 3
Find p, given that 2/9*p**2 + 0 - 4/9*p = 0.
0, 2
Let h(l) = -l**2. Let o(w) = w**2 - 6*w - 5. Let i be o(7). Let g(q) = -i*q**3 + q**3 - q - 1 - 7*q**2 - 2*q. Let r(b) = g(b) - 4*h(b). Solve r(k) = 0.
-1
Factor 10*v**2 - 12*v - 3*v**2 - 16 - 4*v**2 + v**2.
4*(v - 4)*(v + 1)
Let b(g) be the third derivative of 1/24*g**4 + 0 - 1/120*g**6 - 1/210*g**7 + 0*g + 3*g**2 + 1/60*g**5 + 0*g**3. Factor b(w).
-w*(w - 1)*(w + 1)**2
Let l(t) be the third derivative of t**8/1848 - t**7/1155 - t**6/660 + t**5/330 - t**2. Factor l(c).
2*c**2*(c - 1)**2*(c + 1)/11
Let l(n) = -n**3 - 4*n**2 + 4. Let o be l(-4). Suppose 5*q - 20 = 5*d - d, -o*d - 5*q = -20. Factor 0*v + 1/5*v**2 + 3/5*v**5 + 1/5*v**3 - v**4 + d.
v**2*(v - 1)**2*(3*v + 1)/5
Let m(o) be the third derivative of o**7/245 - o**6/84 - o**5/105 + 13*o**2. Suppose m(k) = 0. What is k?
-1/3, 0, 2
Let i be ((-224)/228 - -1)*-1. Let c = i - -20/57. Let 1/3*y**2 + 0 + 0*y + c*y**3 = 0. What is y?
-1, 0
Let k(h) be the first derivative of -h**6/10 + 3*h**5/25 + 3*h**4/20 - h**3/5 + 3. Factor k(z).
-3*z**2*(z - 1)**2*(z + 1)/5
Let j(u) be the third derivative of -2*u**2 + 1/420*u**7 + 0*u**3 + 0 - 1/240*u**6 - 1/120*u**5 + 1/48*u**4 + 0*u. Solve j(h) = 0.
-1, 0, 1
Let u(g) be the first derivative of 0*g**2 - 1/12*g**3 + 1/4*g - 3. Factor u(y).
-(y - 1)*(y + 1)/4
Suppose 2*c + 0*c - a + 39 = 0, -4*a = 5*c + 78. Let p = c - -37/2. Factor -3/2*v**2 - p*v**3 - 1/2 - 3/2*v.
-(v + 1)**3/2
Let l = 3/40 - -27/40. Suppose -3/2 - l*m**3 + 9/4*m + 0*m**2 = 0. Calculate m.
-2, 1
Let s(w) = w**3 - 19*w**2 + 13*w. Let j(d) = 4*d**3 - 56*d**2 + 40*d. Let t(l) = -3*j(l) + 8*s(l). Factor t(y).
-4*y*(y - 2)**2
Let o(g) = g**3 + 2*g**2 - 3*g + 2. Suppose 0*d - 5*z = 4*d + 7, -5*z + 17 = -4*d. Let b be o(d). Factor -2/3*q**3 + 2/3*q + 2/3 - 2/3*q**b.
-2*(q - 1)*(q + 1)**2/3
Suppose 4*y - 4 = -3*u, 2*u = 6*u + 16. Determine w, given that -y*w**4 - w**2 + w**4 + 5*w**3 - w**4 = 0.
0, 1/4, 1
Suppose -9*w + 8*w + 1 = 2*i, 5*w = i - 17. Let s(k) be the first derivative of -7/2*k**i - 3 + 5/3*k**3 + 2*k. Factor s(b).
(b - 1)*(5*b - 2)
Let r(s) be the third derivative of -s**9/13608 - s**8/3780 + s**6/810 + s**5/540 + s**3/6 + 4*s**2. Let w(z) be the first derivative of r(z). Factor w(c).
-2*c*(c - 1)*(c + 1)**3/9
Let y(q) be the third derivative of q**7/1400 - q**6/600 + 7*q**3/6 - 3*q**2. Let n(a) be the first derivative of y(a). Factor n(o).
3*o**2*(o - 1)/5
Let d be 1/(-4)*-4*56. Let u be (-13)/52 - (-30)/d. Factor 0 + u*n - 2/7*n**2.
-2*n*(n - 1)/7
Suppose 5*t - 25 = 0, 0*t + 2*t = 3*h + 7. Let x(p) = p**2 - p - 1. Let g(s) = 3*s**2 - 3*s - 1. Let n(j) = h*g(j) - 5*x(j). Factor n(a).
-2*(a - 2)*(a + 1)
Let n(t) be the third derivative of t**8/1176 - t**7/735 - t**6/70 + t**5/15 - 11*t**4/84 + t**3/7 + 23*t**2. Determine f so that n(f) = 0.
-3, 1
Suppose -4 = -5*u + u. Let a be (-2)/(u/(2/(-16))). Factor a*h**4 + 1/4 + h**3 + 3/2*h**2 + h.
(h + 1)**4/4
Let b(k) = -5*k**4 - 5*k**3 + 16*k**2 - 6*k - 11. Let m(s) = -s**4 - s**3 + 3*s**2 - s - 2. Let z(j) = 6*b(j) - 33*m(j). Let z(o) = 0. Calculate o.
-1, 0, 1
Let a(s) be the second derivative of -s**2 + 1/12*s**4 + 0 - s - 1/6*s**3. What is r in a(r) = 0?
-1, 2
Suppose 23 - 7 = 4*h. Suppose 4*i - 10 = 3*r + 6, r - h = -i. Factor 0 + 2*o**3 + 8/3*o - 4*o**2 - 1/3*o**i.
-o*(o - 2)**3/3
Let t(j) be the third derivative of 7/75*j**5 - 11/60*j**4 + 1/120*j**8 + 1/75*j**6 - 16/525*j**7 + 2/15*j**3 + 0*j + 0 - 4*j**2. Solve t(m) = 0 for m.
-1, 2/7, 1
Find z such that -11*z - 8*z**2 + 7*z + 9*z**3 + 4*z**4 - 4*z**5 + 4 - z**3 = 0.
-1, 1
Let j(q) be the first derivative of -q**8/168 - q**7/105 + q**6/60 + q**5/30 - 3*q**2 - 3. Let l(m) be the second derivative of j(m). Factor l(b).
-2*b**2*(b - 1)*(b + 1)**2
Solve -1/3*q - 2/3 + 1/3*q**2 = 0.
-1, 2
Let n(f) be the second derivative of -f**6/360 + f**5/60 - f**3/2 + 2*f. Let q(t) be the second derivative of n(t). Let q(x) = 0. Calculate x.
0, 2
Let a = 4 - 1. What is w in 6*w**a - 9*w**2 - 2*w**3 + 5*w**2 = 0?
0, 1
Let n be 1/(-2)*0 + 4/6. Let k(z) be the first derivative of -2/3*z + n*z**2 + 3 - 2/9*z**3. Factor k(h).
-2*(h - 1)**2/3
Let s(c) = 5*c**2 - 27*c + 1. Let l(o) = o**2 - 5*o. Let u(h) = -11*l(h) + 2*s(h). Let u(k) = 0. What is k?
-1, 2
Let a be (2/7)/(2/14). Factor -5*v**4 - a + 4*v**2 + v**4 + 0 + 2*v**4.
-2*(v - 1)**2*(v + 1)**2
Let j(c) be the second derivative of c**6/10 - 9*c**5/20 + 3*c**4/4 - c**3/2 - 8*c. Factor j(y).
3*y*(y - 1)**3
Factor 49/2*h**2 + 1/2 + 7*h.
(7*h + 1)**2/2
Suppose 36*h + 12*h**2 + 4/3*h**3 + 36 = 0. Calculate h.
-3
Let r(u) = u**2 + u + 1. Let j(t) = -6*t**2 - 11*t - 4. Let i(b) = 3*j(b) + 21*r(b). Let i(a) = 0. What is a?
1, 3
Let l = -1497/7 + 215. Factor -l*q + 2/7*q**4 - 8/7*q**3 + 12/7*q**2 + 2/7.
2*(q - 1)**4/7
Let w(m) = m + 8. Let j be w(-6). Suppose -j*o**3 + 3*o + o**4 - o**2 - o + o**3 - o = 0. Calculate o.
-1, 0, 1
Let y = -15 + 21. Let c(w) be the third derivative of -1/60*w**5 - w**2 + 0*w + 0 + 1/120*w**y + 0*w**3 - 1/24*w**4 + 1/210*w**7. Suppose c(h) = 0. Calculate h.
-1, 0, 1
Let d(m) = -m**3 - 5*m**2 - 6*m - 1. Let v be d(-4). Let p = -5 + v. Find l, given that 1 - 2*l - 2*l**p - 1 = 0.
-1, 0
Let h(g) be the first derivative of -4*g**5/15 + 5*g**4/2 - 74*g**3/9 + 11*g**2 - 6*g - 21. Find q such that h(q) = 0.
1/2, 1, 3
Let z = -41 + 43. Let t(h) be the third derivative of -h**z + 1/30*h**5 + 0*h - 1/4*h**4 + 2/3*h**3 + 0. Find l such that t(l) = 0.
1, 2
Let x(q) be the third derivative of -q**6/420 - q**5/210 + 7*q**2. Solve x(h) = 0 for h.
-1, 0
Let i(h) = h**2 - h - 1. Let t(m) = -m**3 + 4*m**2 - 2*m - 1. Let r be t(2). Let k be i(r). Solve -1/5*f**4 + 0 + f**2 - 1/5*f**k + 2/5*f + 3/5*f**3 = 0.
-1, 0, 2
Find f such that 380*f - 25*f**2 + 4*f**3 + 45 - 2*f**3 - 365*f + 3*f**3 = 0.
-1, 3
Let y(n) be the first derivative of -3*n**5/10 + 27*n**4/8 - 21*n**3/2 + 57*n**2/4 - 9*n + 13. Factor y(d).
-3*(d - 6)*(d - 1)**3/2
Let v(f) be the first derivative of -f**4/10 - 8*f**3/5 - 48*f**2/5 - 128*f/5 - 43. Factor v(b).
-2*(b + 4)**3/5
Let q(b) be the second derivative of -b + 0 + 7/12*b**4 + 1/6*b**3 + 0*b**2 + 13/16*b**5 + 5/12*b**6. Let q(t) = 0. What is t?
-1/2, -2/5, 0
Let z(j) be the first derivative of j**4/12 + 5*j**3/12 + j**2/2 + j + 3. Let q(v) be the first derivative of z(v). Suppose q(s) = 0. Calculate s.
-2, -1/2
Suppose 0 - 1 - 2*z**2 + 1 = 0. What is z?
0
Factor -8/7*y**2 + 6/7*y + 36/7 - 2/7*y**3.
-2*(y - 2)*(y + 3)**2/7
Solve m**3 + 0*m**2 + m**4 + 0 + 0*m + 1/4*m**5 = 0 for m.
-2, 0
Find t such that 0*t - 2/7*t**2 + 0 + 2/7*t**3 = 0.
0, 1
Let t(b) = 67*b**3 + 197*b**2 + 199*b + 41. Let i(h) = 45*h**3 + 131*h**2 + 133*h + 27. Let w(f) = -7*i(f) + 5*t(f). Determine s, given that w(s) = 0.
-2, -1, -2/5
Solve -7/10*o - 6/5 - 1/10*o**2 = 0 for o.
-4, -3
Let z = 0 + 3. Find o such that 5 + z*o**2 - 5 + 3*o = 0.
-1, 0
Suppose -2*u + 5*u = 1446. Let l be u/12 - (-1)/3. Factor -20*z - 117/2*z**2 - 2 - l*z**3.
-(z + 1)*(9*z + 2)**2/2
Factor -2/3*v**3 + 2*v - 5/3*v**2 + 0 + 1/3*v**4.
v*(v - 3)*(v - 1)*(v + 2)/3
Let r(p) = 5*p**2 - 14*p - 4. Let w(k) = 4*k**2 - 15*k - 4. Let f(y) = -3*r(y) + 2*w(y). Let f(b) = 0. Calculate b.
-2/7, 2
Let o(k) be the second derivative of 0 + k + 0*k**2 - 1/63*k**7 - 2/135*k**6 - 1/27*k**3 + 2/45*k**5 + 1/27*k**4. Solve o(a) = 0.
-1, 0, 1/3, 1
Let o(m) = 8*m - 5. Let y be o(-8). Let s = y - -485/7. Factor s*i**3 - 2/7*i + 2/7*i**2 - 2/7.
2*(i - 1)*(i + 1)**2/7
Let p(i) be the third derivative of -i**7/3780 - i**6/1620 + i**3/2 - 2*i**2. Let l(d) be the first derivative of p(d). Find r, given that l(r) = 0.
-1, 0
Let q = 7 - 5. Determine i, given that 0*i**2 - 6*i**q + 5*i**2 = 0.
0
Factor -45/4*j**3 - 10 - 75/2*j**2 - 35*j.
-5*(j + 2)*(3*j + 2)**2/4
Let j(l) be the first derivative of l**6/27 - 2*l**5/45 - l**4/6 + 10*l**3/27 - 2*l**2/9 - 19. Suppose j(c) = 0. What is c?
-2, 0, 1
Let s(g) = -g + 5. Let v be s(4). Let l(q) = -q**3 + q**2 + q - 1. Let y be l(v). Determine c so that 0*c + 4/5*c**2 + y - 2*c**3 = 0.
0, 2/5
Determine g, given that -275/4*g**3 + 15/2*g**2 + 35*g - 125/4*g**4 - 10 = 0.
-2, -1, 2/5
Let f(u) be the third derivative of -u**6/24 + u**5/4 - 5*u**4/8 + 5*u**3/6 + 28*u**2. What is w in f(w) = 0?
1
Let j(w) be the second derivat