 derivative of -1/54*n**4 + 0*n**3 - 1/180*n**6 - n**2 + 0 + 7/270*n**5 - 1/135*n**7 + 5/1512*n**8 + 0*n. Determine w, given that j(w) = 0.
-1, 0, 2/5, 1
Factor 24/5*q**2 + 54/5 - 63/5*q - 3/5*q**3.
-3*(q - 3)**2*(q - 2)/5
Let b(x) be the second derivative of 7*x**4/18 - 5*x**3/9 - 2*x**2/3 - 9*x. Suppose b(m) = 0. What is m?
-2/7, 1
Let f(b) = -5*b**5 - 2*b**4 + 2*b**3 - b**2 + 3*b. Let q(g) = 14*g**5 + 6*g**4 - 6*g**3 + 2*g**2 - 8*g. Let m(a) = -8*f(a) - 3*q(a). Factor m(c).
-2*c**2*(c - 1)*(c + 1)**2
Let g(j) be the second derivative of -j**4/42 - 2*j**3/21 - j**2/7 - 7*j. Factor g(x).
-2*(x + 1)**2/7
Determine i so that -21/8 + 9/4*i + 3/8*i**2 = 0.
-7, 1
Factor 0*d**4 - 1/3*d**2 + 1/6*d**5 + 0*d - 1/2*d**3 + 0.
d**2*(d - 2)*(d + 1)**2/6
Let i = -10146/11 - -37155/22. Let c(j) = -j**2 - 5*j - 2. Let r be c(-4). Find a, given that -2 - 441*a**5 - 30*a - 357/2*a**r - i*a**4 - 526*a**3 = 0.
-1/2, -1/3, -2/7
Let a = 41 - 39. Let j(w) be the second derivative of 1/12*w**4 - 2/3*w**3 + 0 + a*w**2 - w. Factor j(c).
(c - 2)**2
Factor -6/5 - 42/5*x**2 + 34/5*x - 18/5*x**3.
-2*(x + 3)*(3*x - 1)**2/5
Let g(j) = -j**2 + 7*j - 1. Let m(w) = 3*w**2 - 20*w + 4. Suppose -32 = -0*x - 4*x. Let o(l) = x*g(l) + 3*m(l). Let o(k) = 0. Calculate k.
2
Let n(l) be the first derivative of 3*l**5/20 + 11*l**4/16 + l**3/2 - 3*l**2/2 - 2*l + 26. Factor n(m).
(m - 1)*(m + 2)**2*(3*m + 2)/4
Let q(s) be the second derivative of -3*s**5/5 - 11*s**4/4 - 5*s**3/2 + 3*s**2 - 31*s. Factor q(u).
-3*(u + 1)*(u + 2)*(4*u - 1)
Let w(g) be the third derivative of 1/60*g**5 - 1/2*g**3 + 1/12*g**4 + 0 - g**2 + 0*g. Factor w(i).
(i - 1)*(i + 3)
Let f = 50/91 + 2/91. Let l = -768/7 - -110. Determine u so that 0 - f*u - 6/7*u**2 - l*u**3 = 0.
-2, -1, 0
Let s(k) be the third derivative of k**9/7560 - k**8/1680 + k**7/1260 + k**4/6 + 3*k**2. Let b(r) be the second derivative of s(r). Solve b(d) = 0 for d.
0, 1
Let n = -23 + 10. Let y = n - -16. Factor 0 + 4/3*h**2 - 10/3*h**y + 0*h.
-2*h**2*(5*h - 2)/3
Let r(w) = -w + 1 + 4*w**3 - w**4 - 7*w**3 + 4*w**3 + 2*w**4. Let b(g) = -g**4 + 19*g**3 + 32*g**2 + 15*g - 7. Let a(h) = -2*b(h) - 14*r(h). Factor a(i).
-4*i*(i + 2)**2*(3*i + 1)
Suppose 2/3*p + 1/3*p**2 + 0 - 1/3*p**4 - 2/3*p**3 = 0. What is p?
-2, -1, 0, 1
Let c = -15 - -30. Suppose 3*g - 5*b = -0*g - 6, 2*g + 3*b = c. Suppose 0 + 1/4*l**5 - 1/4*l**g + 0*l - 1/4*l**2 + 1/4*l**4 = 0. Calculate l.
-1, 0, 1
Solve 0 - 2/3*u**2 - 2*u = 0.
-3, 0
Let d(x) be the first derivative of -2/15*x**3 - 4 - 1/10*x**2 - 1/20*x**4 + 0*x. Factor d(w).
-w*(w + 1)**2/5
Suppose 0 = -2*y - 3*y. Suppose -2*c**4 + 2 - 11*c**3 + 7*c**3 + 4*c + y = 0. What is c?
-1, 1
Let o(s) = s**2 + 43*s + 37. Let d(g) = -21*g - 18. Let v(i) = 5*d(i) + 3*o(i). Suppose v(j) = 0. Calculate j.
-7, -1
Let i(h) = -h**2 + h - 1. Let u(m) = -2*m**3 - 2*m**2 + 4*m - 2. Let a be (2/5)/(3/15). Let z(g) = a*i(g) - u(g). Suppose z(q) = 0. Calculate q.
-1, 0, 1
Suppose 0*t - 4*t = -16. Let i be -2 - -4*(t + -3). Find a, given that -a + 0*a**4 + a**5 + 3*a**2 - i*a**4 - a**2 = 0.
-1, 0, 1
Let f(a) be the second derivative of -a**5/4 - 5*a**4/4 + 10*a**2 - 5*a. Solve f(h) = 0.
-2, 1
Let s = -2999/120 - -25. Let k(w) be the third derivative of 0*w**4 - 1/48*w**6 - 2*w**2 + s*w**5 + 0*w + 1/105*w**7 + 0 + 0*w**3. Let k(v) = 0. Calculate v.
0, 1/4, 1
Let r(d) be the third derivative of -d**7/210 - 13*d**2. Factor r(j).
-j**4
Let d(z) be the first derivative of -4*z**5/5 + 3*z**4 + 8*z**3/3 - 24*z**2 + 32*z + 2. Factor d(g).
-4*(g - 2)**2*(g - 1)*(g + 2)
Factor -p**3 - 3*p + 3*p + p.
-p*(p - 1)*(p + 1)
Let k(v) be the third derivative of 2*v**2 - 1/300*v**5 + 0*v**4 + 0 + 1/300*v**6 + 0*v**3 + 0*v - 1/1050*v**7. Find z such that k(z) = 0.
0, 1
Let h(f) = -f**2 - 5*f + 2. Suppose -u = -6*u - 4*d - 17, -4*u - 22 = -d. Let r be h(u). Factor -i**r - 4*i**2 - 2*i**3 + i**2 - 2*i.
-2*i*(i + 1)**2
Suppose 8*m + 6 = 3*m + 3*h, -6 = m - 3*h. Determine n so that 0*n**2 + 0*n - 1/3*n**3 + m = 0.
0
Suppose -4*n - h + 11 = 0, 3 = 2*n + h - 0*h. Suppose 0*r - n = -r. Factor 6*p**4 + 0*p**3 - 4*p**4 + r*p**3 + 2*p**2.
2*p**2*(p + 1)**2
Let y = 1 - -5. Let f(g) be the second derivative of 1/21*g**7 + 0*g**3 + 0 + 1/10*g**5 + 0*g**2 + 2/15*g**y + 2*g + 0*g**4. Factor f(u).
2*u**3*(u + 1)**2
Let u be (-2)/((3 + -2)*-1). Let m(a) = -a**3 + 8*a**2 + a - 6. Let d be m(8). Factor -u*o**d - 7*o**4 + 4*o**3 - 2*o**4 + 7*o**4.
-2*o**2*(o - 1)**2
Let 0*x - 2/9*x**5 + 0*x**3 + 0*x**2 - 4/9*x**4 + 0 = 0. Calculate x.
-2, 0
Let v(n) be the second derivative of n**7/21 - 2*n**6/15 - 3*n**5/10 + 2*n**4/3 + 4*n**3/3 - 6*n. Factor v(b).
2*b*(b - 2)**2*(b + 1)**2
Let j(f) = -2*f - 2. Let v be j(-2). Suppose -2*b**v + b**2 + 2*b**2 + 0*b**2 = 0. Calculate b.
0
Suppose 0 = -0*v + 2*v - 6. What is g in 2*g**3 + 2 - 8*g**v + 3*g**4 - 5 + 0*g**3 + 6*g = 0?
-1, 1
Let p(y) = y**2 + 6*y - 14. Let l be p(-8). Suppose 0 = l*z - z - 5. Factor 0*g**2 + 1/3*g + 1/3*g**z + 0*g**4 - 2/3*g**3 + 0.
g*(g - 1)**2*(g + 1)**2/3
Let v(f) = -2*f + 3. Let t be v(1). Let d(i) be the first derivative of t + 21/4*i**4 - 19*i**3 + 12*i**2 + 12*i. Factor d(q).
3*(q - 2)*(q - 1)*(7*q + 2)
Let v(g) be the second derivative of g**7/10080 - g**6/2880 - g**4/4 - 3*g. Let d(t) be the third derivative of v(t). Factor d(s).
s*(s - 1)/4
Let k be (0 - -5)*(1 + 0). Factor -11*y**3 + 7*y**3 - 2*y**4 - 2*y**k - 2 + 8*y**3 + 4*y**2 - 2*y.
-2*(y - 1)**2*(y + 1)**3
Let p be ((-5)/(-2) - -2) + (-8 - -8). Let h(q) be the first derivative of -3*q**3 - 3*q + 3/4*q**4 - 4 + p*q**2. Factor h(a).
3*(a - 1)**3
Suppose r**2 - 4*r**2 - 6*r**2 + 6 + 11*r + 15*r**2 + r**3 = 0. Calculate r.
-3, -2, -1
Let a(b) be the second derivative of 0*b**2 + 0 + 2*b - 1/10*b**6 + 1/4*b**4 - b**3 + 3/10*b**5. Let a(i) = 0. Calculate i.
-1, 0, 1, 2
Let f(u) be the second derivative of u**9/10584 - u**8/5880 - u**7/2940 + u**6/1260 + 4*u**3/3 - 3*u. Let d(k) be the second derivative of f(k). Solve d(a) = 0.
-1, 0, 1
Let f(t) = -2*t + 3. Let r be f(0). Suppose r*o**4 - 6*o**3 + 6*o - 4*o - 3 - 3*o + 7*o = 0. What is o?
-1, 1
Let o(j) be the second derivative of 3*j**5/20 - 11*j**4/36 + j**3/9 - 13*j. Solve o(u) = 0 for u.
0, 2/9, 1
Let o(j) be the second derivative of 0*j**2 + 1/50*j**5 + 0*j**3 + 0 + 1/30*j**4 - 3*j. Factor o(w).
2*w**2*(w + 1)/5
Let l(g) be the third derivative of g**7/525 + g**6/150 - 2*g**5/75 - g**4/30 + g**3/5 - 71*g**2. Factor l(m).
2*(m - 1)**2*(m + 1)*(m + 3)/5
Let j = -28 + 33. Let v(g) be the second derivative of -2/3*g**4 + 0 + 1/10*g**j + 4/3*g**3 - 3*g + 0*g**2. Find b, given that v(b) = 0.
0, 2
Find l such that -4/3*l - 2/3 - 2/3*l**2 = 0.
-1
Let 5 - 8*u + 6*u**2 + 9*u + 14*u + 4 = 0. What is u?
-3/2, -1
Suppose -5*x = -0*g + g - 9, -2*x = 4*g. Suppose -6/11*p**x + 8/11*p - 2/11 = 0. What is p?
1/3, 1
Let q(z) be the second derivative of 0 + z**2 + 1/6*z**4 - 2/3*z**3 - 5*z. Factor q(u).
2*(u - 1)**2
Let h be 5 + -4 + 118/(-120). Let y(i) be the third derivative of 0 - 2*i**2 - h*i**6 - 1/4*i**4 + 0*i - 1/3*i**3 - 1/10*i**5. Let y(j) = 0. What is j?
-1
Let u(d) be the first derivative of -1/25*d**5 - 1/5*d - 1/5*d**4 - 2/5*d**3 + 4 - 2/5*d**2. Factor u(v).
-(v + 1)**4/5
Let f be ((-3)/(-1))/18*2. Let q be 3 + 18/24*-2. Suppose 2/3*m**5 + 4/3*m**2 - m - q*m**4 + f*m**3 + 1/6 = 0. What is m?
-1, 1/4, 1
Let p = -1/390 - -181/390. Let a = p + 1/26. Factor -a*v - 1/2*v**3 + 0 - v**2.
-v*(v + 1)**2/2
Let d(x) be the second derivative of -x**9/1008 + x**7/140 - x**5/40 - 5*x**3/6 + x. Let t(o) be the second derivative of d(o). Factor t(f).
-3*f*(f - 1)**2*(f + 1)**2
Let a = 123 - 123. Let k be 1*2/9*3. Determine s so that -1/3*s**5 - 2/3*s**2 + 1/3*s + 0*s**3 + a + k*s**4 = 0.
-1, 0, 1
Let d(j) = j**3 - j**2 - j - 1. Let w(m) = -4*m**3 + 4*m**2 + 6*m + 6. Let v(b) = -6*d(b) - w(b). Determine q so that v(q) = 0.
0, 1
Let j(v) be the first derivative of -v**3/9 - v**2/6 + 2*v - 13. Determine o so that j(o) = 0.
-3, 2
Let u(o) be the third derivative of o**5/150 - o**4/15 + 4*o**3/15 + 6*o**2. Determine y so that u(y) = 0.
2
Factor -40/19*x - 2/19*x**4 - 36/19*x**2 - 16/19 - 14/19*x**3.
-2*(x + 1)*(x + 2)**3/19
Factor -2 - 27*j**3 - 4*j + 2*j + 17*j - 9*j**2 - 1.
-3*(j + 1)*(3*j - 1)**2
Let h = 6 - 4. Find s, given that 9*s*