4). Let h(j) be the third derivative of 1/660*j**6 + 0*j + 0*j**4 + 0*j**3 + 0 - u*j**2 + 1/165*j**5. Factor h(t).
2*t**2*(t + 2)/11
Suppose 512/3*w**3 + 46/3*w + 4/3 - 88*w**4 - 298/3*w**2 = 0. What is w?
-2/33, 1/2, 1
Let r(w) = -9*w**3 - 7*w**2 - 7*w - 7. Let x(q) = 4*q**3 + 3*q**2 + 3*q + 3. Let g(z) = 3*r(z) + 7*x(z). Find y such that g(y) = 0.
0
Suppose 6*y - y + 10 = 0. Let g be (1 - 6)*y/5. Find o, given that -8/5*o + 8/5 + 2/5*o**g = 0.
2
Let g be (-4)/4*(-5)/1. Suppose -g*d = -4*d. Find o, given that d - 4/9*o**3 + 0*o + 2/9*o**2 = 0.
0, 1/2
Let v(y) be the second derivative of y**8/1848 - y**7/1155 + y**2 - y. Let t(o) be the first derivative of v(o). What is l in t(l) = 0?
0, 1
What is g in 3/2 + 15/8*g**2 - 3*g - 3/8*g**3 = 0?
1, 2
Let s(z) be the third derivative of z**7/525 - z**6/75 + z**5/25 - z**4/15 + z**3/15 - z**2. Suppose s(i) = 0. What is i?
1
Let c(b) be the third derivative of -1/60*b**6 + 0*b - 1/105*b**7 + 1/336*b**8 + 1/24*b**4 - 7*b**2 + 1/15*b**5 + 0 - 1/3*b**3. Factor c(k).
(k - 2)*(k - 1)**2*(k + 1)**2
Let x(h) be the second derivative of 4/3*h**2 - h + 0 + 49/18*h**4 - 28/9*h**3. Factor x(u).
2*(7*u - 2)**2/3
Let d(w) be the second derivative of -2/7*w**2 + 0 + 1/7*w**3 + 5*w - 1/42*w**4. Let d(i) = 0. Calculate i.
1, 2
Let b(w) be the second derivative of w**9/7560 + w**8/2100 - w**6/450 - w**5/300 - w**3/2 - 2*w. Let u(v) be the second derivative of b(v). Factor u(a).
2*a*(a - 1)*(a + 1)**3/5
Let o = 84 - 84. Let r(c) be the second derivative of -c + 1/35*c**5 + 0 + 0*c**2 + 1/105*c**6 + o*c**3 + 1/42*c**4. Factor r(z).
2*z**2*(z + 1)**2/7
Let o(v) be the first derivative of v**5/15 - v**4/2 + 13*v**3/9 - 2*v**2 + 4*v/3 + 33. Factor o(z).
(z - 2)**2*(z - 1)**2/3
Let x(b) be the second derivative of 2*b**6/3 + 5*b**5/4 + 5*b**4/12 + 12*b. Factor x(u).
5*u**2*(u + 1)*(4*u + 1)
Let h(c) = -c**2 - c. Let q(y) = -2*y**2 + 13*y. Let b(z) = 3*h(z) + q(z). Factor b(m).
-5*m*(m - 2)
Let t(n) = n**2 - 2*n + 1. Let v be t(1). Let c = -131 - -131. Let 0*h + 0*h**3 + 2/7*h**5 + v*h**2 + 0*h**4 + c = 0. What is h?
0
Let s(q) = -q**3 + 8*q**2 + 8*q + 6. Let i be s(9). Let u be 4/(-6)*(0 + i). Suppose -1/3 - 1/3*j**u + 2/3*j = 0. What is j?
1
Let o(f) = f**3 + 14. Let k be o(0). Find t, given that 18*t - 8*t**4 - t**4 - 36*t**2 - 3 + k*t**3 + 16*t**3 = 0.
1/3, 1
Let l(b) = b**2 + 1. Let p(m) = 7*m**2 + m + 8. Let n(g) = 24*l(g) - 3*p(g). Factor n(d).
3*d*(d - 1)
Determine h, given that -2*h - 16*h**5 + 14*h**3 + 22*h**2 + 4*h + 61 - 63 - 20*h**4 = 0.
-1, -1/2, 1/4, 1
Let k(b) be the first derivative of -1/5*b**2 + 2/3*b**3 + 14/25*b**5 - 2/15*b**6 + 0*b + 2 - 9/10*b**4. Solve k(q) = 0.
0, 1/2, 1
Suppose 2*w = 5*s - 4, 0*w + 2*w + s = 8. Let n(b) be the second derivative of 1/3*b**w + b - 1/12*b**4 - 1/2*b**2 + 0. Suppose n(m) = 0. What is m?
1
Let v(z) = -z**2 + 1. Let u(n) = -9*n**2 - 18*n - 9. Let l(c) = -c + 1. Let b be l(-5). Let h(t) = b*v(t) + u(t). Solve h(w) = 0 for w.
-1, -1/5
Let w(j) = -2*j - 5. Let v be w(-4). Solve 0*t**2 + 2*t**2 + 5*t**5 - v*t**5 - 2*t**4 + 0*t**2 - 2*t**3 = 0 for t.
-1, 0, 1
Suppose 0 = -j - 10*j + 33. Find u, given that -12/7*u**2 + 8/7*u**j + 8/7*u - 2/7 - 2/7*u**4 = 0.
1
Factor c - 2*c**3 - 9*c**4 + 50*c**2 - 10*c - 17*c**2 - 13*c**3.
-3*c*(c - 1)*(c + 3)*(3*c - 1)
Let w(p) be the third derivative of p**5/60 - 17*p**4/56 + p**3/3 - 18*p**2. Determine m, given that w(m) = 0.
2/7, 7
Let d(v) be the third derivative of 0 + 0*v - 1/36*v**4 + 0*v**3 + 1/180*v**5 - 3*v**2. Determine c so that d(c) = 0.
0, 2
Let y be 3 + ((-448)/12)/14. Suppose -y*m + 0 + 1/3*m**2 = 0. Calculate m.
0, 1
Let z = -8 + 8. Let d(t) be the second derivative of 1/30*t**4 + 0*t**2 + z + t - 1/15*t**3. Solve d(g) = 0 for g.
0, 1
Let p(t) be the first derivative of 0*t - 3/16*t**4 - 9/20*t**5 + 1/2*t**6 + 2 + 0*t**2 + 0*t**3. Solve p(n) = 0 for n.
-1/4, 0, 1
Let j(m) be the first derivative of -m**7/420 + m**6/60 - m**5/20 + m**4/12 + m**3 + 3. Let i(d) be the third derivative of j(d). Factor i(a).
-2*(a - 1)**3
Let d(h) = 15*h**3 + h**2 + 2*h - 3. Let u be d(2). Factor -u*b**2 + 3*b**3 + 125*b**2 - 3*b**5.
-3*b**3*(b - 1)*(b + 1)
Suppose 2*c = 5*n - 14, 5*n = -c + 9 + 14. Let b(m) = -m**3 - 4*m**2 - 3*m + 2. Let i be b(-3). What is h in c*h**2 + h**3 + 0*h**i - 5*h**2 + 3*h**2 = 0?
-1, 0
Suppose 2*b = -b + 4*p - 20, -2*b = 4*p - 20. Let z be (2/12)/((-2)/(-8)). Factor 4/3*c**2 + b + z*c + 2/3*c**3.
2*c*(c + 1)**2/3
Let s be 2 - (3 - 3/2). Suppose 0 + 2*v**3 - 5/2*v**2 + s*v = 0. Calculate v.
0, 1/4, 1
Let h = -1/397 + 400/1191. Factor 0 - h*c**2 - 4/3*c**3 + c**4 + 2/3*c.
c*(c - 1)**2*(3*c + 2)/3
Let s(o) be the second derivative of o**4/3 + 4*o**3/3 + 2*o**2 + 6*o. Solve s(k) = 0.
-1
Let t(f) = -f**2 + f - 4. Let z(b) = -4. Suppose 4*j - 8 = -2*v + 6, 2*j + 4*v = -8. Let i = j - 8. Let u(l) = i*t(l) + 3*z(l). Factor u(g).
2*(g - 2)*(g + 1)
Let t = 2/529 + 523/1587. Let m(f) be the first derivative of -2/15*f**5 + 1 + 0*f + 2/9*f**3 - 2/3*f**2 + t*f**4. Factor m(v).
-2*v*(v - 2)*(v - 1)*(v + 1)/3
Suppose 5*b = -3*x - 2*x + 30, -8 = -4*x. Let -n + n + 6*n**2 + b*n = 0. What is n?
-2/3, 0
Let f(j) be the second derivative of -j**6/60 + j**5/20 - j**3/6 + j**2/4 - 13*j. Suppose f(a) = 0. What is a?
-1, 1
Let v(k) be the first derivative of -3*k**4/7 + 32*k**3/21 - 8*k**2/7 - 15. Factor v(w).
-4*w*(w - 2)*(3*w - 2)/7
Let a(k) = 2*k**2 - 9*k + 7. Let j(q) = 6*q**2 - 26*q + 20. Let v(d) = 14*a(d) - 5*j(d). Let v(o) = 0. Calculate o.
1
Factor -9*p - 21/2 + 3/2*p**2.
3*(p - 7)*(p + 1)/2
Suppose s + 38 = 20*s. Determine m so that 3/4 - 1/4*m**s + 1/2*m = 0.
-1, 3
Let n(l) be the second derivative of 1/180*l**5 + 2*l + 0*l**4 + 0*l**3 + 0 + 1/2*l**2. Let d(j) be the first derivative of n(j). Factor d(k).
k**2/3
What is d in -11*d - 5*d**3 - 3*d - 12*d**2 + d**3 - 4 + 2*d = 0?
-1
Let y be (-48)/(-9)*15/110. Find t, given that 8/11*t**3 + 2/11 - 2/11*t**2 - y*t = 0.
-1, 1/4, 1
Suppose 2*m = 3*m - 2. Let y(a) be the third derivative of 0 - 1/210*a**5 + 0*a**3 + 1/42*a**4 - 1/105*a**6 + 0*a + 1/245*a**7 + 4*a**m. Factor y(f).
2*f*(f - 1)**2*(3*f + 2)/7
Let r(i) be the second derivative of -4/45*i**5 + 1/36*i**6 - 2*i - 1/9*i**4 + 0 + 0*i**3 - 1/2*i**2. Let l(u) be the first derivative of r(u). Factor l(s).
2*s*(s - 2)*(5*s + 2)/3
Suppose -j - 7 = -10. Let v(z) be the third derivative of 1/6*z**j - 1/210*z**7 + 1/60*z**6 + 0*z + 0 + 0*z**5 + z**2 - 1/12*z**4. Factor v(h).
-(h - 1)**3*(h + 1)
Let y(t) be the first derivative of t**4/20 + t**3/5 + 3*t**2/10 + 4*t + 1. Let b(z) be the first derivative of y(z). Factor b(o).
3*(o + 1)**2/5
Determine s so that -94*s**2 - 361*s + 18*s**2 + 16*s**3 + 473*s - 48 = 0.
3/4, 2
Let l(d) = -d**3 + 4*d**2 + 4*d + 7. Let r be l(5). Suppose -6 + 0 = -r*u. Suppose -6*n**5 + 0*n**5 - 2*n + 4*n**5 + 4*n**u = 0. Calculate n.
-1, 0, 1
Let d(z) be the second derivative of -z**6/10 + 3*z**5/5 - 5*z**4/4 + z**3 + 2*z. Solve d(n) = 0 for n.
0, 1, 2
Let u(x) = 20*x**4 - 2*x**3 - 18*x**2 - 18*x. Let z(a) = a**4 - a**2 - a. Let f(k) = -2*u(k) + 36*z(k). Let f(q) = 0. Calculate q.
0, 1
Let p(f) = -f**3 - 43*f**2 + 85*f - 225. Let x be p(-45). Determine z, given that -14/5*z**5 - 38/5*z**4 + x - 6*z**3 + 4/5*z - 2/5*z**2 = 0.
-1, 0, 2/7
Let y(g) be the second derivative of -3*g + 0 + 0*g**4 + 1/21*g**7 - 2/15*g**6 + 0*g**3 + 0*g**2 + 1/10*g**5. Determine q so that y(q) = 0.
0, 1
Factor -3/4*t**3 + 3/4*t - 3/4*t**2 + 3/4.
-3*(t - 1)*(t + 1)**2/4
Let r(m) = 9*m**3 - 9*m**2 - 6*m + 6. Let y(p) = p**3 - p**2 - p + 1. Let t(u) = -r(u) + 6*y(u). Factor t(a).
-3*a**2*(a - 1)
Suppose 3*c = -2*c - 3*o + 12, -5*o = -c - 20. Factor -1/2*h**2 + 0*h + c.
-h**2/2
Let u(n) = 5*n**3 + 23*n**2 - 13*n + 9. Let w(l) = 2*l**3 + 8*l**2 - 4*l + 3. Let p(s) = -3*u(s) + 8*w(s). Factor p(r).
(r - 3)*(r - 1)**2
Factor q**3 + 4*q**4 + 2*q**3 - 4*q**2 - 3*q**3.
4*q**2*(q - 1)*(q + 1)
Let o(c) be the second derivative of c**5/140 - c**3/42 + 13*c. Determine n so that o(n) = 0.
-1, 0, 1
Find n such that 2/3*n + 0 - 4/9*n**2 - 2/9*n**3 = 0.
-3, 0, 1
Let g(f) be the third derivative of f**6/40 + 9*f**5/20 + 3*f**4 + 8*f**3 + 19*f**2. Find v, given that g(v) = 0.
-4, -1
Let t(h) be the second derivative of -2*h**7/21 - 2*h**6/15 + 2*h**5/5 + 2