t d(n) be the second derivative of z(n). Factor d(t).
2*t**2*(t - 1)**2/17
Let g(s) be the second derivative of -5*s**4/12 - 5*s**3/6 + 19*s. Suppose g(j) = 0. Calculate j.
-1, 0
Let u(r) be the first derivative of 1/6*r**3 + 4 - r**2 + 2*r. Factor u(f).
(f - 2)**2/2
Let o = 27 - 24. Let h(b) be the first derivative of o*b**2 + 1/2*b**4 + 2*b + 2*b**3 + 1. Find z, given that h(z) = 0.
-1
Factor -8/9 + 0*k + 2/9*k**2.
2*(k - 2)*(k + 2)/9
Let f(u) = -u**2 - 4*u + 8. Let r(j) = 4*j - 8. Let o(a) = -4*f(a) - 3*r(a). Suppose o(n) = 0. What is n?
-2, 1
Let b(d) be the first derivative of -1 - 1/24*d**6 + 3/10*d**5 + 0*d - 13/16*d**4 - 1/2*d**2 + d**3. Factor b(t).
-t*(t - 2)**2*(t - 1)**2/4
Let i(f) be the second derivative of f**7/7 - 2*f**6/3 + 6*f**5/5 - f**4 + f**3/3 + 6*f. Let i(d) = 0. What is d?
0, 1/3, 1
Let o(q) = q**3 + 11*q**2 + 4. Let v be o(-11). Let g be 3 - (-1*v)/(-4). Factor 0 - 1/3*n**3 + 2/3*n**g - 1/3*n.
-n*(n - 1)**2/3
Suppose -3*m - 2*x + 2 = 0, -3*m = m + 4*x - 4. Factor 0 + m*n - 3/5*n**4 - n**3 - 2/5*n**2.
-n**2*(n + 1)*(3*n + 2)/5
Let d(z) = z**4 + z**3 + 4*z**2 + 4*z. Let x(m) = -3*m**4 - 2*m**3 - 11*m**2 - 12*m. Let k(l) = -11*d(l) - 4*x(l). Determine o, given that k(o) = 0.
-1, 0, 2
Let g(i) = 2*i + 17. Let w be g(-12). Let p = -3 - w. Find f such that -f**3 - 1/3*f**5 + 0*f + 0 + 1/3*f**2 + f**p = 0.
0, 1
Let w(q) be the third derivative of q**5/20 - 3*q**4/8 + q**3 - q**2. Determine t, given that w(t) = 0.
1, 2
Solve -1/9*d**2 - 1/9*d + 0 = 0 for d.
-1, 0
Let v(b) = -2*b + 38. Let y be v(19). Let m(l) be the second derivative of 0*l**2 - 1/18*l**4 - l + y - 1/9*l**3. Factor m(n).
-2*n*(n + 1)/3
Suppose -80 = -3*z - 29. Suppose -5*t - r = -25, -r = 2*t - 6*r + z. Find j, given that 18*j**5 + 18*j**3 + 4*j**2 + 20*j**t + 14*j**3 + 22*j**4 + 4*j**2 = 0.
-1, -2/3, 0
Let f(b) be the second derivative of 2*b**6/25 + 111*b**5/100 + 117*b**4/20 + 27*b**3/2 + 81*b**2/10 - 7*b. Factor f(p).
3*(p + 3)**3*(4*p + 1)/5
Let z(l) = l**3 + l. Let h(d) = 0*d**2 - 2*d**2 - 3*d**2 + d**2 + 4 + 4*d + 8*d**3. Let y(j) = h(j) - 6*z(j). Factor y(s).
2*(s - 2)*(s - 1)*(s + 1)
Suppose 5*k - 2*u - 10 = 0, -5*k - u = u - 10. Determine c so that -4*c**k - 2/3*c**3 - 16/3 - 8*c = 0.
-2
Let d be (-2)/10 + 26/5. Solve o**d - o**4 - o**5 + o**5 = 0 for o.
0, 1
Factor -9/2*p**2 + 0 + 0*p**3 + 3/2*p**4 + 3*p.
3*p*(p - 1)**2*(p + 2)/2
Let c(q) be the first derivative of 2*q**3/9 + 7. Let c(z) = 0. What is z?
0
Suppose -3*f = -4*a + 2*f, 0 = -3*a - f. Let -2/3*r**4 - 4/3*r**3 + 0*r + a - 2/3*r**2 = 0. Calculate r.
-1, 0
Let z(l) = 2*l**2 + 2*l. Let v(c) = -c**5 + c**4 + 3*c**2 + 3*c. Let r(s) = 4*v(s) - 6*z(s). Determine g, given that r(g) = 0.
0, 1
Let r = -12 + 19. Let t(h) = -4*h**2 + 2*h - 1. Let l(n) = 9*n**2 - 4*n + 2. Let z(a) = r*t(a) + 3*l(a). Factor z(s).
-(s - 1)**2
Let z(n) = -25*n**2 - 10*n + 1. Let g(m) = -1. Let i(l) = -2*g(l) - z(l). Factor i(t).
(5*t + 1)**2
Let h(p) be the first derivative of 8*p**3/9 - 2*p**2/3 + p/6 + 30. Factor h(w).
(4*w - 1)**2/6
Factor -10*q**2 + 2*q**3 - 8*q**3 - 6*q + q + q**3.
-5*q*(q + 1)**2
Let m(b) be the second derivative of b**6/255 + b**5/170 - b**4/102 - b**3/51 + 22*b. Factor m(g).
2*g*(g - 1)*(g + 1)**2/17
Suppose -6 = -2*q + 2. Suppose -b + 4 - 2 = 0. Factor 0*l - 1/2*l**q + 0 + 0*l**b + 1/2*l**3.
-l**3*(l - 1)/2
Let j = 12/31 - -26/93. Factor -j + 2/3*l**2 + 0*l.
2*(l - 1)*(l + 1)/3
Let x(l) be the third derivative of l**8/112 - l**7/35 + 7*l**2. Find d, given that x(d) = 0.
0, 2
Determine g so that 8/11*g**2 + 2/11*g**4 + 10/11*g**3 + 0*g + 0 = 0.
-4, -1, 0
Let p(t) be the second derivative of t**6/150 - t**5/50 + t**3/15 - t**2/10 - 22*t. Suppose p(h) = 0. What is h?
-1, 1
Factor -t**5 - 8*t**3 + 13*t**3 - 4*t**3.
-t**3*(t - 1)*(t + 1)
Let c = 15 - 9. Let u(x) = -2*x**3 + 7*x**2 + 2*x. Let y = -8 + 1. Let w(f) = -2*f**3 + 6*f**2 + 2*f. Let q(m) = c*u(m) + y*w(m). Factor q(p).
2*p*(p - 1)*(p + 1)
Let m be 9 + (7 - 688/44). Determine l, given that 2/11*l**2 - 6/11 - m*l = 0.
-1, 3
Let q = 42 - 125/3. Suppose 1/3*l**4 - 1/3*l - 2/3*l**2 + 2/3*l**3 - q*l**5 + 1/3 = 0. Calculate l.
-1, 1
Let f(g) be the first derivative of -g**5/10 + g**4/6 + 8*g + 8. Let q(n) be the first derivative of f(n). Solve q(o) = 0 for o.
0, 1
Suppose -2*r + 2*y + 5 = -9, -5*r - y = -5. Factor o**2 + o**2 - 3*o**2 + 3*o**4 - r*o**4.
o**2*(o - 1)*(o + 1)
Let l(q) be the first derivative of 0*q - 1/2*q**2 - 1/3*q**3 - 1/60*q**5 - 1 + 1/8*q**4. Let g(p) be the second derivative of l(p). Factor g(t).
-(t - 2)*(t - 1)
Suppose 52 = -0*a + 4*a + 2*h, 2*a - 10 = -5*h. Let g be (-3 - -1) + a/3. Factor 2*w**3 - g*w**3 - w**2 + 4*w + w**4 - 3*w.
w*(w - 1)**2*(w + 1)
Let k(w) be the first derivative of 19*w**3 + 60*w**2 + 12*w - 26. Factor k(d).
3*(d + 2)*(19*d + 2)
Factor 1/4*j + 1/2 - 1/2*j**2 - 1/4*j**3.
-(j - 1)*(j + 1)*(j + 2)/4
Find b such that -3/7*b**3 + 0 + 4/7*b + 4/7*b**2 = 0.
-2/3, 0, 2
Let r be ((-10)/12 + 1)/((-23)/(-46)). Factor 0 + 2/3*m**3 - r*m**2 - 1/3*m**4 + 0*m.
-m**2*(m - 1)**2/3
Let v(j) be the first derivative of 10*j**6/3 + 7*j**5 - 15*j**4/4 - 55*j**3/3 - 25*j**2/2 - 10. Solve v(i) = 0.
-1, 0, 5/4
Suppose 0 = 2*a - 202 + 194. Determine f, given that 2*f - 1/2*f**a + 3/2*f**2 - f**3 - 2 = 0.
-2, 1
Let v(g) be the first derivative of 4*g**5/5 + g**4 - 4*g**3/3 - 2*g**2 + 7. Suppose v(o) = 0. Calculate o.
-1, 0, 1
Let j be (2/(-12))/(36/(-24)). Let g(a) be the second derivative of 1/63*a**7 + 1/15*a**5 + j*a**4 - 1/3*a**3 + 0 - 1/15*a**6 + 1/3*a**2 - a. Factor g(u).
2*(u - 1)**4*(u + 1)/3
Solve 0*g**4 + 0*g - 2/5*g**5 - 4/5*g**2 + 6/5*g**3 + 0 = 0.
-2, 0, 1
Let i = -98 - -98. Factor 2/5*z**2 + i - 2/5*z**4 - 1/5*z + 0*z**3 + 1/5*z**5.
z*(z - 1)**3*(z + 1)/5
Let t be 2 + -1 - (6 - 5). Let r = t - 0. Factor 2/9*d**3 + r*d**2 + 0 + 0*d - 2/9*d**5 + 0*d**4.
-2*d**3*(d - 1)*(d + 1)/9
Let v(j) be the second derivative of -j + 0*j**2 + 0 + 1/3*j**3 + 1/10*j**5 + 1/3*j**4. Factor v(w).
2*w*(w + 1)**2
Let k(c) = 0*c + 2 - 2*c - 2*c + 5*c**2. Let v be (0 - -3) + (-2)/2. Let t(j) = -4*j**2 + 4*j - 2. Let m(f) = v*k(f) + 3*t(f). Find y, given that m(y) = 0.
1
Let m(c) = -c**3 - c - 1. Let d(w) = w - 1. Let g = -13 + 18. Let b(t) = 3*t + 3. Let o(f) = g*d(f) + b(f). Let l(y) = 2*m(y) + o(y). Factor l(a).
-2*(a - 1)**2*(a + 2)
Let t(m) = -m**2 - 5*m + 1. Let i(q) = q - 2*q + 0*q. Let y(v) = -5*i(v) + t(v). Factor y(a).
-(a - 1)*(a + 1)
Let t(k) = k**4 - k**2 - 1. Let r(h) = -h**5 + 2*h**4 + 3*h**3 - 4*h - 4. Let m(z) = -5*r(z) + 20*t(z). Determine x so that m(x) = 0.
-2, 0, 1
Let l(m) be the second derivative of m**6/300 - m**5/30 + 2*m**4/15 - 4*m**3/15 - 2*m**2 + 4*m. Let n(q) be the first derivative of l(q). Factor n(h).
2*(h - 2)**2*(h - 1)/5
Let k(h) be the first derivative of -2 + 0*h**3 - 1/27*h**6 - 1/18*h**4 - 4/45*h**5 + 0*h + 0*h**2. What is i in k(i) = 0?
-1, 0
Let b(a) be the third derivative of a**6/120 - a**5/20 + a**4/8 - a**3/6 + a**2. Factor b(n).
(n - 1)**3
Let g(w) be the third derivative of 49*w**6/60 - 7*w**5/10 - 2*w**4 - 4*w**3/3 - 29*w**2. Factor g(p).
2*(p - 1)*(7*p + 2)**2
Let w = -31 - -33. Factor 1/3*y + 2/3 - 1/3*y**w.
-(y - 2)*(y + 1)/3
Factor -1/5*t**2 + 0 - 2/5*t.
-t*(t + 2)/5
Suppose 3*y - 3*r = 18, -8*y + 2*r = -3*y - 24. Suppose -4*u = -2*u + 4, -u - y = -j. Let 2*s**j - s**5 + 0*s**2 + 2*s**4 - 4*s**4 + s = 0. What is s?
-1, 0, 1
Let f(x) = -x**3 - 3*x**2 - 6*x - 8. Let b be f(-2). Let y(z) = -z. Let m be y(-3). Factor 2/7*p**2 + 2/7*p**5 + 6/7*p**m + b + 0*p + 6/7*p**4.
2*p**2*(p + 1)**3/7
Suppose 3*n - 4 = 2. Let o(i) be the first derivative of 0*i + 1/3*i**n - 2/9*i**3 - 2. Factor o(u).
-2*u*(u - 1)/3
Factor -1 - 5*t**2 + 8 + 13.
-5*(t - 2)*(t + 2)
Let m be (-4)/((-72)/(-39) + -2). Suppose -1 = -5*z + 3*q + m, -28 = -5*z + 2*q. Let 4*i**2 + i**5 + 3*i**4 - 9*i**4 + 2 + 4*i**3 + i**5 - z*i = 0. Calculate i.
-1, 1
Let q(c) be the third derivative of -1/420*c**7 + 0*c + 0*c**6 - c**2 + 0*c**4 + 0 + 0*c**3 + 0*c**5. Suppose q(d) = 0. Calculate d.
0
Let q(n) be the first derivative of n**3/24 + n**2/8 - 11. What is r in q(r) = 0?
-2, 0
Suppose -3*m + 2 = -2*m. Suppose 0*f + 94 = 4*f - 5*p, p = -m. Find n such that -4/3 + f*n**2 - 4/3*n = 0.
-2/9, 2/7
Let m(n) be the second derivative of 5*n**