6/6 + 7*b**5/5 - 7*b**4/2 + 8*b**3/3 - 63. Factor x(p).
-p**2*(p - 4)*(p - 2)*(p - 1)
Factor 0*q**2 + 0 - 6/11*q**3 + 6/11*q.
-6*q*(q - 1)*(q + 1)/11
Factor 53*i + 5*i**2 - 53*i.
5*i**2
Let q(z) be the third de