he second derivative of 7*w**6/10 + 2*w**5/5 - 25*w**4/12 - 4*w**3/3 + 2*w**2 + 2*w + 32. Find d, given that f(d) = 0.
-1, -2/3, 2/7, 1
Let o be 2/(-9) + (-58)/(-18). Suppose -5*a + 12 = 4*l, -a + 3*l + 15 = 8*l. Factor 1/5*k**2 + 2/5*k**o + a + 0*k.
k**2*(2*k + 1)/5
Let o be (-21)/(-14)*2/(-3). Let b be (4/(-12))/(o/15). Determine a so that -2*a**4 - 2*a**5 + 3*a**5 - 3*a**b = 0.
-1, 0
Let w(d) be the second derivative of d**8/3360 - d**7/1680 - d**3/2 + d. Let a(r) be the second derivative of w(r). Factor a(h).
h**3*(h - 1)/2
Factor -8/3 + 2/3*i**3 + 0*i + 2*i**2.
2*(i - 1)*(i + 2)**2/3
Factor 9*p**4 - 11*p - 7 + 4 + 3*p**5 - 6*p**2 + 2*p + 6*p**3.
3*(p - 1)*(p + 1)**4
Let i(h) be the third derivative of h**6/80 - 3*h**5/40 + 3*h**4/16 - h**3/4 + 9*h**2. What is p in i(p) = 0?
1
Suppose 4*r - 5*k = 72, 2*r - 68 = -2*r + 4*k. Suppose 23 = 5*b + 4*y, 5*y = b - 2*b + r. Find q, given that 1/3*q + 1/3*q**b + 0 - 2/3*q**2 = 0.
0, 1
Solve -2/3*b**2 - 512/3 - 64/3*b = 0 for b.
-16
Suppose j - 3*x - 201 = -2*x, 0 = -j - 5*x + 195. Let y = -1394/7 + j. Determine m, given that -4/7 - y*m - 2/7*m**2 = 0.
-2, -1
Let c(s) be the first derivative of -8*s**6/3 - 20*s**5 - 54*s**4 - 208*s**3/3 - 44*s**2 - 12*s + 12. Suppose c(y) = 0. What is y?
-3, -1, -1/4
Suppose q = -2*c - q + 12, -5*c - 6 = -4*q. Solve 3/4*u**c - 1/2 - 1/4*u = 0.
-2/3, 1
Let p(z) = -4*z**3 + z**2 + z - 1. Let g(v) = 3*v**3 - v**2 - v + 1. Suppose 3*w = -6 - 3. Let d = 4 - 6. Let r(n) = d*p(n) + w*g(n). Factor r(y).
-(y - 1)**2*(y + 1)
Let t(g) be the second derivative of g**8/336 + g**7/210 - g**6/40 - g**5/12 - g**4/12 + 5*g**2/2 - 3*g. Let v(l) be the first derivative of t(l). Factor v(m).
m*(m - 2)*(m + 1)**3
Let q(u) be the third derivative of -u**7/210 - u**6/120 + u**5/60 + u**4/24 - 5*u**2. Factor q(l).
-l*(l - 1)*(l + 1)**2
Let l(k) be the first derivative of k**6/3 + 2*k**5/5 - k**4/2 - 2*k**3/3 - 18. Factor l(t).
2*t**2*(t - 1)*(t + 1)**2
Let s(f) be the first derivative of -1 + 0*f**2 + 2/33*f**3 + 0*f - 1/11*f**4. Factor s(n).
-2*n**2*(2*n - 1)/11
Suppose -j + 2 = -1. Let q be j/7 - (-1)/(-7). Factor q*d**4 - 4/7*d**2 + 0*d + 0*d**3 + 2/7.
2*(d - 1)**2*(d + 1)**2/7
Let t(v) be the third derivative of v**7/280 + v**6/60 + v**5/80 - v**4/48 - 8*v**2. Factor t(h).
h*(h + 1)*(h + 2)*(3*h - 1)/4
Let l = -47 + 33. Let x be (-1)/l + 12/28. Suppose 3/2*r + 3/2*r**2 + x*r**3 + 1/2 = 0. What is r?
-1
Let y(o) be the second derivative of -3/80*o**5 + 3/4*o**2 + 5/8*o**3 - 1/40*o**6 + 0 + 3/16*o**4 - o. Let y(b) = 0. What is b?
-1, 2
Let f(c) be the third derivative of c**6/480 - c**4/96 - 6*c**2. Factor f(r).
r*(r - 1)*(r + 1)/4
Suppose 4*o - 15 = -o. Factor 2*m + 0*m - 4*m**2 + 2*m**o + 0*m + 0*m.
2*m*(m - 1)**2
Let u(i) = -7*i**2 - 23*i + 2. Let m(a) = 50*a**2 + 160*a - 15. Let l(r) = 2*m(r) + 15*u(r). Factor l(x).
-5*x*(x + 5)
Let c(s) = -4*s**3 - s**2 - 3*s - 2. Let h be c(-1). Let z(d) be the second derivative of 0*d**2 + 0 - 1/9*d**3 + 0*d**h + 2*d + 1/30*d**5. Factor z(v).
2*v*(v - 1)*(v + 1)/3
Let f(y) be the second derivative of y**5/60 - y**4/8 + y**3/3 + y**2 + y. Let g(z) be the first derivative of f(z). Find n, given that g(n) = 0.
1, 2
Let k be (-3)/(-2)*(3 - -1). Let 3*q - 2 - 9*q + 10*q + k*q**2 = 0. What is q?
-1, 1/3
Let w = 503 + -30179/60. Let o(l) be the third derivative of 0*l**4 + 0*l + 2*l**2 - 1/30*l**5 + 0*l**3 + 0 + w*l**6. Factor o(i).
2*i**2*(i - 1)
Let s = 864 - 859. Factor -1/2*t**s + 1/2*t**3 + 0 + 0*t - 1/2*t**2 + 1/2*t**4.
-t**2*(t - 1)**2*(t + 1)/2
Let r(l) be the second derivative of -l**9/30240 - l**8/6720 - l**7/5040 - l**4/4 - 3*l. Let p(q) be the third derivative of r(q). Let p(m) = 0. Calculate m.
-1, 0
Suppose 0 = 5*c - 2*m + 31 - 107, -54 = -3*c + 4*m. Factor -4 + 3*p**2 - c*p - 9*p**2 - 4*p**3 - 8*p**2 + 0*p**3.
-2*(p + 1)*(p + 2)*(2*p + 1)
Let g(w) be the first derivative of w**4/34 - 2*w**3/51 - 4. Factor g(i).
2*i**2*(i - 1)/17
Let s(t) be the second derivative of -3*t**5/140 + 5*t**4/28 - t**3/2 + 9*t**2/14 - 6*t. Factor s(o).
-3*(o - 3)*(o - 1)**2/7
Let i be (-22)/(-33) - 4/(-3). Solve 1/4*f**3 + 0 - 1/4*f**4 + 0*f**i + 0*f = 0.
0, 1
Let v(h) be the third derivative of -h**7/525 - h**6/150 - h**5/150 + 8*h**2. Factor v(c).
-2*c**2*(c + 1)**2/5
Let z = 2/641 + 3832/4487. Find o, given that 3/7 + z*o + 3/7*o**2 = 0.
-1
Let w(h) be the third derivative of 1/105*h**7 - h**2 + 0*h**3 + 0 - 1/30*h**5 - 1/180*h**6 + 0*h + 1/36*h**4. Determine l so that w(l) = 0.
-1, 0, 1/3, 1
Let y(j) = -2*j**3 - 2*j**2 + j - 3. Let o be y(3). Let p be (3/(-4))/(135/o). Factor p*h**4 - 4/5 + 2/5*h**2 + 6/5*h**3 - 6/5*h.
2*(h - 1)*(h + 1)**2*(h + 2)/5
Let m(b) be the second derivative of -1/4*b**4 - 2*b - 2*b**2 + 0 + 1/40*b**5 + b**3. Factor m(i).
(i - 2)**3/2
Let y(h) be the first derivative of -h**6/30 - h**5/20 + h**4/12 + h**3/6 - 3*h + 3. Let u(q) be the first derivative of y(q). Factor u(x).
-x*(x - 1)*(x + 1)**2
Factor 30/7*f**3 + 0 - 12/7*f**2 - 24/7*f**4 + 0*f + 6/7*f**5.
6*f**2*(f - 2)*(f - 1)**2/7
Suppose 2 = -3*k + 8. Factor -2 + 4*z**3 - 4*z + 2*z**4 + 3*z**2 + 3*z**2 - 6*z**k.
2*(z - 1)*(z + 1)**3
Let z(a) = -a**3 - 4*a**2 - 5*a - 16. Let l be z(-4). Suppose -5*q + 3*q = 0. Factor 4/11*h**5 + q + 10/11*h**2 + 14/11*h**l + 2/11*h + 18/11*h**3.
2*h*(h + 1)**3*(2*h + 1)/11
Let s(n) be the third derivative of 0*n + 0 - 2/27*n**3 + 7/270*n**5 - 4*n**2 + 5/108*n**4. Find a such that s(a) = 0.
-1, 2/7
Let s(l) = -l**3 + 5*l**2 - 4*l - 1. Let q be s(3). Suppose 1 = 2*j - q. Factor m**2 + 2*m**j + m**2 + 0*m**2.
2*m**2*(m + 1)
Let z(b) be the second derivative of b**5/90 - b**4/18 + 4*b**2/9 - 15*b. Solve z(s) = 0.
-1, 2
Let o be 27/12*(-16)/(-6). Suppose -2*u + 5*u**3 - u**3 - 2 - 4 + o*u**2 - 2*u**3 = 0. Calculate u.
-3, -1, 1
Let n(p) be the second derivative of -p**6/6 - p**5/2 - 5*p**4/12 + 15*p. Factor n(j).
-5*j**2*(j + 1)**2
Let v(g) = -3*g**2 + 9*g**3 - g**2 - 6*g - 5 + g**4 - 1 + 0*g**4. Let j(y) = y**3 - y**2 - y - 1. Let b(o) = 6*j(o) - v(o). Factor b(l).
-l**2*(l + 1)*(l + 2)
Let i(n) = -17*n**2 + 11*n + 17. Let m(j) = -6*j**2 + 4*j + 6. Let y be 1*((-38)/2 + -2). Let h = -32 - y. Let u(z) = h*m(z) + 4*i(z). What is a in u(a) = 0?
-1, 1
Let d(v) be the third derivative of -v**7/42 + v**5/12 - 9*v**2. Find r such that d(r) = 0.
-1, 0, 1
Let c(t) = 2*t + 1. Let x be c(-3). Let q = x - -5. Suppose -2/3*g**2 + q + 0*g = 0. What is g?
0
Let 8*w - 13*w - 2*w**4 + 2 + w**5 + 4*w**3 - w**2 + 3*w**2 - 2*w**4 = 0. What is w?
-1, 1, 2
Suppose -3*i + i = -10. Let x(h) = 26*h**3 - 4*h**2 - 18*h + 12. Let g(f) = -17*f**3 + 3*f**2 + 12*f - 8. Let t(o) = i*x(o) + 8*g(o). Let t(y) = 0. Calculate y.
-1, 2/3, 1
Let q(y) = -y**3 + y - 63. Let b be q(0). Let j be b/(-15)*(-12)/(-18). Factor 4/5*k**3 + 2/5 - 11/5*k + 7/5*k**5 - 16/5*k**4 + j*k**2.
(k - 1)**3*(k + 1)*(7*k - 2)/5
Let o(m) be the first derivative of -2*m**5/5 - m**4/2 + 2*m**3/3 + m**2 + 17. Factor o(z).
-2*z*(z - 1)*(z + 1)**2
Let k = -3419/5 - -684. Suppose 0 - k*s + 1/5*s**3 + 0*s**2 = 0. What is s?
-1, 0, 1
Let b(g) be the second derivative of -3*g**5/10 - 5*g**4/3 - 3*g**3 - 2*g**2 + 2*g. Factor b(v).
-2*(v + 1)*(v + 2)*(3*v + 1)
Let c(x) = 28*x**2 + 36*x + 8. Let v(o) = -o**2 - o. Let s(b) = -c(b) - 24*v(b). Determine z so that s(z) = 0.
-2, -1
Find t, given that 4/7*t**4 + 1248/7*t - 96/7*t**3 + 676/7 + 472/7*t**2 = 0.
-1, 13
Let h(u) be the first derivative of -2/3*u**3 + 0*u**2 - 1/6*u**4 - 2 + 8/3*u. Factor h(a).
-2*(a - 1)*(a + 2)**2/3
Suppose 4*o**2 + 0 + 2/3*o**3 + 6*o = 0. Calculate o.
-3, 0
Let a(w) be the first derivative of -1 + 2/33*w**3 + 8/11*w + 4/11*w**2. Factor a(h).
2*(h + 2)**2/11
Determine v, given that 3*v**3 + 2*v + 3 + 10*v + v + 13*v**2 = 0.
-3, -1, -1/3
Let y(g) = -g**2 + 10*g - 9. Let n be y(9). Let r(t) be the second derivative of -1/4*t**2 + n - 1/80*t**5 + 1/24*t**3 - 2*t + 1/24*t**4. Factor r(f).
-(f - 2)*(f - 1)*(f + 1)/4
Solve 1/3*j**2 + 0*j + 0 - j**3 = 0 for j.
0, 1/3
Let x(f) be the third derivative of 2*f**2 + 0 + 1/108*f**6 + 1/135*f**5 - 5/1512*f**8 - 2/945*f**7 + 0*f + 0*f**3 + 0*f**4. Suppose x(m) = 0. Calculate m.
-1, -2/5, 0, 1
Let a = 17 + -17. Let b(f) be the third derivative of 0 + 0*f**3 + 0*f**4 + a*f + 1/150*f**5 - f**2 - 1/300*f**6. Factor b(