t derivative of -2*v**5/25 + 3*v**4/10 - 4*v**3/15 - 3. Determine b, given that x(b) = 0.
0, 1, 2
Suppose -1 = q - y, q + 2*y = -2*y + 14. Let f(i) be the third derivative of 1/12*i**5 + 3*i**q + 0 - 1/6*i**3 + 1/6*i**4 + 0*i. Factor f(x).
(x + 1)*(5*x - 1)
Let n(g) = 3*g**5 + 40*g**4 + 33*g**3 - 13*g**2 - 43*g - 27. Let z(l) = l**5 + 20*l**4 + 16*l**3 - 6*l**2 - 21*l - 14. Let k(j) = -4*n(j) + 7*z(j). Factor k(x).
-5*(x - 1)*(x + 1)**3*(x + 2)
Factor 1/4*b**2 + 0 - 3/4*b.
b*(b - 3)/4
Let l(u) be the first derivative of -u - 2 + u**2 - 1/3*u**3. Find q such that l(q) = 0.
1
Find p, given that 0*p + 15/7*p**4 + 0 + 6/7*p**2 - 3*p**3 = 0.
0, 2/5, 1
Factor -26 + 3*i + 0*i + i**3 + 3*i**2 + 23 - 4*i**3.
-3*(i - 1)**2*(i + 1)
Let w be (-1)/(-2) - (-42)/(-196). Factor 2/7*r**3 - 2/7*r + 2/7*r**4 + 0 - w*r**2.
2*r*(r - 1)*(r + 1)**2/7
Let l be 156/63*3 - 7. Solve 3/7*u**2 - l*u + 0 = 0 for u.
0, 1
Let d be (1/(-2))/((-3)/(-42)). Let n = 9 + d. Factor -4/9*c + 26/9*c**4 - 2/9*c**n + 0 + 10/9*c**5 + 2*c**3.
2*c*(c + 1)**3*(5*c - 2)/9
Let x(z) be the second derivative of -z**4/4 + 3*z**3/2 - 3*z**2 - 8*z. Solve x(v) = 0 for v.
1, 2
Suppose -3*p - 2 + 11 = x, 0 = -p + x + 3. Let t(z) be the third derivative of 0*z**p + 0 + 3*z**2 + 1/120*z**5 + 0*z + 1/24*z**4 - 1/240*z**6. Factor t(j).
-j*(j - 2)*(j + 1)/2
Let c(k) = 15*k**2 + 4*k - 6. Let g(l) = 16*l**2 + 5*l - 7. Let h(s) = -7*c(s) + 6*g(s). Factor h(o).
-o*(9*o - 2)
Let g = 7 - 3. Factor q**g + 4*q**3 + 3*q**2 + q - q**3 + 0*q.
q*(q + 1)**3
Let x(v) be the second derivative of -v**6/60 + v**4/12 + 2*v**2 + 2*v. Let z(u) be the first derivative of x(u). Solve z(q) = 0 for q.
-1, 0, 1
Let d = -102064745/511 - -199735. Let i = -2/73 - d. Factor i*z**2 + 6/7*z + 4/7.
2*(z + 1)*(z + 2)/7
Let v(g) be the second derivative of g**6/50 + 3*g**5/25 + g**4/10 - 2*g**3/5 - 9*g**2/10 - 7*g. Determine c so that v(c) = 0.
-3, -1, 1
Suppose -2*s + 4 = -2*v, 7 - 24 = -5*s - 2*v. Suppose 6*q + s + 4*q**2 - 7 + 0 = 0. Calculate q.
-2, 1/2
Suppose -20*w**2 - 65/3*w**3 - 5/3*w**5 + 0 - 20/3*w - 10*w**4 = 0. Calculate w.
-2, -1, 0
Let u be -2 - (3 - 1 - 7). Let h(a) be the third derivative of 0 - 1/12*a**4 + 0*a**u + a**2 - 1/15*a**5 - 1/60*a**6 + 0*a. What is l in h(l) = 0?
-1, 0
Let m(p) be the first derivative of 21*p**5/5 + 2*p**4 - 25*p**3/3 - 4*p**2 + 4*p - 25. Solve m(i) = 0.
-1, -2/3, 2/7, 1
Let x be 2/5*(-3 - 34/(-8)). Suppose -3/4*o + 1/4*o**2 + x = 0. Calculate o.
1, 2
Let w(z) be the first derivative of z**4/22 - z**2/11 - 1. What is y in w(y) = 0?
-1, 0, 1
Let f(o) be the second derivative of -1/90*o**6 + 0 - 2/3*o**3 - 1/10*o**5 - 13/36*o**4 - 2/3*o**2 + 3*o. Suppose f(x) = 0. What is x?
-2, -1
Let a(m) be the second derivative of m**5/10 - m**4/3 - m**3/3 + 2*m**2 - 7*m. Factor a(p).
2*(p - 2)*(p - 1)*(p + 1)
Let a(n) be the third derivative of -n**7/105 - n**6/20 - n**5/10 - n**4/12 + n**2. Find z such that a(z) = 0.
-1, 0
Let p(k) be the first derivative of k**2/2 + 3. Let a be p(5). Factor -2*w - a - w**2 + 5.
-w*(w + 2)
Suppose 3/2*n**3 + 0*n**2 + 0*n - 3/4*n**4 + 0 = 0. What is n?
0, 2
Let g(z) be the second derivative of -z**6/15 + z**4/2 + 2*z**3/3 + 25*z. Let g(m) = 0. What is m?
-1, 0, 2
Let p(c) be the second derivative of c**4/48 + c**3/4 - 14*c. Factor p(u).
u*(u + 6)/4
Let n(s) be the first derivative of s**5/10 + s**4/6 - 2*s**3/3 + 2*s - 7. Let v(g) be the first derivative of n(g). Factor v(z).
2*z*(z - 1)*(z + 2)
Let g = -1/14 - -19/70. Factor -g*u**2 - 1/5*u + 0.
-u*(u + 1)/5
Let v be (3/2)/(9/30). Factor -1 - u**2 - 3*u**3 + v*u**4 - u**5 - 4*u**3 + 0*u**5 + 8*u - 3.
-(u - 2)**2*(u - 1)**2*(u + 1)
Let l(i) = 3*i**2 + 24*i. Let r be l(-8). What is u in -2/7*u - 2/7*u**2 + r = 0?
-1, 0
Let v be (-37)/(-3) + (-2)/6. Factor v*b + 12*b**3 + 24*b**2 + 2*b**4 + 0*b**4 - 9*b + 13*b.
2*b*(b + 2)**3
Let f(s) be the first derivative of s**6/18 + s**5/5 + s**4/12 - s**3/3 - s**2/3 - 8. Factor f(m).
m*(m - 1)*(m + 1)**2*(m + 2)/3
Suppose -15 = 3*l - 8*l. Factor 0 + 4/7*a**2 + 2/7*a + 2/7*a**l.
2*a*(a + 1)**2/7
Let -1/2*f**3 + 0*f - 1/4*f**2 + 0 - 1/4*f**4 = 0. Calculate f.
-1, 0
Determine d, given that 5 + 2*d - 5*d - 7*d + 5*d**2 = 0.
1
Let p(v) be the second derivative of v**7/420 + v**6/180 + v**3/2 + 2*v. Let u(y) be the second derivative of p(y). Factor u(c).
2*c**2*(c + 1)
Let b(v) be the second derivative of 0 + 4/3*v**3 - 2*v**2 - 1/3*v**4 + 5*v. Factor b(c).
-4*(c - 1)**2
Suppose -2*y - j = -0*y - 6, 15 = 5*y - 5*j. Suppose -3 = -y*x + 6. Factor 0 - 22/5*a**2 + 32/5*a**x + 4/5*a - 14/5*a**4.
-2*a*(a - 1)**2*(7*a - 2)/5
Let w be -2 - -3 - 8/9. Let n(b) be the first derivative of -1/3*b**2 - w*b**3 - 1/3*b - 4. Let n(c) = 0. What is c?
-1
Let l be -2*(170/(-55) - -3). Let -2/11*v**3 + l*v**2 + 0 + 4/11*v = 0. What is v?
-1, 0, 2
Let b(q) be the third derivative of q**5/150 - q**4/30 - q**3/5 - 6*q**2. Factor b(f).
2*(f - 3)*(f + 1)/5
Let q(k) be the third derivative of 0 - 1/18*k**4 - 1/270*k**5 - 1/3*k**3 + k**2 + 0*k. Factor q(r).
-2*(r + 3)**2/9
Let o(u) be the second derivative of u**6/720 - u**5/360 - 3*u**2/2 + 5*u. Let i(r) be the first derivative of o(r). Solve i(w) = 0.
0, 1
Let s be 5/2 - (-24)/16. Suppose -5 = -3*w - s*r, 2*w + 0 = -3*r + 3. Let 14/3*b**2 + 8/9 + 16/3*b - 98/9*b**w = 0. What is b?
-2/7, 1
Let i be (-3 + (-805)/(-270))*-3. Let d(t) be the second derivative of -t + i*t**4 - 2/9*t**3 + 1/3*t**2 + 0. Solve d(l) = 0.
1
Let 176*h**2 - 6*h + 5*h**3 - 87*h**2 - 4*h - 84*h**2 = 0. Calculate h.
-2, 0, 1
Let l(f) be the third derivative of -1/4*f**3 + 0 - 2*f**2 + 1/8*f**4 + 0*f - 1/40*f**5. Find x, given that l(x) = 0.
1
Let n be 2684/48 - (-1)/3. Let c = n + -56. Factor c*x - 1/4*x**2 + 0.
-x*(x - 1)/4
Solve -1/2*p**4 + 1/2*p + p**2 - p**3 + 1/2*p**5 - 1/2 = 0.
-1, 1
Let j(g) be the third derivative of -3*g**5/5 - g**4 - 2*g**3/3 + 10*g**2. Factor j(f).
-4*(3*f + 1)**2
Factor h**2 - 1/3*h**3 - 1/3*h**4 + 2/3 + 5/3*h.
-(h - 2)*(h + 1)**3/3
Let u = 21 - 17. Let a(h) be the second derivative of -4/3*h**2 + 0 - 3*h - 7/18*h**u - 16/9*h**3. Solve a(j) = 0.
-2, -2/7
Factor 2*y**2 + 5*y + 6*y**2 + 12 + 7*y**2 + 31*y.
3*(y + 2)*(5*y + 2)
Let v = 11 - 4. Let u(l) = -2*l**4 - 9*l**3 + 7*l**2 - 7*l. Let i(d) = d**4 + 6*d**3 - 5*d**2 + 5*d. Let m(n) = v*i(n) + 5*u(n). Factor m(t).
-3*t**3*(t + 1)
Suppose 0 = 4*x - 4*h + 64, 0 = -4*h + 3 + 9. Let t be (-39)/x - (-19)/(-7). Factor -4/7*o**2 - t*o**3 + 0 - 2/7*o.
-2*o*(o + 1)**2/7
Let z(k) = -7*k**3 - 8*k**2 - k + 3. Let n(a) = -76*a**3 - 88*a**2 - 12*a + 32. Let u(f) = 3*n(f) - 32*z(f). Factor u(b).
-4*b*(b + 1)**2
Suppose 3*m - 2*j = -0*m - 5, -3*j + 12 = 0. Suppose -y + 9 = 3*c, -2*c + c - y = -m. Suppose 4 + c*t**2 - 3*t**2 - 5 = 0. What is t?
-1, 1
Let b(i) be the third derivative of i**5/60 + i**3/2 + i**2. Let w be b(0). What is d in 1/4*d**2 - 1/4*d**w + 0 + 1/2*d = 0?
-1, 0, 2
Suppose z + 5 - 2 = 0, 2*a + 2*z = 0. Let m be -2 - (-1522)/20 - 18/30. Factor 2 - 343/4*g**a + m*g**2 - 21*g.
-(7*g - 2)**3/4
Let w be -5 - (1/(-3) - (-650)/(-120)). What is y in 0*y + 3/4*y**3 - w*y**2 + 0 = 0?
0, 1
Factor 10 + q - 12*q**2 + 9*q**2 + 5*q - 1.
-3*(q - 3)*(q + 1)
Let h(j) be the second derivative of j**4/4 - 5*j**3 + 75*j**2/2 + 8*j. Factor h(g).
3*(g - 5)**2
Suppose 0*b - 2*b + 6 = 0. Find j, given that -j**3 - j + 4*j**b - 2*j - 6*j**3 - 6*j**2 = 0.
-1, 0
Factor 2/7*y**2 + 18/7 - 12/7*y.
2*(y - 3)**2/7
Let x(t) be the second derivative of -t**4/48 + t**3/12 - t**2/8 + 2*t. Factor x(u).
-(u - 1)**2/4
Let r = -114 + 343/3. Let v(c) be the first derivative of 11/2*c**4 + 0*c + r*c**2 - 20/9*c**3 + 16/9*c**6 - 16/3*c**5 - 1. Let v(n) = 0. Calculate n.
0, 1/4, 1
Let i(f) be the first derivative of 2/5*f**2 - 1/4*f**4 + 2/5*f**3 - 8/5*f - 2 + 1/25*f**5. Find o, given that i(o) = 0.
-1, 2
Suppose -4*a = 11 - 19, 4*y + 5*a - 18 = 0. Factor -w + 1 + 1/4*w**y.
(w - 2)**2/4
Let z(t) be the second derivative of -t**7/2520 + t**6/300 - t**5/150 - t**4/2 + 5*t. Let a(k) be the third derivative of z(k). Factor a(w).
-(w - 2)*(5*w - 2)/5
Let m(x) be the second derivative of -x**4/36 + x**3/18 + 6*x. Factor m(h).
-h*(h - 1)/3
Let c = 14/3 - 112/33. Factor -4/11*p - 10/11*p**3 - c*p**2 + 0.
-2*p*(p + 1)*(5*p + 2)/11
Suppose -11*u + 39 = -27. Let d(t) be 