
Let d(h) be the first derivative of h**5/10 - 2*h**4/3 + 5*h**3/3 - 2*h**2 - 7*h - 1. Let j(g) be the first derivative of d(g). Find k such that j(k) = 0.
1, 2
Let l(w) be the third derivative of w**5/12 - 10*w**3/3 + 17*w**2. Factor l(d).
5*(d - 2)*(d + 2)
Let g(s) be the second derivative of s**7/63 - 7*s**6/45 + 19*s**5/30 - 25*s**4/18 + 16*s**3/9 - 4*s**2/3 + 4*s. Factor g(c).
2*(c - 2)**2*(c - 1)**3/3
Let d(j) be the second derivative of -j**7/168 + j**6/120 + j**5/80 - j**4/48 + 11*j. Find l such that d(l) = 0.
-1, 0, 1
Let l = 18 - 11. Let x(r) = 13*r**2 - 13*r + 7. Let g(a) = -4*a**2 + 4*a - 2. Let t = -4 + 6. Let n(z) = l*g(z) + t*x(z). Let n(k) = 0. What is k?
0, 1
Let y(a) be the third derivative of -a**10/30240 - a**9/15120 + 7*a**4/24 - 2*a**2. Let q(s) be the second derivative of y(s). Factor q(b).
-b**4*(b + 1)
Let c be -2 + (3 - -5) + -1. Suppose 4*f = -5*p + 41, c*f - p - 10 = p. Factor 4*q**5 + 3*q**3 + 3*q**5 - 7*q**5 + q**2 + q**5 + 3*q**f.
q**2*(q + 1)**3
Let q = -1547 - -1549. Factor 4/5 - q*j + 8/5*j**2 - 2/5*j**3.
-2*(j - 2)*(j - 1)**2/5
Let c = -40 + 124/3. Let l(y) be the first derivative of -1 - 1/3*y**3 + c*y + 3/4*y**4 - 4/3*y**2. Suppose l(z) = 0. What is z?
-1, 2/3
Suppose d - 7 + 2 = 0, -2*d = s - 10. Let w(l) be the second derivative of -1/15*l**4 + s*l**3 + 1/75*l**6 + 1/5*l**2 + 0 + 0*l**5 + 2*l. Solve w(x) = 0 for x.
-1, 1
Let o(p) = p**4 + 5*p**3 - 7*p**2 - 9*p + 2. Let l(n) = 2*n**4 + 9*n**3 - 13*n**2 - 17*n + 3. Let j(u) = -4*l(u) + 7*o(u). Factor j(r).
-(r - 2)*(r + 1)**3
Find g such that g + 1/2*g**2 + 1/2 = 0.
-1
Suppose -6 = -4*u + 2. Solve 3 + u*n**3 - 3 + 2*n**2 - 2*n**4 - 2*n + 0 = 0.
-1, 0, 1
Let l(j) = -10*j**3 + 34*j**2 - 24*j + 14. Let a(k) = 2*k**3 - 7*k**2 + 5*k - 3. Let n(z) = 28*a(z) + 6*l(z). Determine w, given that n(w) = 0.
0, 1
Let r = -3 + 5. Let y be r/(-9) + (-112)/(-18). Suppose 3*g - y*g**2 + 2 + 4*g**2 + 0 - 3*g**3 = 0. What is g?
-1, -2/3, 1
Let p(a) be the third derivative of a**7/420 - a**6/36 + 2*a**5/15 - a**4/3 - a**3/2 - 2*a**2. Let g(z) be the first derivative of p(z). Factor g(n).
2*(n - 2)**2*(n - 1)
Let c = -17 - -19. Suppose 5*y - 6 = c*y. Factor -1/2*m + 2*m**2 - 3*m**3 + 0 + y*m**4 - 1/2*m**5.
-m*(m - 1)**4/2
Let w(d) be the first derivative of -d + 1/2*d**3 - 1/4*d**4 + 3 + 0*d**2. Let o(m) be the first derivative of w(m). Factor o(j).
-3*j*(j - 1)
Let x(h) be the third derivative of h**5/60 - h**4/4 + 4*h**2 - 8. What is g in x(g) = 0?
0, 6
Let 5*g + 4 + 3*g - 8*g**2 + 4*g**4 - 8*g = 0. What is g?
-1, 1
Factor -16/5 + 14/5*p**2 + 52/5*p.
2*(p + 4)*(7*p - 2)/5
Let r(l) = -3*l**3 - 21*l**2 + 51*l - 12. Let p(q) = -q**3 - 5*q**2 + 13*q - 3. Let w(x) = 15*p(x) - 4*r(x). Factor w(h).
-3*(h - 1)**3
Let y be (3 - 1) + (3 - 1). Let a = 8 - y. Determine s so that 11/2*s**3 - s**2 - 15/2*s**a + 0 + 0*s = 0.
0, 1/3, 2/5
Let r = 474 + -471. Factor 0 + 2*n**r - 5/2*n**2 + n - 1/2*n**4.
-n*(n - 2)*(n - 1)**2/2
Factor 20/3*q + 1/9*q**4 + 46/9*q**2 + 25/9 + 4/3*q**3.
(q + 1)**2*(q + 5)**2/9
Factor 10*y**3 - 5*y**2 - y**2 + 2*y**2 + 2*y**5 - 8*y**4.
2*y**2*(y - 2)*(y - 1)**2
Let k(f) be the third derivative of -f**7/420 - f**6/90 + 3*f**3/2 - 5*f**2. Let d(m) be the first derivative of k(m). Factor d(s).
-2*s**2*(s + 2)
Suppose -4*r + z - 21 = -89, 0 = r + z - 22. Factor 9/2*q**2 + 3/8*q**3 + r*q + 24.
3*(q + 4)**3/8
Let k be ((-2 - 0) + 4)*1. Let p + 0*p - p + 1 - p**k = 0. Calculate p.
-1, 1
Let 2 + 6*a + 3/2*a**3 + 11/2*a**2 = 0. What is a?
-2, -1, -2/3
Let k = -213/16 + 111/8. Let n(z) be the first derivative of 0*z - 1/2*z**3 - 1 - 1/8*z**2 - 1/5*z**5 - k*z**4. Solve n(p) = 0 for p.
-1, -1/4, 0
Let d(f) = -f**4 - 5*f**3 - 16*f**2 - 12*f + 2. Let w(a) = -5*a**4 - 24*a**3 - 80*a**2 - 60*a + 11. Let k(z) = 11*d(z) - 2*w(z). Factor k(h).
-h*(h + 2)**2*(h + 3)
Let a = -89 + 91. Factor 2/7*y**a + 0 + 2/7*y.
2*y*(y + 1)/7
Let p be 95/360 + 2/18*-2. Let v(r) be the third derivative of 0*r**3 + 0*r**7 - 1/60*r**6 + 0*r**5 + 0 + 1/336*r**8 + p*r**4 + 0*r + r**2. Factor v(a).
a*(a - 1)**2*(a + 1)**2
Suppose 4*y = y - 15, -5*c - 5*y - 75 = 0. Let m be 9*9/((-405)/c). Factor 2/9 + 0*f**m - 4/9*f**3 + 4/9*f - 2/9*f**4.
-2*(f - 1)*(f + 1)**3/9
Let p(f) be the first derivative of -f**6/540 + f**4/36 + 2*f**3/3 - 3. Let t(s) be the third derivative of p(s). Factor t(h).
-2*(h - 1)*(h + 1)/3
Let x(c) be the first derivative of 2*c**3 - c**2 - 4*c + 26. Factor x(u).
2*(u - 1)*(3*u + 2)
Let d be (2/(-3)*3)/(5/(-2)). Suppose d*z + 2/5*z**2 + 2/5 = 0. What is z?
-1
Let q = 85 + -83. Determine g, given that -1/4*g**q + 1/2 - 1/4*g = 0.
-2, 1
Let c(q) = 2*q**4 + 6*q**3 + 4*q**2 - 8*q - 6. Let v(d) = d**2 - d - 1. Let m(u) = c(u) - 2*v(u). What is j in m(j) = 0?
-2, -1, 1
Factor -34*m**3 + 21*m**3 + 15*m**3 - 4*m**2.
2*m**2*(m - 2)
Let 4/3 - 14/3*u - 8/3*u**2 = 0. What is u?
-2, 1/4
Suppose -k = -10 + 1. Suppose 2*i - 3*h = 14, 4 = i - 3*h - k. Factor 5*p**2 - i - p**2 + 2*p - 5*p**2 + 0*p**2.
-(p - 1)**2
Let b(x) be the second derivative of -3/35*x**5 + 0*x**3 + 6*x - 1/7*x**4 - 1/70*x**6 + 0 + 0*x**2. Find v such that b(v) = 0.
-2, 0
Let d(f) = f**2 + 3*f + 2. Let c be d(0). Let 2*o - c*o**2 + 1/2*o**3 + 0 = 0. What is o?
0, 2
Suppose 2*b = h + 7, 2*h + 2*b - 25 = -3*h. Let n(z) be the first derivative of 0*z**4 - 1/21*z**6 - 2/35*z**5 + 1 + 0*z + 0*z**h + 0*z**2. Factor n(q).
-2*q**4*(q + 1)/7
Let r(g) be the second derivative of -g**6/6 + g**5 - 25*g**4/12 + 5*g**3/3 + 21*g. Let r(j) = 0. Calculate j.
0, 1, 2
Factor 0 + 0*c**2 + 0*c + 3/4*c**3 + 3/4*c**4.
3*c**3*(c + 1)/4
Factor -1/2*b**3 + 0 + 0*b**2 + 1/2*b.
-b*(b - 1)*(b + 1)/2
Let 6/7*p**2 + 0*p - 2/7*p**3 - 8/7 = 0. What is p?
-1, 2
Let q(r) be the third derivative of 2*r**7/105 - r**6/15 - r**5/15 + r**4/3 + 8*r**2. Suppose q(t) = 0. What is t?
-1, 0, 1, 2
Suppose 2*n = 17 - 3. Suppose -9 + n = -i. Factor -i*z**3 + 4*z**2 + 1/3*z**4 - 8/3*z + 0.
z*(z - 2)**3/3
Let c(d) = d**5 + d**4 - d**3 + d**2 - 1. Let o(b) = -4*b**5 + b**4 + 18*b**3 + 7*b**2 + 4*b + 5. Let v(k) = 15*c(k) + 3*o(k). Determine x so that v(x) = 0.
-2, -1, 0
Factor 2/9*n - 2/9*n**3 - 2/9*n**2 + 2/9.
-2*(n - 1)*(n + 1)**2/9
Suppose 3*x - 5*w + 4 = -1, 4*x - 2*w - 12 = 0. Suppose -x*t = -3*t. Suppose -1/6*k**2 + t + 0*k = 0. What is k?
0
Let k(n) be the second derivative of 0*n**3 - 6*n + 1/4*n**4 + 0*n**2 + 0 - 3/20*n**5. Suppose k(g) = 0. What is g?
0, 1
Let r = -40 - -42. Suppose -2/3 + 20/3*i - 50/3*i**r = 0. What is i?
1/5
Let p = 586/11 + 21/44. Let d = 54 - p. Determine s so that 0 + 1/4*s**3 - 1/4*s + d*s**2 - 1/4*s**4 = 0.
-1, 0, 1
Solve -26*q**5 + 3*q**4 - 2*q**2 + 27*q**5 + 3*q**3 + 4*q**2 - q**2 = 0.
-1, 0
Let j(x) be the first derivative of 25/6*x**3 + 5*x**2 + 2*x - 2. Let j(m) = 0. What is m?
-2/5
Determine y so that 43*y - 13*y**2 - 9*y**2 + 0*y**3 - 39*y + 18*y**3 = 0.
0, 2/9, 1
Suppose 0 = -4*t + c + 4*c + 19, 5*t - 3*c = 14. Suppose -8 = 4*g - 4*j, -j = t - 5. Suppose 4 - 2*q - 8*q + 7*q**2 - q**g = 0. What is q?
2/3, 1
Factor -4*p + 2/3*p**2 + 0.
2*p*(p - 6)/3
Let s = -34 + 34. Let r(v) be the first derivative of -4 + s*v - 2/3*v**3 + 1/3*v**2. Solve r(y) = 0 for y.
0, 1/3
Suppose -4*v + 1 = -3*v, 5*n = -3*v + 13. Factor -y - y - 9*y**3 + y**n + 3*y - 4*y**5 + 11*y**4.
-y*(y - 1)**3*(4*y + 1)
Let n(w) be the first derivative of -2*w**3/3 - w**2 + 4*w - 45. Factor n(d).
-2*(d - 1)*(d + 2)
Factor -24 + 8*g**2 + 9 - 23*g**2 - 39*g + 3*g**3 - 6.
3*(g - 7)*(g + 1)**2
Let o(h) be the second derivative of h**7/42 + h**6/30 - h**5/10 - h**4/6 + h**3/6 + h**2/2 + 4*h. Factor o(u).
(u - 1)**2*(u + 1)**3
Let b(x) be the third derivative of -x**8/112 + 2*x**7/35 + x**6/20 - 3*x**5/5 - 9*x**4/8 - 30*x**2. Factor b(p).
-3*p*(p - 3)**2*(p + 1)**2
Let z(k) = k + 16. Let n be z(-16). Factor n - 4/7*f**4 + 4/7*f**2 + 2/7*f**5 - 2/7*f + 0*f**3.
2*f*(f - 1)**3*(f + 1)/7
Let l(m) be the first derivative of m**7/42 + m**6/30 - m**5/20 - m**4/12 - 2*m - 4. Let r(d) be the first derivative of l(d). Suppose r(a) = 0. What is a?
-1, 0, 1
Let n(y) be the second derivative of 1/6*y**4 + 0 - 2/3*y**3 - 1/5*y**6 + 0*y**2 + 4*y + 2/5*y**5. Factor n(f).
-2*f*(f - 1)**2*(3*f + 2)
Let c(n) be the second derivative of n**5/100 + n**4/60 - n**3/30 - n**2/10 - 2*n. Determine b so that c(b