+ 1/15*a**3 + 2*a + 0*a**2 + 1/30*a**4. Let p(v) be the first derivative of k(v). Find m, given that p(m) = 0.
-1, 0
Let y(u) be the third derivative of -u**8/60480 - u**7/15120 + u**5/60 + 6*u**2. Let l(k) be the third derivative of y(k). What is b in l(b) = 0?
-1, 0
Let b be (-4)/8*(-6)/9. Solve -1/3*f**3 - f - f**2 - b = 0.
-1
Let z = -39 + 40. Let k(l) be the first derivative of -1/4*l + 1/8*l**2 - z + 1/4*l**3 - 1/10*l**5 - 1/16*l**4. Find j, given that k(j) = 0.
-1, 1/2, 1
Let v(k) = 3*k + 5*k - 2 - 3*k**2 - 3*k. Let m(r) = -3*r**2 + 5*r - 2. Let a(x) = 3*x. Let b be a(-1). Let d(c) = b*m(c) + 4*v(c). Factor d(s).
-(s - 1)*(3*s - 2)
Let a(g) be the first derivative of 1/4*g - 1/16*g**4 - 3/8*g**2 - 3 + 1/4*g**3. Factor a(k).
-(k - 1)**3/4
Suppose 3*u = 7*u. Factor -1/4*t**5 + 0*t + 0*t**3 + u*t**4 + 0 + 0*t**2.
-t**5/4
Let d(g) = -5*g**5 + 3*g**4 + 8*g**3 - 8*g. Let n(a) = 3*a**5 - 2*a**4 - 5*a**3 + 5*a. Suppose -p + 2*p = -5. Let t(z) = p*d(z) - 8*n(z). Factor t(i).
i**4*(i + 1)
Suppose 0*d**3 + 4*d**3 - 5*d**3 = 0. Calculate d.
0
Find b, given that -1/2*b**5 + b - 1/2*b**3 + 3/2*b**4 + 0 - 3/2*b**2 = 0.
-1, 0, 1, 2
Let y(r) be the third derivative of 11/24*r**4 + 0 + 0*r**3 + 0*r + r**2 - 1/12*r**5. Let a(o) = -2*o**2 + 5*o. Let t(i) = -7*a(i) + 3*y(i). Factor t(m).
-m*(m + 2)
Let t be 3 + -1 + 8 + -7. Determine w, given that w**3 + t*w**3 - 7*w**3 + 2*w**4 + w**2 + w**5 - 3*w**4 + 2*w = 0.
-1, 0, 1, 2
Solve 0*q**2 - 2/7*q**3 + 0 + 0*q + 2/7*q**5 + 0*q**4 = 0.
-1, 0, 1
Let l(o) be the first derivative of -4*o + o**2 - o**4 + 1/3*o**6 - 4/5*o**5 + 8/3*o**3 - 1. Solve l(s) = 0.
-1, 1, 2
Let p(i) = -7 + 4 + i + 0*i**2 + i**2 + 4. Let c(u) = -2*u**3 + 3*u**2 - 7*u - 3. Let b(v) = -2*c(v) - 6*p(v). Factor b(y).
4*y*(y - 2)*(y - 1)
Solve 2/5 + 0*g**2 + 1/5*g**3 - 3/5*g = 0 for g.
-2, 1
Let s(y) be the first derivative of -7*y**6/15 + y**5/5 + 7*y**4/6 - 2*y**3/3 - 3*y + 1. Let g(t) be the first derivative of s(t). Suppose g(d) = 0. What is d?
-1, 0, 2/7, 1
Suppose -a - 3 - 1 = 0. Let i = a + 32/7. Find m such that 0*m**3 + 0 + 2/7*m**2 + 0*m - 6/7*m**4 - i*m**5 = 0.
-1, 0, 1/2
Suppose 5*d + 1 = -3*s, 0 = 4*d - d + 6. Factor g - 2*g - 2*g**4 + 2*g + 5*g**s - 4*g**2.
-g*(g - 1)**2*(2*g - 1)
Let j(z) be the third derivative of -1/10*z**3 + 1/350*z**7 + 0*z**5 + 2*z**2 + 0 + 0*z + 1/20*z**4 - 1/100*z**6. Factor j(g).
3*(g - 1)**3*(g + 1)/5
Let n be (-2)/((-2)/1 - -1). Let w(f) be the first derivative of -2/5*f**5 - 3/2*f**4 + n - f**2 - 2*f**3 + 0*f. Factor w(s).
-2*s*(s + 1)**3
Let p(u) be the first derivative of -u**4/60 + u**2/10 + 3*u - 7. Let y(t) be the first derivative of p(t). Factor y(r).
-(r - 1)*(r + 1)/5
Suppose -6*o = -11*o + 15. Let i(m) be the third derivative of -1/630*m**7 - m**2 + 0 + 1/72*m**6 - 1/20*m**5 + 0*m + 7/72*m**4 - 1/9*m**o. Solve i(b) = 0.
1, 2
Suppose -2 = -b + n + 2, -3*b + 2*n = -10. Let j**3 - 2/5*j**b + 0 - j**5 + 2/5*j**4 + 0*j = 0. What is j?
-1, 0, 2/5, 1
Let a(m) be the second derivative of -11*m**5/130 + m**4/6 - 2*m**3/39 + 38*m. Factor a(f).
-2*f*(f - 1)*(11*f - 2)/13
Let n(m) = -23*m**2 + 1. Let w be n(1). Let v be w/(-14) - (-2)/(-2). Factor 2/7*j**2 + 2/7 - v*j.
2*(j - 1)**2/7
Suppose -3*m - 12 = -7*m. Determine i so that -m*i**2 - 4*i + 3*i**3 + 4*i + 0*i**3 = 0.
0, 1
Suppose -2/5 + 3/5*m**2 - 1/5*m - 1/5*m**4 + 1/5*m**3 = 0. Calculate m.
-1, 1, 2
Let t be (45/20)/(1*6/8). Let r = 25/7 + -15/7. Suppose -r*d**2 + 8/7*d + 4/7*d**t - 2/7 = 0. Calculate d.
1/2, 1
Let l(y) be the first derivative of -y**7/70 + y**6/240 + y**5/30 + y**4/48 - y**2 - 6. Let a(z) be the second derivative of l(z). Find n, given that a(n) = 0.
-1/2, -1/3, 0, 1
Let t = 1572 - 1572. Factor t + 2/9*h**4 + 0*h + 2/9*h**2 - 4/9*h**3.
2*h**2*(h - 1)**2/9
Let k(h) = -3*h**3 + 12*h**2 - 75*h + 36. Let o(f) = -f**3 + 3*f**2 - 19*f + 9. Let s(q) = -4*k(q) + 15*o(q). Solve s(z) = 0.
-3, 1
Let j(g) be the third derivative of g**10/151200 + g**9/30240 - g**7/2520 - g**6/720 - g**5/15 - g**2. Let o(z) be the third derivative of j(z). Factor o(h).
(h - 1)*(h + 1)**3
Let w(d) = d**4 - d**2 - d. Let y(x) = -4*x**4 + x**3 + 4*x**2 + 2*x. Let m(p) = 3*w(p) + y(p). Factor m(a).
-a*(a - 1)**2*(a + 1)
Let f(h) be the first derivative of -h**5/5 - 3*h**4/4 + h**3/3 + 3*h**2/2 + 10. Determine o, given that f(o) = 0.
-3, -1, 0, 1
Factor -11*c**3 + 2*c + 10*c**3 - c - 2*c**2 + c**4 + c**2.
c*(c - 1)**2*(c + 1)
Let w(p) be the first derivative of -4/25*p**5 + 0*p**3 + 0*p**2 + 0*p**4 - 1/15*p**6 + 0*p + 2. Factor w(b).
-2*b**4*(b + 2)/5
Let a be 4*-1*(-1)/9. Let n(s) be the first derivative of -2/3*s + 1/3*s**2 + a*s**3 - 2. Factor n(d).
2*(d + 1)*(2*d - 1)/3
Suppose 2*s - 8 = -2*s, 0 = -5*d + 5*s. Let w(x) be the second derivative of -2*x + 0 + 0*x**d + 1/6*x**4 + 1/3*x**3. Factor w(r).
2*r*(r + 1)
Let w(u) be the second derivative of u**8/84 - u**6/30 - 2*u**2 - 8*u. Let d(h) be the first derivative of w(h). Factor d(m).
4*m**3*(m - 1)*(m + 1)
Let z(h) be the second derivative of -2*h**2 - 1/12*h**4 + 0 + 2/3*h**3 + 3*h. Factor z(t).
-(t - 2)**2
Let r(w) be the third derivative of w**8/336 - w**7/210 - w**6/60 + w**5/30 + w**4/24 - w**3/6 + 12*w**2. Factor r(n).
(n - 1)**3*(n + 1)**2
Let x(r) be the first derivative of -1/2*r**2 - 1/20*r**5 + 2*r + 1/6*r**3 + 1 + 1/12*r**4. Let a(j) be the first derivative of x(j). Factor a(u).
-(u - 1)**2*(u + 1)
Let s = 125/4 + -31. Factor -3/4*p**2 - 1/4 - s*p**3 - 3/4*p.
-(p + 1)**3/4
Let o(l) = -4*l**3 + 2*l**2 + 10*l - 2. Let c(z) = z**3 - z**2 - z + 1. Let h(g) = -4*c(g) - 2*o(g). Suppose h(f) = 0. Calculate f.
-2, 0, 2
Suppose -4*a = -2*r - 12, -8 = r + 3*r - 4*a. Suppose o - 1 - 1 = 0. Factor -4 + 0*g - 6*g**r + 6*g + 4*g**o.
-2*(g - 2)*(g - 1)
Let k(y) = y**3 - 8*y**2 + 4. Let o be k(8). Suppose 6*d + 0*d**3 + 4 - 2*d**4 - 2*d**3 - 2*d**2 - o*d**3 = 0. What is d?
-2, -1, 1
Let b(n) be the third derivative of -n**5/36 + 5*n**4/36 - 5*n**3/18 + 4*n**2. Solve b(j) = 0.
1
Let q be 0*(2/4 - 0). Let h = -5 + 9. Find v, given that 0*v**2 + 0*v**3 + q*v + 0 - 4/11*v**5 - 2/11*v**h = 0.
-1/2, 0
Let i(p) = -3*p**3 - 7*p + 2. Suppose 4*t + 4 = 5*t. Let l(b) = -8*b**3 - 20*b + 5. Let m(f) = t*l(f) - 11*i(f). Determine k, given that m(k) = 0.
-1, 2
Let f = 30 + -27. Let p(u) be the second derivative of -1/40*u**5 + 0 + 0*u**2 + 2*u + 1/24*u**4 - 1/60*u**6 + 1/12*u**f. What is c in p(c) = 0?
-1, 0, 1
Suppose 0 = 2*l - 5*t + 3*t - 16, 2*l + 2*t - 16 = 0. Factor -2*s**2 + 3*s**2 - 3*s + 8 - l.
s*(s - 3)
Let i(c) be the first derivative of 2/5*c**5 + 5 + 3*c**4 + 8*c**3 + 0*c + 8*c**2. Determine b so that i(b) = 0.
-2, 0
Let n = -356 - -358. Determine t so that 3*t - 1/2*t**n - 9/2 = 0.
3
Let j(b) = b + 2. Let t be j(-5). Let p = t + 8. Factor q**4 + 5 + 2*q**3 - p.
q**3*(q + 2)
Let y = 214 + -211. Find f, given that -1/3*f**2 - y + 2*f = 0.
3
Factor 64/5 + 16/5*c + 1/5*c**2.
(c + 8)**2/5
Let k be (-1088)/(-60) - 2/15. Let r be ((-25)/(-30))/(10/k). Factor 3/2 - 3*a**2 + 0*a + 0*a**3 + r*a**4.
3*(a - 1)**2*(a + 1)**2/2
Factor 5*q**3 + 4*q + 23*q**2 + 9*q**3 - 5*q**2.
2*q*(q + 1)*(7*q + 2)
Let h(k) be the third derivative of -k**7/1050 + k**6/50 - 9*k**5/50 + 9*k**4/10 - 27*k**3/10 - 7*k**2. Factor h(f).
-(f - 3)**4/5
Let o(f) = -20*f**2 + 40*f - 11. Let a(w) = 4*w**2 - 8*w + 2. Let v(c) = -11*a(c) - 2*o(c). Suppose v(y) = 0. What is y?
0, 2
Factor -11*r**2 - r**4 - 6*r + 2*r**5 + 19*r**2 - 7*r**4 + 4*r**3.
2*r*(r - 3)*(r - 1)**2*(r + 1)
Let t(q) be the first derivative of 0*q**4 + 0*q + 0*q**2 + 3 - 1/6*q**3 + 1/10*q**5. Factor t(f).
f**2*(f - 1)*(f + 1)/2
Let c(g) = -5 + 10*g**2 - 5*g - 4*g**3 + 14*g**2 - 19*g**2. Let d(v) = 2*v**3 - 2*v**2 + 2*v + 2. Let k(z) = 2*c(z) + 5*d(z). Suppose k(p) = 0. Calculate p.
0
Let p(l) be the first derivative of -32*l**5/5 + 8*l**4 - 4*l**3 + l**2 - 3*l + 4. Let a(v) be the first derivative of p(v). Factor a(t).
-2*(4*t - 1)**3
Let y(p) = p**4 - 5*p**3 + 2*p. Let d(b) be the second derivative of -b**6/30 + 3*b**5/10 + b**4/12 - b**3/2 - b. Let z(q) = -4*d(q) - 6*y(q). Factor z(r).
-2*r**2*(r - 2)*(r - 1)
Factor -4*v**3 + 13*v**4 - 10*v**2 - 3*v**4 + 5*v**5 - v**3.
5*v**2*(v - 1)*(v + 1)*(v + 2)
Let o(u) be the third derivative of 3*u**2 + 1/70*u**7 + 1/12*u**6 + 1/12*u**4 + 3/20*u**5 +