 4/5*i**b + 2/5 - 9/5*i = 0.
1/4, 2
Let u(b) be the third derivative of -b**7/70 - 3*b**6/40 - b**5/10 - 60*b**2. Determine v so that u(v) = 0.
-2, -1, 0
Let c be 5 + (148/(-16) - -5). Let s(h) be the third derivative of 0 - c*h**4 - 9/2*h**3 + 0*h - 1/20*h**5 - 3*h**2. Factor s(i).
-3*(i + 3)**2
Let p(h) = -h**2 + 11*h + 2. Let z be p(11). Let x be z/(-3) + (2 - 0). Factor -14/3*n**4 + x*n**2 + 0*n - 10/3*n**3 + 0.
-2*n**2*(n + 1)*(7*n - 2)/3
Let h(s) = 2*s**3 - 2*s**2 - 7*s - 3. Let i(b) = b**3 + b**2. Let l(m) = h(m) - 3*i(m). Factor l(r).
-(r + 1)**2*(r + 3)
Let n(w) be the first derivative of 4/5*w + 2 - 2/15*w**3 - 1/5*w**2. Factor n(t).
-2*(t - 1)*(t + 2)/5
Suppose 5*z = z + 16. Let -z*c**2 + c**2 + c - c**2 + 5*c**2 = 0. Calculate c.
-1, 0
Let w be (9/(-120))/(10/(-80)). Solve 0 + 1/5*z**5 - w*z**3 - 1/5*z**4 + 2/5*z + 1/5*z**2 = 0.
-1, 0, 1, 2
Factor 0*o**4 - 4*o**4 - o**4 + 5*o**2 + 15*o**3 + 0*o**3 - 15*o.
-5*o*(o - 3)*(o - 1)*(o + 1)
Solve m**5 - m**2 + 10*m**2 - 2*m**4 - m - 7*m**2 = 0 for m.
-1, 0, 1
Let x(d) be the second derivative of d**2 - 1/6*d**4 + 0*d**3 + 0 + 3*d. Factor x(v).
-2*(v - 1)*(v + 1)
Let g(t) = -t - 2. Let c be g(2). Let n(b) = 3*b**2 + 4*b - 3. Let y(h) = -4*h**2 - 5*h + 4. Let v(o) = c*y(o) - 5*n(o). Factor v(x).
(x - 1)*(x + 1)
Suppose 2*c = -4*j + 2, 5*j + 0*j = 3*c + 30. Suppose n + 2 = j*n. Suppose -1 - 2*m**2 + 2*m + n = 0. Calculate m.
0, 1
Let p(u) = u**2 + 10*u - 8. Let z be p(-11). Let q(v) be the second derivative of 1/21*v**4 + 1/21*v**z - v + 0*v**2 + 0. Find m, given that q(m) = 0.
-1/2, 0
Let z(g) be the first derivative of g**3/9 - 4*g/3 + 21. Solve z(k) = 0.
-2, 2
Factor -4*g**4 + 2916*g - 972*g**2 + 83 - 83 + 108*g**3.
-4*g*(g - 9)**3
Let h(k) be the second derivative of 5*k**4/12 + 20*k**3/3 + 40*k**2 - 15*k. Factor h(t).
5*(t + 4)**2
Let a(r) be the third derivative of -7/60*r**5 - r**2 + 0*r + 1/3*r**3 + 0 + 5/24*r**4. Let a(l) = 0. What is l?
-2/7, 1
Suppose -5*h - 5*k + 10 = 0, -2*h + 2*k = 53 - 57. Suppose -16/7 + 172/7*w**h + 80/7*w**3 + 16/7*w = 0. Calculate w.
-2, -2/5, 1/4
Factor 4/13*v**3 - 2/13*v**5 + 0*v**4 - 2/13*v + 0*v**2 + 0.
-2*v*(v - 1)**2*(v + 1)**2/13
Let s(n) = 4*n**2 + 5*n - 4. Let p(x) = -6*x**2 - 7*x + 6. Let b(v) = 5*p(v) + 7*s(v). Factor b(k).
-2*(k - 1)*(k + 1)
Let q be (36/(-77))/(44/(-154)). Determine c, given that 10/11*c**2 - q*c**4 + 8/11 + 24/11*c - 24/11*c**3 = 0.
-1, -2/3, 1
Let l be (1*3/(-2))/(-2 + -4). Factor -1/4*g**2 - l*g + 0.
-g*(g + 1)/4
Let c(b) be the first derivative of b**3/5 + 6*b**2/5 + 9*b/5 - 9. Let c(s) = 0. Calculate s.
-3, -1
Let x(s) be the third derivative of -1/100*s**6 + 0*s**3 + 0*s + 1/75*s**5 + 1/60*s**4 - 2*s**2 + 0. Determine q so that x(q) = 0.
-1/3, 0, 1
Suppose -2*o = -3*m + 15, -5*m + 15 = -m - o. Let -2/3*a**2 + 2/3*a**m + 0*a + 0 = 0. What is a?
0, 1
Let l(g) be the second derivative of 16*g**6/105 + 12*g**5/35 + 3*g**4/14 + g**3/21 + 2*g. Factor l(h).
2*h*(h + 1)*(4*h + 1)**2/7
Factor 0 + 1/3*i**2 - 1/3*i**4 - 2/3*i + 2/3*i**3.
-i*(i - 2)*(i - 1)*(i + 1)/3
Let w(x) be the third derivative of -2*x**2 + 0 + 1/24*x**4 + 0*x - 1/4*x**3 + 1/120*x**5. Solve w(l) = 0.
-3, 1
Factor 3/4*c**4 + 1/4*c**2 + 0 - 3/4*c**3 - 1/4*c**5 + 0*c.
-c**2*(c - 1)**3/4
Let c(w) be the third derivative of -2*w**7/35 - w**6/6 + w**5/3 + 5*w**4/6 - 4*w**3/3 + 5*w**2. Let c(t) = 0. Calculate t.
-2, -1, 1/3, 1
Let p(t) be the first derivative of -11*t**6/12 + t**5/5 + 11*t**4/8 - t**3/3 - 13. Suppose p(u) = 0. Calculate u.
-1, 0, 2/11, 1
Let c be ((-328)/48 - -6)*1/(-10). Let x(u) be the second derivative of -c*u**4 + 0 + 0*u**3 + 2*u + 0*u**2. Determine n, given that x(n) = 0.
0
Let w = -170/399 - -9/19. Let q(a) be the third derivative of 0 - w*a**3 + a**2 - 1/42*a**4 + 0*a - 1/210*a**5. Solve q(g) = 0.
-1
Let v(a) = -a**3 + a + 2. Let j(u) = -u**3 + u**2 + 1. Suppose -4*p - 14 = 5*y, -4*y + p - 3 = -4*p. Let q(m) = y*j(m) + v(m). Factor q(z).
z*(z - 1)**2
Factor 7*t**4 + 2*t - 2*t**2 - 2*t**3 - 5*t**4 + 0*t**2.
2*t*(t - 1)**2*(t + 1)
Let l(z) = -z**3 - z + 1. Let d(y) = 4*y**3 - 15*y**2 + 6*y. Let q(t) = d(t) - 3*l(t). Let s(k) be the first derivative of q(k). Factor s(c).
3*(c - 1)*(7*c - 3)
Let t = -166 + 166. What is c in 0*c + t + 2/9*c**2 - 2/9*c**3 = 0?
0, 1
Let x(k) be the second derivative of 3/5*k**5 + 2*k + 11/12*k**4 + 1/3*k**3 + 0*k**2 + 0. Factor x(a).
a*(3*a + 2)*(4*a + 1)
Suppose 4*r = -4*f + 36, -4*r - 3*f + 2*f + 21 = 0. Suppose 15 = 5*t - 5*l, 4*t = -2*l + r*l + 10. Let 3*m**2 + 5*m - m - 4 - 4*m**t = 0. What is m?
2
Let b(a) = -a**3 + 6*a**2 - a + 3. Let k be b(6). Let w be 25/30*k/(-10). Factor 1/4*h**3 - w*h**5 + 1/4*h**4 + 0 + 0*h - 1/4*h**2.
-h**2*(h - 1)**2*(h + 1)/4
Let k(b) = -3*b + 1. Let t be k(-3). Let o be 5/t*8/1. Suppose i + i**o + 3*i - i**2 - 3*i - i**3 = 0. What is i?
-1, 0, 1
Let f = -19 - -21. Factor 3*p**f + p + 2*p**3 + 14 - 14.
p*(p + 1)*(2*p + 1)
Let w(q) be the third derivative of q**5/20 - q**4/2 - 5*q**3/2 - 6*q**2 - 1. Factor w(i).
3*(i - 5)*(i + 1)
Let y(j) be the second derivative of -j**9/7560 + j**8/4200 + j**7/2100 - j**6/900 + j**3/2 + 4*j. Let d(k) be the second derivative of y(k). Factor d(z).
-2*z**2*(z - 1)**2*(z + 1)/5
Let d(x) be the first derivative of -3*x**2 - 3/4*x**4 - 3*x**3 + 0*x - 1. Let d(l) = 0. Calculate l.
-2, -1, 0
Let v(t) be the first derivative of t**6/8 - 3*t**5/20 - 3*t**4/8 + t**3/2 + 3*t**2/8 - 3*t/4 - 1. Suppose v(f) = 0. Calculate f.
-1, 1
Let h(u) = -u**3 - 4*u**2 - 5*u. Let n(o) = 4*o**2 + 9*o + 5. Let m(p) = 4*p**2 + 8*p + 4. Let x(w) = 5*m(w) - 4*n(w). Let v(r) = 4*h(r) + 5*x(r). Factor v(i).
-4*i**2*(i - 1)
Let y(g) be the second derivative of -g**5/60 + g**4/18 - g**3/18 - 11*g. Find r, given that y(r) = 0.
0, 1
Let x(k) be the first derivative of -13*k**3 - 3*k**4 - 6*k - 4 - 33/2*k**2. Factor x(g).
-3*(g + 1)*(g + 2)*(4*g + 1)
Factor 2/13*w**2 + 80/13*w + 800/13.
2*(w + 20)**2/13
Let w be 8 - 4 - (-19)/(-5). Let x be 0*1/3*1. Factor 1/5 - w*h**2 + x*h.
-(h - 1)*(h + 1)/5
Let u be 32/39 + 5*4/(-130). Factor -4*c - u*c**2 - 6.
-2*(c + 3)**2/3
Let x = -5 + 7. Suppose 5*d - 8 = x. Factor -d + 3*j - 3*j + 4*j + j**2 - 3*j.
(j - 1)*(j + 2)
Let m(h) be the first derivative of -9*h**3 + 33*h**2/2 - 6*h - 6. Factor m(q).
-3*(q - 1)*(9*q - 2)
Let f(v) = -5*v**5 - 34*v**4 - 52*v**3 - 54*v**2 - 11*v. Let b(p) = p**4 - 2*p**3 + p**2 - p. Let g(i) = -4*b(i) - f(i). Suppose g(w) = 0. Calculate w.
-3, -1, 0
Let f be 76/(-20) - 12/(-7 - -4). Solve -1/5*x**4 + 2/5*x**2 - 2/5*x**3 + 1/5*x - 1/5 + f*x**5 = 0 for x.
-1, 1
Let o(g) be the second derivative of -g**7/3360 + g**3/6 - 3*g. Let s(w) be the second derivative of o(w). Factor s(r).
-r**3/4
Let s(c) be the third derivative of -c**7/70 - 3*c**6/10 - 27*c**5/10 - 27*c**4/2 - 81*c**3/2 - 2*c**2. Factor s(d).
-3*(d + 3)**4
Let h = -32/5 - -226/35. Let n(u) be the first derivative of -h*u**5 - 2/21*u**3 + 1 + 0*u + 0*u**2 + 1/7*u**4. Factor n(f).
-2*f**2*(f - 1)**2/7
Suppose 5*r + 41 = 51. Suppose 2/9*u + 4/9*u**r - 2/9 = 0. What is u?
-1, 1/2
Let g(n) be the third derivative of 1/420*n**6 - 1/210*n**5 + 0*n**3 - 2*n**2 + 0*n + 0 + 0*n**4. Determine z, given that g(z) = 0.
0, 1
Let k = 316 + -2531/8. Let m = k + 7/8. Factor -m*o**2 - o - 1/2.
-(o + 1)**2/2
Suppose 5*b - 13 = -3. Find h such that 6 + 5*h - 3*h + 9*h**b + 13*h = 0.
-1, -2/3
Let n = 438/791 - -2/113. Let q be 2/3 - 24/63. Factor q*v + 2/7*v**3 + 0 + n*v**2.
2*v*(v + 1)**2/7
Factor -144*w**2 - 124*w**3 - w - 4 - 39*w - 100*w**3 - 128*w**4.
-4*(2*w + 1)**3*(4*w + 1)
Let v(x) be the first derivative of 64*x**5/5 - 72*x**4 + 388*x**3/3 - 72*x**2 + 16*x - 51. Factor v(p).
4*(p - 2)**2*(4*p - 1)**2
Let z(c) be the second derivative of -c**5/60 + c**4/12 - c**2/2 - 2*c. Let t(p) be the first derivative of z(p). Solve t(l) = 0 for l.
0, 2
Let p(m) = -3*m**3 + 7*m**2 - 8*m. Let o(q) = -48*q**3 + 111*q**2 - 129*q. Let f(v) = -2*o(v) + 33*p(v). Factor f(i).
-3*i*(i - 2)*(i - 1)
Let u(p) be the second derivative of p**4/6 - p**3 - 5*p. Suppose u(k) = 0. What is k?
0, 3
Let r = 28 + -20. Let q(s) = 2*s - 4. Let m be q(4). Find b, given that -2 - r*b**3 + m*b**2 + 14*b**2 - 12*b + 4 = 0.
1/4, 1
Solve -24*w**2 - 5*w**4 + 14*w**2 + 2*w**3 + 13*w**3 = 0.
0, 1, 2
Let b(o) be the f