5) + -3. Let 0*l + u*l**2 + 0 = 0. What is l?
0
Suppose 20/3*n**3 + 0 - 8/3*n + 4*n**2 - 8*n**4 = 0. Calculate n.
-2/3, 0, 1/2, 1
Let q(i) be the second derivative of 1/3*i**3 + 0 - 1/18*i**4 - 2/3*i**2 + i. Factor q(d).
-2*(d - 2)*(d - 1)/3
Let r be 3/4 + 2/8. Let z = 2 + r. Factor 6/5*p**2 + 6/5*p**z + 0 + 2/5*p + 2/5*p**4.
2*p*(p + 1)**3/5
Suppose -5*s - 9 + 19 = 0. Let v(o) be the first derivative of 1 + 0*o + 7/12*o**4 + 5/9*o**3 - 1/3*o**s. Determine w so that v(w) = 0.
-1, 0, 2/7
Let t(b) be the third derivative of -b**5/80 - b**4/96 + b**3/12 - 70*b**2. Factor t(u).
-(u + 1)*(3*u - 2)/4
Factor -2/7*o**2 + 0 - 1/7*o**3 - 1/7*o.
-o*(o + 1)**2/7
Let b(t) be the first derivative of 2*t**5/5 - 2*t**3 + 2*t**2 + 4. Find m, given that b(m) = 0.
-2, 0, 1
Let s(w) = -w**5 - w**4 - w**3 + w**2 + w + 1. Let r(m) = 16*m**5 + 10*m**4 - 11*m**3 + 5*m**2 + 5*m + 5. Let d(p) = -r(p) + 5*s(p). Factor d(f).
-3*f**3*(f + 1)*(7*f - 2)
Let v be 4/10*((-570)/(-24))/19. Factor 1/4*h + 0 + v*h**4 + h**2 + 5/4*h**3.
h*(h + 1)**2*(2*h + 1)/4
Let n(m) be the second derivative of 0 - 3/2*m**3 - m - m**2 - 7/12*m**4. Factor n(d).
-(d + 1)*(7*d + 2)
Let f(i) = -4*i**2 - 16*i - 3. Let y(l) = -2*l**2 - 8*l - 2. Let p(j) = -6*f(j) + 13*y(j). What is k in p(k) = 0?
-2
Let t(i) be the first derivative of -34*i**2 + 3 - 2*i + 81*i**3 + 14*i - 20*i**2. Let t(b) = 0. What is b?
2/9
Let h be (3/(-6))/((-1)/16). Let a be h/(-12)*(-2 - 4). Find t such that 2/3*t**a + 0 + 2*t**2 - 2/3*t - 2*t**3 = 0.
0, 1
Let -4/9*q**4 + 0*q**3 - 4/9 + 0*q + 8/9*q**2 = 0. What is q?
-1, 1
Let l(v) be the second derivative of v**7/42 - 7*v**6/30 + 9*v**5/10 - 5*v**4/3 + 4*v**3/3 + 4*v. Factor l(p).
p*(p - 2)**3*(p - 1)
Let r be 4/(-1) - (-10 + 10). Let b be (-3 - 3 - r) + 4. Solve 0*a + 0 + 1/2*a**3 + 1/2*a**b = 0 for a.
-1, 0
Let b = -97/2 - -197/4. Solve b*s**2 + 0 - 3/4*s = 0 for s.
0, 1
Suppose -v - 2*v = -4*g - 20, 2*v + 2*g + 10 = 0. Factor -2/7*q**5 - 24/7*q**4 - 216/7*q**2 + v - 108/7*q**3 - 162/7*q.
-2*q*(q + 3)**4/7
Let g(a) be the second derivative of -2*a**6 + 67*a**5/10 - 7*a**4 + a**3 + 2*a**2 + 2*a - 5. Suppose g(n) = 0. Calculate n.
-1/6, 2/5, 1
Suppose -34 = -3*o + 38. Factor 3*i**2 - 9*i**4 - 21*i**2 - 3 + o*i**3 + 6.
-3*(i - 1)**3*(3*i + 1)
Factor 88*s - 76*s + 4*s**2 - s**2.
3*s*(s + 4)
Let y(v) be the second derivative of -v**6/1980 - v**5/220 - 2*v**3/3 - 3*v. Let j(b) be the second derivative of y(b). Determine t, given that j(t) = 0.
-3, 0
Let h be (-76)/(-10) - (-9)/(-15) - 2. Let b(s) be the third derivative of 0 - 1/12*s**4 - 1/60*s**h + 0*s - 2*s**2 - 1/6*s**3. Factor b(o).
-(o + 1)**2
Suppose -5*y = -4*o - 16, -3*o - 16 = 4*y + 27. Let a = 11 + o. Factor 1/5*v**3 + 1/5*v + 2/5*v**a + 0.
v*(v + 1)**2/5
Suppose -a = -2*k + 7, 0*a - a = 5*k - 14. Suppose -2*j + k*j = 2. Factor 3*m**3 + 2*m**2 + m**3 + 2*m**4 + 0*m**j.
2*m**2*(m + 1)**2
Let k(v) be the first derivative of -1/14*v**4 + 1/7*v**2 - 2/21*v**3 - 2 + 2/7*v. What is s in k(s) = 0?
-1, 1
Let b(m) be the third derivative of -1/8*m**4 + 0 - 1/10*m**5 + 0*m - 5*m**2 + m**3 + 1/40*m**6. Factor b(j).
3*(j - 2)*(j - 1)*(j + 1)
Factor 6 + 9*v**2 + 42*v - 94*v + 37*v.
3*(v - 1)*(3*v - 2)
Let a(s) be the first derivative of -2*s**5/25 + s**4/2 - 14*s**3/15 + 3*s**2/5 + 3. Find c such that a(c) = 0.
0, 1, 3
Let t be 1 + -2 + 1 + 0. Suppose 16/3*m**4 + 0*m + 10/3*m**5 + 2/3*m**3 + t - 4/3*m**2 = 0. Calculate m.
-1, 0, 2/5
Let w be (-10)/(-12) - ((-25)/30)/(-5). Suppose 0 + 2/3*k + w*k**2 = 0. What is k?
-1, 0
Let o(p) be the second derivative of p**8/4200 + p**7/1050 + p**6/900 + p**3/2 + 2*p. Let z(m) be the second derivative of o(m). Factor z(u).
2*u**2*(u + 1)**2/5
Suppose -5*i = i - 12. Factor -3*r**i - 12/5 + 24/5*r + 3/5*r**3.
3*(r - 2)**2*(r - 1)/5
Let b(h) be the second derivative of 0 - 1/231*h**7 + 0*h**3 + 0*h**2 - 1/55*h**6 + 2*h - 1/66*h**4 - 3/110*h**5. Factor b(z).
-2*z**2*(z + 1)**3/11
Let m(w) be the second derivative of w**4/4 - 3*w**3/2 - 6*w**2 - 11*w. Factor m(q).
3*(q - 4)*(q + 1)
Let c(v) be the second derivative of v**6/45 - 7*v**5/15 + 2*v**4 - 34*v**3/9 + 11*v**2/3 + 17*v. Factor c(k).
2*(k - 11)*(k - 1)**3/3
Let x = -79 - -83. Let b(r) be the second derivative of 0 + 0*r**2 - 1/12*r**3 + 1/6*r**x + 2*r. Let b(a) = 0. What is a?
0, 1/4
Let t be 371/3 + (-14 - -11). Let a = 122 - t. Suppose -1/3*r**2 + a*r - 4/3 = 0. What is r?
2
Let c = -4 + 6. Factor -24*v + 5 - 19*v**2 - c*v**3 - 21 + 7*v**2.
-2*(v + 2)**3
Suppose -4 = -2*b, 0 = a + 5*b - 5 - 8. Determine h so that -9*h**a + h**5 - 4*h**5 - 5*h**4 + 5*h**2 + 12*h**4 - h + h**5 = 0.
0, 1/2, 1
Factor 3*s + s**2 + 36*s**3 + 34*s**2 + s - 11*s**2.
4*s*(3*s + 1)**2
Let z be 4*((-27)/(-4))/9. Let r(y) be the first derivative of 1/16*y**4 + 0*y**2 + 1/12*y**3 - 1/24*y**6 + 0*y - 1/20*y**5 - z. Find x, given that r(x) = 0.
-1, 0, 1
Let u(d) be the second derivative of d**4/3 + 2*d**3/3 + 12*d. Suppose u(f) = 0. What is f?
-1, 0
Let z(l) = 3 + 0 + 10 - l. Let s be z(9). Suppose 3/2*h**3 + 1/2*h + 0 + 3/2*h**2 + 1/2*h**s = 0. What is h?
-1, 0
Let g = 13 + -11. Factor -6/5*h**5 - 22/5*h**4 + 0 - 6*h**3 - 4/5*h - 18/5*h**g.
-2*h*(h + 1)**3*(3*h + 2)/5
Let y be (-8)/(-8) + 1 + 3. Let b(u) be the third derivative of -1/270*u**y + 0 - 1/108*u**4 + 0*u + 0*u**3 - 2*u**2. Let b(i) = 0. Calculate i.
-1, 0
Let z be 19/42 + 2/(-12). Let r be 42/(-56)*(-8)/21. Solve -4/7*u + r*u**2 + z = 0.
1
Let a be 0 + (-3)/(27/(-6)). Let c(f) be the third derivative of a*f**3 + 0 - f**2 - 1/12*f**5 + 1/3*f**4 + 0*f. Factor c(n).
-(n - 2)*(5*n + 2)
Let l be (-1)/(4 + (-85)/20). Factor 1/4*c + 0 + 1/4*c**5 + 3/2*c**3 - c**2 - c**l.
c*(c - 1)**4/4
Let p = 37 - 31. Suppose -p = 2*k + 4*j, 4*k + 3*j + 0*j = 3. Let 10/7*x**k + 18/7*x**2 + 4/7 + 2*x + 2/7*x**4 = 0. What is x?
-2, -1
Let n(p) be the second derivative of p**9/10584 - p**8/5880 - p**7/2940 + p**6/1260 + p**3/2 - 2*p. Let s(r) be the second derivative of n(r). Factor s(y).
2*y**2*(y - 1)**2*(y + 1)/7
Suppose 5 = 5*a, 5*t - 48 = 4*a - 2*a. Suppose 10 + t = 5*x. Solve 4*q + q**x + 0*q**3 - 1 - 6*q + 2*q**3 = 0 for q.
-1, 1
Suppose 5*r - r - 8 = 0. Factor 4*h**3 - 2*h - r*h**5 - 2*h**3 - 2*h**2 + 2*h + 2*h**4.
-2*h**2*(h - 1)**2*(h + 1)
Let t(v) be the third derivative of -v**6/30 - 11*v**5/15 - 35*v**4/6 - 50*v**3/3 + 26*v**2. Let t(h) = 0. Calculate h.
-5, -1
Let j(x) = x - 6. Let i be j(8). Let k be ((-9)/(-15) - 0)*5. Factor k*m - 2*m + 2*m**i + m.
2*m*(m + 1)
Let -4/3*n + 8/3*n**3 + 4/3*n**4 - 4/3*n**5 + 4/3 - 8/3*n**2 = 0. Calculate n.
-1, 1
Suppose 0 = -0*x + x - 1, -q = 3*x - 15. Suppose 2*b + q = 5*g - 0, -g - 5*b - 3 = 0. Factor 3*k - 4*k**g + k**3 - k - 2 + 3*k.
(k - 2)*(k - 1)**2
Suppose 4*j - 6 = 5*d, -2*j + 12 = -4*d + 3*j. Let v(w) be the first derivative of 1/12*w**4 + 0*w**d + 0*w + 2 + 1/9*w**3. Let v(b) = 0. What is b?
-1, 0
Let u(t) be the first derivative of 4*t**3/3 + 4*t**2 + 5. Factor u(g).
4*g*(g + 2)
Suppose -2*o + 6 = -0*o + 5*w, 4*o = -5*w + 12. Let y be (-2)/(-3) - (-4)/o. Suppose y*i**2 + 0*i + i - 3*i = 0. What is i?
0, 1
Let j(v) = -v**2 + 8*v - 3. Let o be j(7). Let b(i) be the first derivative of -1/9*i**3 + 0*i**2 + 2 - 1/12*i**o + 0*i. Solve b(a) = 0 for a.
-1, 0
Let i(w) be the second derivative of w**6/120 - w**5/40 - w**4/4 - w**3/2 - 2*w. Let l(b) be the second derivative of i(b). Find c, given that l(c) = 0.
-1, 2
What is l in 2/3*l**5 + 0*l**2 + 0*l**4 - 4/3*l**3 + 0 + 2/3*l = 0?
-1, 0, 1
Suppose 0 - 1/2*k**2 + 0*k = 0. Calculate k.
0
Let d = -68 + 48. Let u be (-2)/(-10) + (-56)/d. Factor 4*f + 2*f**2 + 13 - 13 - 2*f**u.
-2*f*(f - 2)*(f + 1)
Let z = 2 + 0. Let u be (z/(-4) + 0)*-4. Suppose 0*q - q**u + q + 0*q = 0. Calculate q.
0, 1
Let d be 4/10*5*(-5)/(-40). Factor -1/4*a + 1/4*a**2 + 1/4*a**3 - d.
(a - 1)*(a + 1)**2/4
Let s(o) be the second derivative of -o**5/40 - o**4/12 + o**3/12 + o**2/2 - 71*o. Find y such that s(y) = 0.
-2, -1, 1
Let a(d) = 8*d**2 - 5*d - 6. Let w(z) = -z**2 + z + 1. Let q(m) = -3*a(m) - 21*w(m). Let q(y) = 0. Calculate y.
-1
Let w = -17 - -17. Let l(a) be the second derivative of 2*a**2 + 2*a - 5/3*a**3 + 1/2*a**4 + w. Factor l(j).
2*(j - 1)*(3*j - 2)
Let i(c) be the third derivative of c**9/1512 - c**7/210 + c**5/60 + c**3/6 + 2*c**2. Let m(p) be the