1 - 56*o**2. Let y(k) = -15*t(k) - 6*u(k). Factor y(z).
3*z*(3*z - 2)
Let x(y) be the first derivative of 5*y**4/24 - 95*y**3/3 + 1805*y**2 - 137180*y/3 + 240. Factor x(v).
5*(v - 38)**3/6
Suppose -15*v = -18*v. Let o be (v - (-3 - -1)) + 77/(-44). Factor o - 1/4*j - 1/2*j**2.
-(j + 1)*(2*j - 1)/4
Let a(w) = -219*w**5 + 432*w**4 - 222*w**3 + 9*w**2 - 5*w. Let j(s) = -110*s**5 + 216*s**4 - 111*s**3 + 5*s**2 - 3*s. Let h(b) = -6*a(b) + 10*j(b). Factor h(k).
2*k**2*(k - 1)**2*(107*k - 2)
Let c = 244/5 - 3889/80. Let l(a) be the second derivative of c*a**5 + 0*a**2 + 3/16*a**4 - 5/24*a**6 + a + 1/24*a**3 + 0. Factor l(q).
-q*(q - 1)*(5*q + 1)**2/4
Let g = 90153/4 + -22538. Let -6*j + g*j**2 + 36 = 0. What is j?
12
Let l(m) be the second derivative of -m**5/4 - 47*m**4/12 - 29*m**3/3 - 8*m**2 + 19*m + 1. Let l(b) = 0. Calculate b.
-8, -1, -2/5
Let c be 2*(-3)/(-6)*3. Suppose 0*o - 2*o**3 + c*o**3 - o**2 + o + 3*o**2 = 0. Calculate o.
-1, 0
Let z(m) = 4*m**2 + m + 2. Let p be z(0). Factor 14*i - 3*i**2 - 17*i + i**2 + p - 2*i**3 + 5*i.
-2*(i - 1)*(i + 1)**2
Let -27/2 + 1/2*i**2 + 3*i = 0. Calculate i.
-9, 3
Suppose -6*r + 197 = 179. Let b(c) be the first derivative of 49/6*c**6 + 20/3*c**r - 14*c**5 + 4 + 2*c**2 + 0*c - 3/4*c**4. Solve b(f) = 0 for f.
-2/7, 0, 1
Factor -720*g - 1836 - 35*g**2 + 12*g**2 - 68*g**2 + 4*g**2 - 3*g**3.
-3*(g + 6)**2*(g + 17)
Determine i, given that -5/3*i**5 - 17/3*i**4 + 0 + 2*i - 1/3*i**3 + 17/3*i**2 = 0.
-3, -1, -2/5, 0, 1
Let s(n) be the first derivative of 0*n**2 + 2 - 1/180*n**6 + 5*n + 1/72*n**4 + 1/60*n**5 - 1/18*n**3. Let p(z) be the first derivative of s(z). Factor p(b).
-b*(b - 2)*(b - 1)*(b + 1)/6
Let r(f) be the first derivative of -f**3/30 + 7*f**2/4 - 383. Let r(u) = 0. What is u?
0, 35
Let m(y) = -5*y**3 + 40*y**2 + 40*y - 5. Let g(b) = 2*b**3 - 21*b**2 - 20*b + 3. Let x(w) = 5*g(w) + 3*m(w). What is c in x(c) = 0?
-1, 0, 4
Let k = -2170 + 2172. Let z(c) be the second derivative of 0*c**k - 3/80*c**5 + 0 - 1/16*c**4 - 1/120*c**6 - 1/24*c**3 + 2*c. Solve z(w) = 0 for w.
-1, 0
Solve -3*d**3 - 18 + 15*d + 12 + 6*d**3 - 12*d**2 = 0.
1, 2
Let t(x) be the first derivative of -x**8/2240 - x**7/224 - x**6/60 - x**5/40 - 5*x**3/3 + 6. Let d(w) be the third derivative of t(w). Factor d(o).
-3*o*(o + 1)*(o + 2)**2/4
Let f be 20/(-5 + 16/4). Let h = f - -22. Factor h*t**2 + 0*t**3 + 24*t - t**3 - 25*t.
-t*(t - 1)**2
Let s(b) be the third derivative of 0*b**3 + 0*b**4 + 10*b**2 - 1/90*b**6 - 1/180*b**5 - 1/210*b**7 + 0 + 0*b. Factor s(v).
-v**2*(v + 1)*(3*v + 1)/3
Let r(l) be the first derivative of -1/12*l**4 - 6 - 1/6*l**3 + 3*l + 1/20*l**5 + 1/2*l**2. Let c(k) be the first derivative of r(k). Factor c(d).
(d - 1)**2*(d + 1)
Let x(d) = -23*d + 207. Let q be x(9). Let i(w) be the first derivative of 0*w**3 + w**5 + 2 + q*w + 0*w**2 - 1/2*w**4. Solve i(k) = 0.
0, 2/5
Factor 216 - 44/3*z**3 + 2/3*z**4 + 314/3*z**2 - 264*z.
2*(z - 9)**2*(z - 2)**2/3
Suppose 0 = 2*u - 11*u. What is y in 6 - 47*y + u*y**2 + 2*y**2 + 39*y = 0?
1, 3
Let c(p) be the first derivative of p**3/4 + 3*p**2/4 - 18*p + 38. Determine h so that c(h) = 0.
-6, 4
Let w(p) be the third derivative of p**8/1344 + p**7/420 - p**6/120 - p**5/30 - 305*p**2. Solve w(c) = 0 for c.
-2, 0, 2
Suppose 17*x - 19 = 49. Let s(c) be the second derivative of 2/21*c**x + 1/70*c**5 + 6*c + 0 - 4/105*c**6 + 0*c**2 - 1/21*c**3. Let s(r) = 0. Calculate r.
-1, 0, 1/4, 1
Let j = 65837/131682 - -2/65841. Let t(g) = g**3 - 4*g**2 + g. Let r be t(4). Let a**4 + a**3 - r*a**2 - j*a**5 - 1 + 7/2*a = 0. Calculate a.
-2, 1
Suppose 8*q - 5*q = w + 4, q = 2. Suppose 34/5*k**w + 2*k**3 + 8/5 + 32/5*k = 0. Calculate k.
-2, -1, -2/5
Let a(w) be the second derivative of 3*w**5/20 - 11*w**4/12 + 3*w. Let l(n) = 2*n**3 - 4*n**3 - 6*n**2 + 4*n**3. Let b(r) = -4*a(r) + 7*l(r). Factor b(q).
2*q**2*(q + 1)
Let b be (11 + 123/(-12))*8/14. Let r = 21/4 - 123/28. What is g in -6/7*g**4 + 3/7*g**5 - b*g + r*g**2 + 0*g**3 + 0 = 0?
-1, 0, 1
Factor -184*a - 909 - 2129 - a**2 + 130 - 3425 - 2131.
-(a + 92)**2
Let k be (-9)/(-2)*12/27. Factor -289*l + 280*l - l**2 + 4*l**k.
3*l*(l - 3)
Factor -6*m + 5 + 9/4*m**2 - 1/4*m**3.
-(m - 5)*(m - 2)**2/4
Let s(z) be the first derivative of 0*z**2 + z + 0*z**3 + 1/12*z**4 - 1/20*z**5 - 10. Let v(i) be the first derivative of s(i). Let v(d) = 0. Calculate d.
0, 1
Determine a, given that 0 - 4/7*a**3 + 2*a**2 - 4/7*a - 6/7*a**4 = 0.
-2, 0, 1/3, 1
Let j = -893/140 - -45/7. Let r(f) be the first derivative of 1/16*f**4 + 2 - 1/8*f**2 + 0*f + 1/12*f**3 - j*f**5. Factor r(z).
-z*(z - 1)**2*(z + 1)/4
Let y be 27/(-18)*20/(-6). Let -8*g**y - 6*g**5 + 15*g**5 = 0. What is g?
0
Let p be (-7)/4*(7 - 3). Let o = p + 10. Factor -o*k**5 - 7*k**4 + 7*k**4.
-3*k**5
Let h(j) be the first derivative of -j**7/630 - j**6/90 - j**5/60 + j**2 - 16*j + 28. Let v(t) be the second derivative of h(t). Factor v(f).
-f**2*(f + 1)*(f + 3)/3
Let q(i) be the first derivative of -3*i**4/4 + 32*i**3 - 261*i**2/2 + 461. Determine r so that q(r) = 0.
0, 3, 29
Find q such that -22*q**4 - 577 - 73*q**2 + q**4 + 316*q**2 - 186*q + 36*q**3 + 505 = 0.
-3, -2/7, 1, 4
Suppose -3 = -4*i + b, 3*i - 11 = -8*b + 7*b. Let l(m) be the second derivative of 1/5*m**3 + 0*m**i - m + 0 - 9/20*m**4. Factor l(y).
-3*y*(9*y - 2)/5
Suppose -5*o - 72 = -v, v + 2*v = 3*o + 36. Let l be (o/9)/(12/(-54)). Determine n so that l*n**2 + n + 0 + 125/8*n**4 + 75/4*n**3 = 0.
-2/5, 0
Let q(a) be the second derivative of -a**4/6 - 9*a**3 - 26*a**2 - 54*a. Factor q(r).
-2*(r + 1)*(r + 26)
Let n(d) = d**2 + 342*d - 343. Let q be n(1). Let w = -304 + 922/3. Factor 8/3*k**4 + q + 0*k - w*k**3 + 2/3*k**2.
2*k**2*(k - 1)*(4*k - 1)/3
Let r(s) be the first derivative of 1/9*s**3 - 1/3*s + 0*s**2 + 27. Solve r(u) = 0 for u.
-1, 1
Let d(j) be the first derivative of 14/55*j**5 - 12/11*j**2 - 3 + 8/11*j + 6/11*j**4 - 2/3*j**3. Find n such that d(n) = 0.
-2, -1, 2/7, 1
Let t(q) be the third derivative of 3*q**5/140 - 5*q**4/56 - q**3/7 - 80*q**2 - 2*q. Determine f, given that t(f) = 0.
-1/3, 2
Let i = 133 - 136. Let c(v) = -22*v**2 + 24*v + 10. Let w(y) = 5 - 7*y**2 + 4*y - 2 + 4*y. Let m(j) = i*c(j) + 10*w(j). Factor m(z).
-4*z*(z - 2)
Let l(m) be the third derivative of -m**6/420 - m**5/105 + m**4/84 + 2*m**3/21 - 116*m**2. Solve l(b) = 0.
-2, -1, 1
Let p(v) be the third derivative of -1/672*v**8 + 0 + 0*v**3 + 0*v**5 + 9*v**2 + 0*v**4 - 1/15*v**6 + 0*v + 2/105*v**7. Solve p(h) = 0.
0, 4
Let z = 191/642 + -14/107. Solve -z - 1/2*j**2 + 2/3*j = 0.
1/3, 1
Let l(t) = 46*t - 43. Let g be l(1). Let n(d) be the first derivative of -1/5*d**g + 3/10*d**2 + 6/5*d + 1. Factor n(p).
-3*(p - 2)*(p + 1)/5
Let y(h) = -h**3 - h**2 - 3*h - 5. Let p be y(-2). Factor p*x**3 - 10*x + 8*x**2 - 5*x**4 + 12*x**2 - 10*x.
-5*x*(x - 2)*(x - 1)*(x + 2)
Suppose 3*d + 2*d - 4*o + 5 = 0, 0 = 5*d + 5*o - 40. Factor 3*l**2 + l**2 + l - 4*l**d + 5*l + 2*l.
-4*l*(l - 2)*(l + 1)
Let v(u) be the first derivative of 5*u**3/3 + 25*u**2/2 + 21. Determine d, given that v(d) = 0.
-5, 0
Factor 0 - 32/13*c**2 + 32/13*c - 2/13*c**3 + 2/13*c**4.
2*c*(c - 4)*(c - 1)*(c + 4)/13
Suppose -4*m = -m. Let g(s) be the second derivative of m*s**2 - 2*s + 5/72*s**4 + 1/18*s**3 + 0. Suppose g(n) = 0. What is n?
-2/5, 0
Factor 55/2*k - 50 - 5/4*k**2.
-5*(k - 20)*(k - 2)/4
Suppose -5*j**3 - 45/4 + 15/4*j + 10*j**2 = 0. What is j?
-1, 3/2
Let l = -81202859/109487 + 2/328461. Let z = -735 - l. Factor -z - 5/3*h**2 - 25/3*h.
-5*(h + 1)*(h + 4)/3
Let y(s) = 6*s**3 - 73*s**2 + 56*s + 875. Let b(q) = 4*q**3 - 49*q**2 + 38*q + 583. Let d(j) = 7*b(j) - 5*y(j). Factor d(t).
-2*(t - 7)**2*(t + 3)
Solve 9*l**3 - 28/5*l + 7/5*l**4 - 2/5*l**5 + 0 + 32/5*l**2 = 0 for l.
-2, 0, 1/2, 7
Let r(l) = l**5 - l**4 + l**2 + l + 1. Let f(v) = -5*v**5 - 5*v**4 + 33*v**3 - 11*v**2 - 56*v - 6. Let q(z) = -5*f(z) - 30*r(z). Find y such that q(y) = 0.
-1, 0, 2, 5
Let v(g) be the third derivative of -g**6/1020 - 2*g**5/255 - g**4/68 + g**2 - 520*g. Factor v(y).
-2*y*(y + 1)*(y + 3)/17
Factor -55*g + 91*g**2 - 44*g**2 - 52*g**2.
-5*g*(g + 11)
Suppose -58 = -b + m, -4*b + m = -0*m - 238. Let o be (-16)/(-6)*45/b. What is p in 2*p**2 - o*p + 3*p**2 - 2*p**2 - 4*p = 0?
0, 2
Let k be (-3)/(-2*(-4)/8) + 5. Let b**2 + 0*b**4 - 7