 + 1/84*m**4 + m**2 + 0*m + 0 + 1/1260*m**6 - 1/210*m**5. Let i(q) be the first derivative of l(q). Factor i(x).
2*(x - 1)**2/7
Let r be (-6)/(-9) - (-30)/9. Let c(m) be the third derivative of 1/12*m**r - 2*m**2 + 1/3*m**3 + 0*m + 0 - 1/60*m**6 - 1/30*m**5. Factor c(b).
-2*(b - 1)*(b + 1)**2
Let h = 35 - 31. Let -2/9*y**2 - 2/9*y**3 + 2/9*y + 2/9*y**h + 0 = 0. Calculate y.
-1, 0, 1
Let o(t) be the third derivative of -4*t**7/945 - t**6/60 - t**5/135 - 7*t**2. Solve o(q) = 0.
-2, -1/4, 0
Let i be ((6/(-4))/1)/(126/(-21)). Let l(u) be the second derivative of i*u**4 + 0*u**2 + 0 - 2*u - 1/2*u**3. Factor l(v).
3*v*(v - 1)
Let f(s) = -s**4 + s**5 - s - 4*s**3 + 4*s**3 + s**2. Let a(u) = -u**5 - u**4 + 2*u**3 - u + 1. Let d(k) = a(k) + 2*f(k). Solve d(t) = 0.
-1, 1
Suppose 2*x + 21 = 3*h, -2*h + 9 + 13 = -4*x. Suppose -4*r + 11 + h = 0. Factor -1/3*o**2 + 1/3*o**r + 0*o**3 + 0 + 0*o.
o**2*(o - 1)*(o + 1)/3
Suppose 0 = -0*u + 3*u + 12. Let m be u/(-10) + 24/15. Find o such that -4*o**3 - 2/5 - 4*o**m - 2*o**4 - 2/5*o**5 - 2*o = 0.
-1
Let c(o) be the third derivative of -o**7/210 - o**6/45 - o**5/30 + 11*o**3/6 + 6*o**2. Let x(q) be the first derivative of c(q). Find m such that x(m) = 0.
-1, 0
Let g = -9/61 - -515/183. Let d be -2*((-1)/3 - 0). Solve -2*t - g*t**2 + d = 0 for t.
-1, 1/4
Let v(p) be the second derivative of p**5/210 + p**4/84 - 2*p**3/21 - p**2/2 - 2*p. Let r(o) be the first derivative of v(o). Factor r(y).
2*(y - 1)*(y + 2)/7
Let j(f) be the second derivative of 6*f - 1/12*f**4 + 1/9*f**3 + 0 + 0*f**2 + 0*f**5 + 1/90*f**6. Solve j(w) = 0.
-2, 0, 1
Let a(u) be the first derivative of -2*u**5/15 + 16. Suppose a(p) = 0. Calculate p.
0
Let y be (-18)/(-24)*(-2 + (-62)/(-27)). Let p = -1 + 1. Factor -2/9*h + p - y*h**3 - 4/9*h**2.
-2*h*(h + 1)**2/9
Let u(j) be the first derivative of -2*j**6 + 16*j**5/5 + 2*j**4 - 16*j**3/3 + 2*j**2 - 15. Suppose u(o) = 0. Calculate o.
-1, 0, 1/3, 1
Find q, given that 0*q**3 + 3*q**3 + 675*q**4 + 2*q**2 - 674*q**4 = 0.
-2, -1, 0
Factor 0 + 2/7*n**4 + 6/7*n**3 + 0*n + 0*n**2.
2*n**3*(n + 3)/7
Let v be 54/20*56/(-3). Let m = -50 - v. Let 2*p**4 + 0 - 8/5*p**5 + m*p - 2*p**2 + 6/5*p**3 = 0. Calculate p.
-1, 0, 1/4, 1
Let w(t) be the first derivative of -t**4/2 + 8*t**3/9 + 5*t**2/3 - 4*t/3 + 20. Factor w(q).
-2*(q - 2)*(q + 1)*(3*q - 1)/3
Let m be (3/2)/((-12)/(-32) - 0). Let z(w) be the second derivative of 1/12*w**3 - 1/24*w**4 + 0 - 1/40*w**5 + 1/4*w**2 - m*w. Determine u so that z(u) = 0.
-1, 1
Let c(n) = n**2 - n - 1. Let l(i) = 15*i**2 - 18*i - 18. Let o(d) = -18*c(d) + l(d). Factor o(k).
-3*k**2
Factor 0 - 2/3*f**3 + 2/3*f**2 - 2/3*f**4 + 2/3*f.
-2*f*(f - 1)*(f + 1)**2/3
What is w in 4*w**3 + 6 - 6 + 4*w**4 = 0?
-1, 0
Let r(m) be the first derivative of -25*m**4/4 + 65*m**3/9 + 5*m**2/3 - 19. Determine l so that r(l) = 0.
-2/15, 0, 1
Let n(u) be the third derivative of u**7/10080 - u**6/720 + u**5/120 + 3*u**4/8 - 8*u**2. Let j(m) be the second derivative of n(m). Factor j(f).
(f - 2)**2/4
Factor 0*s + 0*s**2 + 0 + 2/7*s**4 - 2/7*s**3.
2*s**3*(s - 1)/7
Let a(v) be the third derivative of -5*v**8/112 + 3*v**7/70 + 7*v**6/40 - 3*v**5/20 - v**4/4 - 6*v**2. Solve a(b) = 0.
-1, -2/5, 0, 1
Let d be -3 + 1 - (-3)/(-108). Let k = d + 9/4. Find y such that 0*y**2 + 4/9*y**4 + 0 - k*y**3 + 0*y - 2/9*y**5 = 0.
0, 1
Let l = -53/2 + 27. Solve -i - l - 1/2*i**2 = 0 for i.
-1
Let o = 23/39 + 1/13. Factor -2/3 + 2*z - 2*z**2 + o*z**3.
2*(z - 1)**3/3
Find w such that -1/6*w**2 + 1/6*w**3 + 0*w + 0 = 0.
0, 1
Let j(a) be the first derivative of -a**8/840 - a**7/420 - a**3/3 + 1. Let k(p) be the third derivative of j(p). Find g such that k(g) = 0.
-1, 0
Solve 0*g + 0 + 1/4*g**5 - g**4 + g**3 + 0*g**2 = 0.
0, 2
Let s(k) = -k**4 + 4*k**3 - 5*k**2 - 10*k + 4. Let p(v) = -3*v**4 + 9*v**3 - 9*v**2 - 21*v + 9. Let a(g) = 4*p(g) - 9*s(g). Factor a(c).
-3*c*(c - 2)*(c + 1)**2
Let h(n) be the third derivative of -n**6/540 + 4*n**5/135 - 4*n**4/27 + n**2. Factor h(r).
-2*r*(r - 4)**2/9
Let i(t) = 3*t**2 - 9*t + 11. Let z(a) = -3*a**2 + 9*a - 12. Suppose -2*l = -9 - 1. Let g(q) = l*z(q) + 6*i(q). Find c, given that g(c) = 0.
1, 2
Let v(b) be the first derivative of b**4/6 - b**2/3 - 13. Solve v(k) = 0 for k.
-1, 0, 1
Let u = 1564/21 - 74. Let z(h) be the first derivative of 3 + u*h**3 + 0*h - 2/7*h**2. Factor z(a).
2*a*(5*a - 2)/7
Find m, given that 0 - 2/3*m + 4/3*m**2 - 2/3*m**3 = 0.
0, 1
Let x(o) be the first derivative of o**6/36 - o**5/15 + o**4/24 - 11. Factor x(h).
h**3*(h - 1)**2/6
Let t be 1*4*(-18)/(-24). Factor -5*s - t*s**3 + 5*s - 3*s**2.
-3*s**2*(s + 1)
Let o(k) = -3*k**3 - 5*k**2 + 3*k - 5. Let s(n) = 5*n**3 + 8*n**2 - 5*n + 8. Let v(d) = -8*o(d) - 5*s(d). Factor v(j).
-j*(j - 1)*(j + 1)
Factor -s**2 + 16*s + 16*s**2 - s + 5 + 7*s**3 - 2*s**3.
5*(s + 1)**3
Let w(v) be the second derivative of -v**4/36 + v**3/6 - 2*v + 9. Factor w(b).
-b*(b - 3)/3
Suppose -4*z - 2*f = -8, -3*z = 3*f - 7*f - 28. Determine k so that -5*k**3 - k**4 + 3*k**5 - 3*k**2 + z*k**4 + 2*k**3 = 0.
-1, 0, 1
Let f(m) be the second derivative of -m**5/60 + m**4/12 - m**3/6 - m**2/2 - 2*m. Let a(j) be the first derivative of f(j). Factor a(v).
-(v - 1)**2
Let t(v) = v**3 - 6*v**2 + 2*v - 8. Let m be t(6). Factor -7*a**m - 12*a + 22*a**3 + a**4 - 16*a**2 + 4*a.
-2*a*(a - 2)**2*(3*a + 1)
Let g(d) be the first derivative of 4*d**3/3 + 12*d**2 + 44. Solve g(b) = 0 for b.
-6, 0
Let o be (-2)/(-12) - 179/66. Let j = 106/33 + o. What is w in 1/3*w + 0 + 1/3*w**3 + j*w**2 = 0?
-1, 0
Let b = -12 - -18. Let v(a) be the third derivative of 0 - 2*a**2 + 1/60*a**5 - 1/120*a**b - 1/210*a**7 + 1/24*a**4 + 0*a**3 + 0*a. Let v(j) = 0. Calculate j.
-1, 0, 1
Let x(i) be the second derivative of -i**7/70 - 2*i**6/25 - 3*i**5/25 - i. Let x(m) = 0. What is m?
-2, 0
Let v(r) be the second derivative of -r**7/350 + r**6/40 - 2*r**5/25 + r**4/10 - 5*r**2/2 - 6*r. Let j(n) be the first derivative of v(n). Factor j(y).
-3*y*(y - 2)**2*(y - 1)/5
What is i in -4/3*i - 2/3*i**2 - 2/3 = 0?
-1
Factor -5*x**3 + 5*x - x**2 + 5*x**4 - 12*x**2 + 8*x**2.
5*x*(x - 1)**2*(x + 1)
Let s(c) be the second derivative of c**6/120 - c**5/40 + c**4/48 + 31*c. Factor s(y).
y**2*(y - 1)**2/4
Let t(p) be the first derivative of -p**6/60 - 3*p**5/40 - p**4/8 - p**3/12 + 3*p - 1. Let y(j) be the first derivative of t(j). Find w, given that y(w) = 0.
-1, 0
Let f = 75 - 75. Let j(m) be the first derivative of -1/4*m**4 + f*m + 1/2*m**2 - 3 + 0*m**3. Suppose j(w) = 0. Calculate w.
-1, 0, 1
Factor -3/7*h**2 + 9/7 + 6/7*h.
-3*(h - 3)*(h + 1)/7
Factor 8/11*q + 2/11*q**5 - 6/11*q**3 + 0 + 4/11*q**4 - 8/11*q**2.
2*q*(q - 1)**2*(q + 2)**2/11
Let u(q) = -5*q**2 + 5*q - 3. Let t(c) = -4*c**2 + 6*c - 4. Let d(z) = -3*t(z) + 2*u(z). Find x, given that d(x) = 0.
1, 3
Let r(d) = d**3 - 1. Suppose -4*u - 6 = -2. Let v(w) = 2*w**3 - 2*w**2 - w - 3. Let y(t) = u*v(t) + 3*r(t). Factor y(z).
z*(z + 1)**2
Let n(x) be the first derivative of -x**6/24 + x**5/5 - 3*x**4/8 + x**3/3 - x**2/8 - 7. Suppose n(l) = 0. Calculate l.
0, 1
Let r(n) be the first derivative of 1 - n**3 + 0*n**6 + 0*n**2 + 0*n - 1/360*n**5 + 1/2520*n**7 + 0*n**4. Let v(a) be the third derivative of r(a). Factor v(u).
u*(u - 1)*(u + 1)/3
Solve 12*d**3 + 36*d - 6*d**2 - 12 + 3*d**2 - 48*d**3 + 15*d**4 = 0 for d.
-1, 2/5, 1, 2
Let t be (-229)/(-126) - 4/18. Let s = -2/21 + t. Factor s*g**3 - 1/2*g**4 + 0 + 1/2*g - 3/2*g**2.
-g*(g - 1)**3/2
Let v(u) be the third derivative of -u**5/15 - 2*u**4/3 - 2*u**3 + 6*u**2. Factor v(i).
-4*(i + 1)*(i + 3)
Let k(t) = 8*t. Let m be k(-1). Let g(u) = u**3 + 9*u**2 + 7*u - 4. Let l be g(m). Solve l*i - 4*i + 2*i**2 = 0.
0
Factor -2 - 2/3*j**2 + 10/3*j - 2/3*j**3.
-2*(j - 1)**2*(j + 3)/3
Suppose -2*j + 7*j = 20, 3*n - j = 8. Suppose 5 = n*b - 3. Suppose 5*z**2 - z**2 - 6*z**b = 0. What is z?
0
Let b(q) be the second derivative of -q**5/4 + 5*q**4/6 - 5*q**3/6 + 4*q. Find n such that b(n) = 0.
0, 1
Let z = 11 - 32/3. Suppose 1/6*q**2 - 1/2*q + z = 0. Calculate q.
1, 2
Factor 9*b - 9/2*b**2 + 12 - 3/2*b**3.
-3*(b - 2)*(b + 1)*(b + 4)/2
Let i be (-4)/16*(5 + -5). Factor -2/7*h**2 - 2/7*h**3 + 0 + i*h + 2/7*h**4 + 2/7*h**5.
2*h**2*(h - 1)*(h + 1)**2/7
Let 1/6*n**3 + 0 + 0*n + 1/3*n**2 = 0. What is n?
-2, 0
Suppose 8*h =