 4. Let j(y) = c*i(y) - s(y). Factor j(w).
-3*w*(w - 1)*(w + 1)
Find q such that -1/5*q**2 + 2/5 - 1/5*q**4 + 3/5*q - 3/5*q**3 = 0.
-2, -1, 1
Suppose -5*p + 2*h - h - 234 = 0, -238 = 5*p - 2*h. Let m be p/(-40) + (-90)/24 + 4. Find y such that 9/5*y**4 - m*y**5 + 0 + 2/5*y + y**3 - 9/5*y**2 = 0.
-1, 0, 2/7, 1
Let z(y) be the third derivative of y**7/1260 + y**6/30 + 13*y**5/40 - 169*y**4/72 + 239*y**2. Factor z(n).
n*(n - 2)*(n + 13)**2/6
Let a be 1716/990 + (-7)/5. Factor -a*b**2 - 2/3 + b.
-(b - 2)*(b - 1)/3
Let c(l) be the third derivative of -2/105*l**7 + 0*l**5 + 0 + 0*l + 2/3*l**4 + 0*l**3 + 15*l**2 - 1/10*l**6. Let c(z) = 0. What is z?
-2, 0, 1
Let d be (70/78 + -1)/(-29 - (-85)/3). Let 36/13*g**2 - 8/13*g**3 + 14/13 - d*g**4 - 40/13*g = 0. Calculate g.
-7, 1
Let b = 12 + -16. Let x(j) = -j**3 + 19*j**2 + 16*j + 4. Let f(o) = -20*o**2 - 15*o - 5. Let n(u) = b*f(u) - 5*x(u). Factor n(r).
5*r*(r - 4)*(r + 1)
Suppose 15/2*s**3 - 6*s**4 + 3/2*s**5 + 0 - 3*s**2 + 0*s = 0. What is s?
0, 1, 2
Let f = -11 + 12. Let c = 0 - -2. Suppose 1 + 0*z**c - f + 2 + 2*z**2 - 4*z = 0. What is z?
1
Let q(a) be the third derivative of -a**8/6720 + a**7/336 - a**6/60 + a**5/30 + 9*a**2. Let s(h) be the third derivative of q(h). Factor s(f).
-3*(f - 4)*(f - 1)
Let x be 18/3*6/12 + 1. Suppose -2*h + 4 = -m, 5*h - 6 = 3*m + x. Factor -1/2*l**4 + 0*l + h*l**3 + 0 - 2*l**2.
-l**2*(l - 2)**2/2
Let m(w) be the second derivative of w**5/30 + 19*w**4/72 + 7*w**3/9 + w**2 + 72*w. Find k such that m(k) = 0.
-2, -3/4
Let v be 56 - 0/(-4) - 1. Let a = v - 55. Factor -4/5*i**2 - 2/5*i**3 - 2/5*i + a.
-2*i*(i + 1)**2/5
Solve 32*h - 16/9*h**3 + 224/9*h**2 + 64/9 - 14/9*h**5 - 20/3*h**4 = 0 for h.
-2, -2/7, 2
Suppose 495 - 493 = k. Let s(c) = 2*c**2 + 2*c. Let g be s(-2). Determine z so that 4/7*z**k - 2/7*z**3 + 2/7*z**5 + 0*z + 0 - 4/7*z**g = 0.
-1, 0, 1, 2
Let k(d) be the third derivative of d**8/168 - d**7/35 - d**6/6 - d**5/15 + 3*d**4/4 + 5*d**3/3 + d**2. Factor k(p).
2*(p - 5)*(p - 1)*(p + 1)**3
Find c such that -2/5*c**2 + 0 + 6/5*c = 0.
0, 3
Let d(t) be the first derivative of 3*t**4/4 - 9*t**2/2 - 6*t - 10. Solve d(y) = 0 for y.
-1, 2
Let v be (-55)/(-2) - (-4 - 7/(-2)). Determine j so that -v - 20*j - 12*j**2 + 10 + 10 = 0.
-1, -2/3
Determine d so that 0*d + 50*d**4 + 40/3*d**5 + 5*d**2 + 95/3*d**3 + 0 = 0.
-3, -1/2, -1/4, 0
Let p(x) be the second derivative of -12*x + 1/30*x**4 + 0 + 0*x**3 + 0*x**2. Suppose p(v) = 0. What is v?
0
Let r(k) be the third derivative of -k**8/84 + 4*k**7/105 - 2*k**5/15 + k**4/6 + 72*k**2. Let r(m) = 0. What is m?
-1, 0, 1
Suppose -10*q + 11*q = 90. Let c = q - 179/2. Factor 1/2*d**4 + 1/2 + c*d**5 + 1/2*d - d**2 - d**3.
(d - 1)**2*(d + 1)**3/2
Suppose 11*r + z - 11 = 9*r, -2*r + 17 = 3*z. Let q(w) be the second derivative of 1/3*w**2 + 0 - 1/36*w**r + 1/18*w**3 + w. Determine l, given that q(l) = 0.
-1, 2
Let o(v) = -5*v**2 + 41*v + 90. Let a(c) = 5*c**2 - 40*c - 85. Let f(t) = 4*a(t) + 5*o(t). Factor f(l).
-5*(l - 11)*(l + 2)
Let r = -311 + 182. Let g = 134 + r. Factor 2/13*l - 4/13*l**3 + 4/13*l**2 + 2/13*l**g - 2/13*l**4 - 2/13.
2*(l - 1)**3*(l + 1)**2/13
Let q = 11 + 6. Let p(o) = o**3 - 11*o**2 + 6*o + 6. Let h(c) = -2*c**3 + 32*c**2 - 17*c - 17. Let j(y) = q*p(y) + 6*h(y). What is t in j(t) = 0?
-1, 0
Let s(c) be the second derivative of c**4/60 - 28*c**3/15 + 392*c**2/5 - 6*c. What is d in s(d) = 0?
28
Let x(c) = c**5 + c**4 - c**3 - c**2 - 1. Let n(h) = 10*h**5 + 5*h**4 - 10*h**3 - 5*h**2 - 15. Let g(l) = -n(l) + 15*x(l). Factor g(o).
5*o**2*(o - 1)*(o + 1)*(o + 2)
Suppose 5*i + 16 = 26. Suppose 4*m = 5*m - i. Factor -3*p - 3*p**m + 0*p + 12 + 3*p.
-3*(p - 2)*(p + 2)
Let p(u) be the second derivative of 3*u**6/80 + 3*u**5/16 - 23*u**4/96 + u**3/12 + 339*u. Let p(y) = 0. What is y?
-4, 0, 1/3
Let n(g) = 2*g + 14. Let i be n(10). Determine t, given that i*t**4 + 19*t**3 - 19*t**4 + 10*t**2 + 26*t**3 + 20*t**4 = 0.
-1, -2/7, 0
Let y = -541 - -543. Factor -2*c**4 - 2 - 92/9*c**y + 22/3*c + 2/9*c**5 + 20/3*c**3.
2*(c - 3)**2*(c - 1)**3/9
Let c(k) = k**3 + 22*k**2 - 70*k + 127. Let h be c(-25). Solve 4*j**3 + 24*j - 74/5*j**h - 72/5 - 2/5*j**4 = 0 for j.
2, 3
Let p(s) be the first derivative of 5*s**6/72 + s**5/24 + 4*s**3 + 1. Let c(x) be the third derivative of p(x). Factor c(y).
5*y*(5*y + 1)
Determine u so that 162/5*u**2 + 42/5*u**3 + 12 + 174/5*u - 6/5*u**4 = 0.
-1, 10
Let n(f) be the third derivative of -f**5/30 + 2*f**4/3 - 7*f**3/3 - 6*f**2 - 2. Solve n(c) = 0 for c.
1, 7
Let k be (-2262)/(-504) + (-1)/(-12). Factor -4/7*h**2 + k*h - 64/7.
-4*(h - 4)**2/7
Let j(t) = 6*t**3 - 6*t**2 - 11*t. Let v(d) = 19*d**3 - 19*d**2 - 35*d + 1. Let i(y) = -21*j(y) + 6*v(y). Let i(o) = 0. Calculate o.
-1/2, 2
Let l(m) be the second derivative of 0*m**2 + 1/60*m**6 - 3*m + 0 - 1/24*m**4 - 3/40*m**5 + 1/4*m**3. Factor l(w).
w*(w - 3)*(w - 1)*(w + 1)/2
Suppose -4*o + 3*i + 33 = 0, 4*i - 9*i + 14 = o. Suppose o*z = 13*z - 8. Factor -4*k**2 + z*k**2 + 7*k**5 - 4*k**4 - 5*k**3 - 8*k**5.
-k**2*(k + 1)**2*(k + 2)
Let g be 3*1/(2/(-46)). Let d = g - -127. Factor -4*u**2 - d*u + u**2 + 49*u - 6.
-3*(u + 1)*(u + 2)
Let y(q) be the third derivative of -q**8/180 - 2*q**7/105 + 2*q**6/135 + q**3/6 + 7*q**2. Let s(i) be the first derivative of y(i). Factor s(w).
-4*w**2*(w + 2)*(7*w - 2)/3
Let z(n) = -3*n - 8. Let w be z(-4). Suppose -w = -2*i + 4. Let -2*c - c**3 + i*c**3 - c = 0. What is c?
-1, 0, 1
Let f(c) be the first derivative of -c**8/560 - c**7/350 + c**6/200 + c**5/100 + 17*c**2/2 + 1. Let z(r) be the second derivative of f(r). Solve z(j) = 0 for j.
-1, 0, 1
Suppose 3*d = 0, 7*p - 4*d - 20 = 3*p. Suppose -n + 9 = 5*s, -5*s - n + p = -2*s. Determine g so that 9/2*g + 3/4*g**s + 27/4 = 0.
-3
Let w(h) be the second derivative of h**6/30 + h**5/20 - h**4/2 + 55*h. Find u, given that w(u) = 0.
-3, 0, 2
Let d = -9 + 9. Let g(k) = k**2 - k + 3. Let l be g(d). Determine r so that -12*r**3 + 6*r**3 - 9*r**4 + 3*r**l + 8*r**2 + 4*r = 0.
-2/3, 0, 1
Factor 5*g**3 + 3*g**2 + 4*g**2 - 14*g**2 - 30*g + 2*g**2.
5*g*(g - 3)*(g + 2)
Let f(p) be the third derivative of 1/16*p**4 + 0*p - 14*p**2 + 1/40*p**6 - 1/8*p**3 + 7/80*p**5 + 0. Let f(s) = 0. What is s?
-1, 1/4
Let r be ((-42)/(-35))/(-1 - 32/(-20)). Suppose x = -2*s + 4*x - 12, 5*s - 4 = -x. Solve 0*t - 1/2*t**r + s = 0.
0
Let r(j) = j + 10. Let f be r(-8). Determine i, given that -6 - 3*i**2 + i**f - 10 - 2*i**2 + 16*i = 0.
2
Let q(d) be the third derivative of 1/120*d**5 + 1/6*d**3 + 0*d - 1/16*d**4 + 0 + 2*d**2. Suppose q(w) = 0. Calculate w.
1, 2
Let k(j) = -j**2 - 4 + 2*j**2 - 5 + 15*j - 16*j. Let d be k(4). Solve 23*m + 49 + 15*m**2 - 21*m**d + 25*m - 37 = 0 for m.
-1, -2/7, 2
Let n = -2/9 + 19/45. Suppose n*z**3 + 3/5*z**4 - 3/5*z**2 - 1/5*z + 0 = 0. Calculate z.
-1, -1/3, 0, 1
What is a in 1736*a - 4*a**5 - 17*a**3 - 3*a**4 + 3*a**2 - 1736*a + 2*a**3 + 19*a**5 = 0?
-1, 0, 1/5, 1
Suppose -r = -11*r + 80. Suppose r*s - 3*s = s. Factor 0*u**2 + 3*u**3 - 3/2*u**5 - 3/2*u + 0*u**4 + s.
-3*u*(u - 1)**2*(u + 1)**2/2
Let r(z) be the third derivative of -z**9/30240 + z**8/5040 - z**7/2520 + z**5/5 - 12*z**2. Let y(f) be the third derivative of r(f). Factor y(t).
-2*t*(t - 1)**2
Let p(d) = 9*d**2 + 29*d. Let m(t) = -11*t + t + 0*t + 0*t**2 - 3*t**2. Let v be (-60)/24 - 1/(-2). Let b(l) = v*p(l) - 7*m(l). Factor b(n).
3*n*(n + 4)
Solve -3/2*f**3 - 9*f**2 + 9 + 3/2*f = 0 for f.
-6, -1, 1
Let x(b) be the third derivative of -b**8/5760 + b**7/1120 - b**6/720 + b**5/5 + 11*b**2. Let n(q) be the third derivative of x(q). Factor n(v).
-(v - 1)*(7*v - 2)/2
Let j(p) = p**5 - p**3. Let z(u) = -u**5 - 3*u**4 - 4*u**3 - u. Let d(k) = -3*j(k) - z(k). Let g(m) = -m**4 - m**3 - m. Let r(i) = 2*d(i) + 6*g(i). Factor r(l).
-4*l*(l - 1)**2*(l + 1)**2
Suppose -v = 5*p + 12, 4*p + 169 - 46 = -5*v. Let y = 29 + v. Factor 10/7*w**y + 6/7 + 16/7*w.
2*(w + 1)*(5*w + 3)/7
Find g, given that -480*g**2 - 472 + 729*g + 176*g + 43*g + 4*g**3 = 0.
1, 118
Let w(o) be the first derivative of 11*o**8/840 + 8*o**7/175 + o**6/20 + o**5/75 + 9*o**2/2 + 10. Let u(q) be the second derivative of w(q). Factor u(x).
2*x**2*(x + 1)**2*(11*x + 2)/5
Let c(u) be the first derivative of -u**3/3 - 25*u**2/2 - 18. Factor c(f).
-f*(f + 25)
Let r = 311