he first derivative of 3*t**5/5 + 3*t**4/4 - 5. Factor n(z).
3*z**3*(z + 1)
Suppose 8 = k + 3*k. Let z be (k/3)/(16/18). Determine v so that -1/4 + 1/4*v**3 - 3/4*v**2 + z*v = 0.
1
Let v(z) = 15*z**3 - 55*z**2 + 42*z + 22. Let w(p) = 75*p**3 - 275*p**2 + 211*p + 111. Let o(h) = -11*v(h) + 2*w(h). Determine t, given that o(t) = 0.
-1/3, 2
Let f(o) be the first derivative of 1/3*o**2 - 3 - 2/9*o**3 + 0*o. Factor f(w).
-2*w*(w - 1)/3
Suppose 0 = 3*b - 2*o - 15, 4*b + 5*o + 2 = 22. Let d be (-24)/84 - 32/(-14). Suppose -d*i**5 + i**3 - i**5 + 2*i**b = 0. What is i?
-1, 0, 1
Suppose 4*r + 6*p = p + 35, -4*r = 4*p - 32. Let t(d) be the second derivative of 0*d**2 + 0 + d + 1/50*d**r - 1/30*d**4 + 0*d**3. Factor t(k).
2*k**2*(k - 1)/5
Let n(c) be the second derivative of -c**5/45 + 4*c**4/27 - 8*c**3/27 - c. Find j, given that n(j) = 0.
0, 2
Let p = -56 + 61. Let b(a) be the second derivative of 0 - 4*a + 1/50*a**p + 1/15*a**4 - 1/15*a**3 - 2/5*a**2. Factor b(u).
2*(u - 1)*(u + 1)*(u + 2)/5
Let a(j) be the first derivative of -j**6/180 + j**5/30 - j**4/12 + j**3/3 + 1. Let g(f) be the third derivative of a(f). Factor g(c).
-2*(c - 1)**2
Let b(s) be the first derivative of -s**6/6 + 2*s**5/5 - 2*s**3/3 + s**2/2 - 5. Factor b(v).
-v*(v - 1)**3*(v + 1)
Let r(o) = o**3 + 2*o**2 + 6*o + 5. Let q be r(-1). Factor 0 + q*z - 2/7*z**2.
-2*z**2/7
Let f(l) be the third derivative of 2*l**7/105 - l**6/30 - l**5/5 + l**4/6 + 4*l**3/3 + 11*l**2. Factor f(v).
4*(v - 2)*(v - 1)*(v + 1)**2
Let q be (3 - (-1 - 0))/(415/83). Suppose 5*t + 4 = 2*o, -3*o + 6 = 2*t - 0*t. Factor q*h**3 - 4/5*h - 2/5 + 2/5*h**4 + t*h**2.
2*(h - 1)*(h + 1)**3/5
Let p be (2/4)/(4/928). Let t be p/10 - (-4)/10. Solve -3 - 1 + 2 - 18*n**2 + t*n = 0.
1/3
Let g be 2 - (1 + -2*3/6). What is z in 4/3 + 2*z - 14/3*z**2 - g*z**3 + 10/3*z**4 = 0?
-1, -2/5, 1
Suppose 36/7*i**2 - 16/7*i**3 - 32/7*i + 10/7 + 2/7*i**4 = 0. What is i?
1, 5
Let r = 145/14 + -141/14. Let 0 - r*s**3 + 0*s + 2/7*s**2 = 0. Calculate s.
0, 1
Let j = 8 - 8. Suppose c - 3 = -j*c. Factor 0 + y**4 + 1/2*y**5 - y**2 - 1/2*y + 0*y**c.
y*(y - 1)*(y + 1)**3/2
Suppose 0 = -2*p - p + 9. Let h(b) be the first derivative of -1/3*b + 1/3*b**2 + 1 + 1/3*b**p. Solve h(v) = 0 for v.
-1, 1/3
Factor -3/7*k**5 - 12/7*k**4 + 0 - 15/7*k**3 - 6/7*k**2 + 0*k.
-3*k**2*(k + 1)**2*(k + 2)/7
Let w(x) be the second derivative of -5*x**4/6 + 5*x**3/2 + 5*x**2 + 4*x. Factor w(s).
-5*(s - 2)*(2*s + 1)
Let j(v) be the second derivative of -v**6/360 - v**5/120 - v**3/2 + 3*v. Let f(r) be the second derivative of j(r). Determine d, given that f(d) = 0.
-1, 0
Let v(j) = j**2 - 3*j - 1. Let w be (20/(-6) + 0)*3. Let m = w + 14. Let z(l) = -l**2 + 4*l + 1. Let b(c) = m*v(c) + 3*z(c). Factor b(q).
(q - 1)*(q + 1)
Suppose -4*d = 16, -2*d - 2 = -0*l + 2*l. What is x in -9/2*x**2 + 0 - 3/2*x + 6*x**4 + 0*x**l = 0?
-1/2, 0, 1
Factor 5 - 2*k + 2*k**2 - 2 - 3.
2*k*(k - 1)
Suppose 6 = 2*f - 0. Find i such that 56*i**2 - 2*i**f - i**4 + 7*i**4 - 60*i**2 = 0.
-2/3, 0, 1
Let r(o) be the second derivative of -o**4/6 + 2*o**3/3 - o**2 + 20*o. Factor r(x).
-2*(x - 1)**2
Let b(a) = -7*a**2 + 9*a - 5. Let g be -1*(0 + (-9 - -2)). Let q(s) = 25*s**2 - 3*s**2 + g*s + 16 - 16*s - 19*s. Let c(z) = -16*b(z) - 5*q(z). Factor c(i).
2*i*(i - 2)
Suppose 113*u - 20 = 108*u. Factor -8/9*s**u + 0 - 2/9*s - 8/9*s**2 - 2/9*s**5 - 4/3*s**3.
-2*s*(s + 1)**4/9
Let i be 18/14 - 8/8. Let f be 3 + (52/12)/((-7)/3). Factor f*q**3 - i*q**4 + 0 - 8/7*q**2 + 0*q.
-2*q**2*(q - 2)**2/7
Let p(g) be the third derivative of -g**5/30 - g**4/4 - 2*g**3/3 - 4*g**2. Let w(i) = -i**2 - 3*i - 2. Let j(q) = 3*p(q) - 5*w(q). Suppose j(c) = 0. What is c?
-2, -1
Let f(y) be the third derivative of -y**8/1176 + y**7/735 + y**6/140 - y**5/210 - y**4/42 + 17*y**2. Let f(q) = 0. What is q?
-1, 0, 1, 2
Let g be (-2)/(-6)*-3 - -4. Let f = 8 - 3. Factor d**5 - 2*d + d**3 + 2*d**4 - 13*d**g + 6*d**4 + 8*d**2 - 3*d**f.
-2*d*(d - 1)**4
Let g(f) be the second derivative of 0 + 1/3*f**6 - 2/21*f**7 - 5/48*f**4 - 5/16*f**5 + 5/24*f**3 + 7*f + 1/8*f**2. Suppose g(t) = 0. What is t?
-1/4, 1
Factor 17*y + 12 + y**2 - 27*y - 4*y**2 + 19*y.
-3*(y - 4)*(y + 1)
Suppose -2*s = -5*s. Solve -2 + 0 + 4 - 2*n**2 + s*n**2 = 0 for n.
-1, 1
Suppose 0 + 1/3*t - 1/3*t**2 = 0. What is t?
0, 1
Let h(j) be the third derivative of j**8/224 + j**7/140 - j**6/40 - j**5/20 + j**4/16 + j**3/4 - 10*j**2. Let h(k) = 0. What is k?
-1, 1
Let r(u) = -u**3 + 4*u**2 + 4*u + 7. Let g be r(5). Let i(y) be the first derivative of -2*y**3 - 5 + y**3 - 2*y + 5*y + 3*y**g + 2*y**3. Factor i(z).
3*(z + 1)**2
Factor -98 - 1/2*m**2 - 14*m.
-(m + 14)**2/2
Let p(v) = 20*v**3 + 23*v**2 - 14*v + 17. Suppose 4*m = 2*m - 34. Let u(r) = 7*r**3 + 8*r**2 - 5*r + 6. Let h(z) = m*u(z) + 6*p(z). Factor h(o).
o*(o + 1)**2
Let p(s) be the second derivative of -s**5/10 + s**4/3 - 6*s. Find d such that p(d) = 0.
0, 2
Let r(t) be the third derivative of -t**7/735 + t**6/420 + t**5/210 - t**4/84 + 2*t**2. Factor r(h).
-2*h*(h - 1)**2*(h + 1)/7
Let r(z) = -7*z**2 - 2*z. Let b(j) = -20*j**2 - 6*j. Let k(l) = 6*b(l) - 17*r(l). Let q(n) = 2*n**2 + 4*n. Let g(d) = -5*k(d) - 2*q(d). Solve g(v) = 0.
-2, 0
Let v = 87/2 - 43. Find z, given that 0 + 0*z**3 - 1/2*z**4 + 0*z + v*z**2 = 0.
-1, 0, 1
Suppose 3*c + 3*b - 12 = 0, -2*c + 4*b = -c + 6. Factor -u + 7*u - u - c - u**3 - 2*u.
-(u - 1)**2*(u + 2)
Suppose -4*s + 8 = 0, -3*w - 3*s + 49 = -26. Factor w - 3*i**2 - 26 - 6*i + 0*i**2.
-3*(i + 1)**2
Let q(l) be the first derivative of 0*l**2 + 0*l**4 + 0*l**3 + 0*l + 0*l**5 + 1 - 1/9*l**6. Solve q(r) = 0 for r.
0
Let c be (-28)/(-33) + (-7 - (-525)/77). Factor 1/3*m**2 + 0 + c*m**3 + 1/3*m**4 + 0*m.
m**2*(m + 1)**2/3
Let q = -38 - -40. Let j(o) be the first derivative of -4/7*o + 3/7*o**2 - 2/21*o**3 - q. Let j(r) = 0. What is r?
1, 2
Let d(l) be the first derivative of -2*l**5/75 + 2*l**3/45 + 14. Factor d(m).
-2*m**2*(m - 1)*(m + 1)/15
Let d(l) be the second derivative of 0*l**2 + 1/75*l**6 + 0 + 1/10*l**4 + 1/15*l**3 + l + 3/50*l**5. Determine t so that d(t) = 0.
-1, 0
Let l be (-2)/(-5 + 3)*2. Factor 3*n**4 + 0*n**l + 0*n + 0 - 3/2*n**3 - 3/2*n**5.
-3*n**3*(n - 1)**2/2
Let n(j) = j**2 - 19*j - 15. Let x be n(20). Let 1/2*k**2 - 5/2*k**3 + 2 + 1/2*k**x + 4*k - 1/2*k**4 = 0. Calculate k.
-1, 2
Let y = -18 - -22. Suppose h = -h + y. Determine s so that -2/7 - 2/7*s**h - 4/7*s = 0.
-1
Let b be 22*(-3)/6 + 3. Let r(w) = 3*w**4 - 11*w**2 + 8*w - 8. Let p(h) = -2*h**4 + 7*h**2 - 5*h + 5. Let n(a) = b*p(a) - 5*r(a). Let n(k) = 0. Calculate k.
-1, 0, 1
Let b be (-418)/(-88) - 2/(-8). Factor 0*j + 1/2*j**b + 0 - 3/2*j**4 - 1/2*j**2 + 3/2*j**3.
j**2*(j - 1)**3/2
Let q(m) be the third derivative of -m**8/1176 - m**7/245 - m**6/210 + m**5/105 + m**4/28 + m**3/21 + 12*m**2. Factor q(d).
-2*(d - 1)*(d + 1)**4/7
Let w(c) be the first derivative of 2*c**3/15 - 4*c**2/5 + 8*c/5 + 9. Solve w(y) = 0 for y.
2
Factor 0 + 24/5*q + 3/5*q**4 - 9/5*q**3 - 18/5*q**2.
3*q*(q - 4)*(q - 1)*(q + 2)/5
Let t(j) be the first derivative of 2/35*j**5 + 1/7*j**4 + 0*j**2 - 8 + 2/21*j**3 + 0*j. Find z such that t(z) = 0.
-1, 0
Let f(s) = 12*s**2 + 32*s + 18. Let i(a) = 24*a**2 + 64*a + 37. Let r(l) = -5*f(l) + 2*i(l). Solve r(o) = 0 for o.
-2, -2/3
Factor -20/3 - 25/3*r**3 + 20*r - 5*r**2.
-5*(r - 1)*(r + 2)*(5*r - 2)/3
Let j be -1*1 + -3 + 25. Let g = j + -19. Factor 2/3*v**3 + 0 + 4/3*v**4 + 0*v + 2/3*v**5 + 0*v**g.
2*v**3*(v + 1)**2/3
Let s be (0/(-3) + -1)*3. Let v be s/2*(-4)/27. Find i, given that -2/9 - 4/9*i - v*i**2 = 0.
-1
Let m = -4111/9 + 457. Solve -8/9 + 0*z + m*z**2 = 0 for z.
-2, 2
Let b = -1592/3 + 531. Suppose b*r**5 - 1/3*r**2 + 0 + 1/3*r**4 + 0*r - 1/3*r**3 = 0. What is r?
-1, 0, 1
Let s(w) be the second derivative of 3/10*w**5 - 9/10*w**6 + 0*w**4 + 0 + 0*w**2 + w + 0*w**3 + 1/2*w**7. Factor s(u).
3*u**3*(u - 1)*(7*u - 2)
Let w = 2387/150420 - -2/2507. Let j(m) be the third derivative of 0*m + 0 + 0*m**3 + 1/12*m**4 + 3*m**2 + w*m**6 - 1/15*m**5. Factor j(t).
2*t*(t - 1)**2
Let p(y) = -3*y + 0 - y**4 + 0*y**4 - y**3 - 1 + 4*y. Let j(g) = g**5 + g**3 - g + 1. Let m(c) = -j(c) - p(c). Factor m(a).
-a**4*(a - 1)
Let y(c) = -11*c**2 - 87*c + 8. Let a be y(-8). Let r be -2 - -1 - 14/(-8). Factor a - 1/4*i**3 + r*i