15 + t**5/10 + t**4/6 - t**3/3 - t. Let q(v) = 0. Calculate v.
-1, 0, 1
Let j(l) be the second derivative of 1/2*l**5 + 0*l**3 + 4/15*l**6 + 1/3*l**4 + 1/21*l**7 + 0 - 3*l + 0*l**2. Find p such that j(p) = 0.
-2, -1, 0
Factor -4/15*v - 2/15*v**2 - 2/15.
-2*(v + 1)**2/15
Let m(p) = -3*p**4 + p**3 + p**2 - 3. Let t(l) = -19*l**4 + 5*l**3 + 7*l**2 - 17. Let u(s) = -34*m(s) + 6*t(s). Factor u(j).
-4*j**2*(j + 1)*(3*j - 2)
Let w(s) = -s**3 + 4*s**2 + 3. Let n be w(4). Let p(j) be the first derivative of 1/2*j**2 - 1/3*j**n - 1 + 0*j. Factor p(k).
-k*(k - 1)
Let u(m) be the second derivative of -m**6/120 + m**5/40 - m**4/48 - 17*m. Factor u(b).
-b**2*(b - 1)**2/4
Let b(y) = y**2 + 7*y + 6. Let g be b(-4). Let w be g*((-1)/(-3) + -1). Factor f**2 - 3*f**2 - 2*f**4 + w*f**3 + 0*f**4.
-2*f**2*(f - 1)**2
Factor 2/5*p**4 + 8/5*p**3 + 0*p + 0 + 8/5*p**2.
2*p**2*(p + 2)**2/5
Suppose -m - 3*x + 15 + 4 = 0, 3*m + 3*x = 27. Let n(c) = -c**3 + 6*c**2 - 4*c - 1. Let f be n(5). Let -f*t**3 - 5*t**m + 4*t**4 + 5*t**3 = 0. Calculate t.
0, 1
Let a = 50 + -35. Let b be 6/a*(-1 - -3). Factor b*o - 4/5*o**3 + 0 - 2/5*o**2 + 2/5*o**4.
2*o*(o - 2)*(o - 1)*(o + 1)/5
Let i be (8/20)/((-1)/(-10)). Let 5*o - o**i - 5*o - o**3 = 0. What is o?
-1, 0
Factor 7*q**3 + 0*q**3 - 4*q**3 + q**3 - 4*q - 2*q**4 + 2.
-2*(q - 1)**3*(q + 1)
Let d(a) be the second derivative of -a**4/42 - 10*a**3/7 - 225*a**2/7 - 65*a. Determine h so that d(h) = 0.
-15
Suppose -5*j = 5*w + 30, -4*j + j - 2 = -w. Let m be (0 - (-4)/j) + 7. Determine i, given that -i - m*i**2 + 2*i + 1 + 3*i**2 = 0.
-1/2, 1
Let d = -5 - -4. Let x be (5 + d)*1/2. Factor -1 + 5*w**4 + 3*w - 2*w**2 - w**4 + w**5 - x*w**3 - w**4 - 2*w**5.
-(w - 1)**4*(w + 1)
Let m(q) = -5*q**2 + 6*q + 5. Let w(z) = 9*z**2 - 12*z - 10. Let k(x) = 11*m(x) + 6*w(x). Factor k(u).
-(u + 1)*(u + 5)
Factor 3 + y**3 - 4*y + 4*y**2 + 2 - 9 + 3*y**3.
4*(y - 1)*(y + 1)**2
Factor 1/6*x**4 + 0 - 1/3*x**3 - 1/6*x**2 + 1/3*x.
x*(x - 2)*(x - 1)*(x + 1)/6
Suppose 4/5*j**5 + 8/5*j - 12/5*j**3 + 0 + 4/5*j**4 - 4/5*j**2 = 0. Calculate j.
-2, -1, 0, 1
Let a(c) = c**3 - 5*c**2 + 9*c - 5. Let y(d) = 4*d**2 - 8*d + 4. Let g(q) = 4*a(q) + 5*y(q). Suppose g(p) = 0. Calculate p.
-1, 0, 1
Factor 2*c**2 - 8 + 3*c**2 + 2*c - c**2 + 2*c.
4*(c - 1)*(c + 2)
Let b be (-4 - -3)/(((-9)/(-6))/(-1)). Factor 4/3 + 2/3*y - b*y**2.
-2*(y - 2)*(y + 1)/3
Let w(b) be the third derivative of b**9/272160 - b**8/90720 - b**7/11340 - b**5/60 + b**2. Let j(k) be the third derivative of w(k). What is d in j(d) = 0?
-1, 0, 2
Let p be 26/(-7) + (-8)/28. Let g(y) = 3*y**3 - 9*y**2 - 3*y + 4. Let o(i) = -i**3 + 4*i**2 + i - 2. Let z(v) = p*g(v) - 10*o(v). Find j such that z(j) = 0.
-2, -1, 1
Let u(n) be the first derivative of -2*n**5/65 - 5*n**4/26 - 6*n**3/13 - 7*n**2/13 - 4*n/13 + 3. Factor u(y).
-2*(y + 1)**3*(y + 2)/13
Let r = -28 + 85/3. Let z(d) be the second derivative of 0*d**2 + 0 - r*d**3 - 3/5*d**5 - d + 4/15*d**6 + 2/3*d**4 - 1/21*d**7. Factor z(k).
-2*k*(k - 1)**4
Let b(y) = 7*y**4 - 11*y**3 + 9*y**2 + 23*y. Let n(t) = -6*t**4 + 12*t**3 - 9*t**2 - 24*t. Let x(d) = 3*b(d) + 4*n(d). Factor x(g).
-3*g*(g - 3)**2*(g + 1)
Let f be -2 + -1 + (-261)/(-81). Determine u so that -2/9*u + 2/9*u**3 - 2/9*u**2 + f = 0.
-1, 1
Let f(a) be the first derivative of -a**4/26 - 4*a**3/13 + a**2/13 + 12*a/13 + 15. Factor f(r).
-2*(r - 1)*(r + 1)*(r + 6)/13
Suppose -15*i + 18*i = 15. Let q(m) be the first derivative of 0*m + 2/25*m**i - 1 - 1/5*m**2 + 2/5*m**3 - 3/10*m**4. Factor q(v).
2*v*(v - 1)**3/5
Suppose 5*m - 5 = -5*q, 7*q - 3*q - 12 = 4*m. Factor i**4 - q*i**2 + 2*i - 1 - 2*i + 2.
(i - 1)**2*(i + 1)**2
Let d(b) be the first derivative of -98/15*b**5 + 8/3*b + 10*b**3 - 28/3*b**2 + 2 + 14/3*b**4. Find l, given that d(l) = 0.
-1, 2/7, 1
Let n(l) = 7*l - 7. Let x = 9 - 0. Let u be n(x). Factor -2*v + u*v**2 + 4*v - 1 - 3.
2*(4*v - 1)*(7*v + 2)
Let x(t) be the first derivative of -t**4/24 - t**3/6 - t**2/4 + 5*t + 3. Let g(f) be the first derivative of x(f). Factor g(s).
-(s + 1)**2/2
Let u(l) be the first derivative of -22/15*l**3 + 2*l**5 - 12/5*l**2 - 4 + 3*l**4 + 8/5*l. Factor u(b).
2*(b + 1)**2*(5*b - 2)**2/5
Let k(g) be the third derivative of -5*g**8/336 + g**7/14 - g**6/12 + 4*g**2. Solve k(d) = 0.
0, 1, 2
Suppose -n + 5*b = 7*b - 12, 15 = 3*b. Solve -n*q**2 - 8/7 - 32/7*q = 0.
-2, -2/7
Determine a, given that 0*a + 0 - 3/8*a**4 + 0*a**2 - 3/4*a**3 = 0.
-2, 0
Suppose 0 = -4*n - 4*p, 2*n = 5*n - 3*p. Suppose 0*i + 0*i**2 + n + 1/2*i**4 - 1/2*i**3 = 0. What is i?
0, 1
Factor -33/5*g - 12/5 + 9/5*g**2.
3*(g - 4)*(3*g + 1)/5
Suppose 6*w**4 + 63*w**3 + w - 55*w**3 - 4*w**5 - 6*w**2 - 5*w = 0. What is w?
-1, -1/2, 0, 1, 2
Let c(v) be the first derivative of -v**3 + 0*v - 6 + 3*v + 2. Suppose c(g) = 0. Calculate g.
-1, 1
Suppose -2/11 - 4/11*r**5 + 8/11*r - 8/11*r**2 - 4/11*r**3 + 10/11*r**4 = 0. What is r?
-1, 1/2, 1
Suppose -6 = -2*j + 5*h - 2*h, -2*h = -4*j + 4. Let 2/7*c**2 + j*c - 2/7 = 0. What is c?
-1, 1
Suppose 7*p - 17 = -3. Suppose 7*q = 2*q + 5*x + 25, 0 = -2*q + 4*x + 12. Let 1/3*z**5 + 0*z**p + 0 + 1/3*z**3 + 0*z - 2/3*z**q = 0. What is z?
0, 1
Let f(b) be the second derivative of b**8/1680 - b**6/120 - b**5/60 - 3*b**3/2 - 9*b. Let a(w) be the second derivative of f(w). Factor a(s).
s*(s - 2)*(s + 1)**2
Factor 0 - 1/4*o**3 - 9*o + 3*o**2.
-o*(o - 6)**2/4
Let j be 0 + -4*1/(-2). Factor 0*o**2 + o - o - 2*o**j.
-2*o**2
Let t(c) = -9*c**4 + 2*c**3 + 2*c**2 - 2*c + 7. Let a = -2 + 5. Let f(j) = j - j**2 + 4*j**4 + 5*j - 3 - 5*j - j**3. Let p(y) = a*t(y) + 7*f(y). Solve p(i) = 0.
-1, 0, 1
Factor 1/2*a**3 + 1 + 2*a**2 + 5/2*a.
(a + 1)**2*(a + 2)/2
Let j = 19 + -14. Let h(f) be the second derivative of -1/30*f**6 + 1/12*f**4 - 3*f - 1/6*f**3 + 0*f**2 + 0 + 1/20*f**j. Factor h(l).
-l*(l - 1)**2*(l + 1)
Factor 0 + 2/3*q**3 + 2/9*q - 2/9*q**4 - 2/3*q**2.
-2*q*(q - 1)**3/9
Let x(d) be the third derivative of 0*d**4 + 0 + 2*d**2 + 8/735*d**7 - 2/105*d**6 - 1/588*d**8 + 0*d**3 + 0*d**5 + 0*d. Find o such that x(o) = 0.
0, 2
Let b be 1/(-4)*3*(-224)/252. Factor 4/3*t - b*t**2 + 0.
-2*t*(t - 2)/3
Let f(y) = y**2 + 4*y + 2. Let h be f(-4). Let n = h + 0. Factor 9/2*u**2 + 6*u + n.
(3*u + 2)**2/2
Let w(l) be the third derivative of 4*l**5/15 - l**4/2 - 2*l**3/3 - 9*l**2. Factor w(u).
4*(u - 1)*(4*u + 1)
Factor -14/5*j - 2*j**3 - 22/5*j**2 - 2/5.
-2*(j + 1)**2*(5*j + 1)/5
Let m(h) = -50*h**2 + 68*h - 8. Let p(s) = -s**2. Let w(k) = m(k) + 10*p(k). Let w(q) = 0. What is q?
2/15, 1
Let l = -7 - -29/4. Let 1/4*u**4 - 1 - 2*u - l*u**5 - 1/4*u**2 + 5/4*u**3 = 0. Calculate u.
-1, 2
Suppose -24 = 2*i - 5*i. Let o = i - 0. Factor 0*u - o*u**5 + 0 - 1/2*u**2 - 4*u**4 + 7/2*u**3.
-u**2*(u + 1)*(4*u - 1)**2/2
Let b(t) be the third derivative of t**8/840 + t**7/1050 - t**6/50 + t**5/30 + t**4/60 - t**3/10 + t**2. Determine w so that b(w) = 0.
-3, -1/2, 1
Suppose t - 3*t + 6 = 0. Let w(z) be the second derivative of 7/12*z**3 - 1/6*z**4 + 1/2*z**2 + t*z + 0. Find n, given that w(n) = 0.
-1/4, 2
Determine m, given that -2/13*m**3 + 0 - 2/13*m**5 + 4/13*m - 6/13*m**4 + 6/13*m**2 = 0.
-2, -1, 0, 1
Suppose 0 + 28/3*n**3 - 8/3*n + 20/3*n**2 = 0. What is n?
-1, 0, 2/7
Let y be (1/2 - 0)*0. Suppose 4*m + 4 + 28 = 5*z, 0 = -z + 5*m + 19. Let 0*q + 4/5*q**z + y + q**3 + 1/5*q**2 = 0. What is q?
-1, -1/4, 0
Let u = 87/140 - 4/7. Let m(f) be the third derivative of 2*f**2 + 0*f + 0 + u*f**5 + 1/210*f**7 - 1/40*f**6 - 1/24*f**4 + 0*f**3. Factor m(p).
p*(p - 1)**3
Let u = 74 + -443/6. Let a(b) be the second derivative of 1/12*b**4 + u*b**3 + 0 + 0*b**2 - b. Factor a(w).
w*(w + 1)
Let g(b) be the first derivative of b**5/60 - b**4/24 - b**3/3 - b**2/2 - 2. Let i(h) be the second derivative of g(h). Factor i(y).
(y - 2)*(y + 1)
Factor -2/7 + 0*v**2 + 4/7*v**3 - 4/7*v + 2/7*v**4.
2*(v - 1)*(v + 1)**3/7
Let u(b) be the first derivative of -b**4 + 4*b**3/3 + 10*b**2 + 12*b - 34. Factor u(i).
-4*(i - 3)*(i + 1)**2
Let b(t) = t**3 + t**2 + 1. Let r(k) = 14*k**3 + 20*k**2 + 8*k + 12. Suppose 2 + 1 = -3*x. Let a(u) = x*r(u) + 12*b(u). Determine d so that a(d) = 0.
-2, 0
Let u be -5 + 15*(-67)/(-21). Find c such that -284/7*c**2 + u*c**4 - 16/7 + 250/7*c**5 - 120/7*c - 130/7*c**3 = 0.
-1, -2/5, 1
Let l(k) be the first derivative of -k