(n) = n**3 + 12*n**2 + 9*n - 20. Let w be f(-11). Solve -11 + 28*q**4 + 11 + 3*q**2 + 5*q**w - 36*q**3 = 0 for q.
0, 2/7, 1
Let b(p) be the first derivative of -5*p**2 - 5/4*p**4 + 4 + 0*p - 5*p**3. Factor b(f).
-5*f*(f + 1)*(f + 2)
Let v = 218/3 - 72. Let w = 1181 + -3542/3. Factor v*o**4 + 0*o**3 - w*o - 2/3*o**2 + 0 + 1/3*o**5.
o*(o - 1)*(o + 1)**3/3
Find u such that 60*u + 0 - 3/2*u**2 = 0.
0, 40
Suppose 90*f = 72*f + 72. Find s such that -10*s**2 + 0 - 14*s**f + 4/3*s + 68/3*s**3 = 0.
0, 2/7, 1/3, 1
Let j = 40 + -38. Let n(q) be the first derivative of -3/2*q**j + 4 + 1/3*q**3 + 2*q. Determine v so that n(v) = 0.
1, 2
Suppose -2*k = -5*x - 49 - 134, -4*x - 271 = -3*k. Factor 45*m**3 - 4*m**2 + 48*m**3 - k*m**3.
4*m**2*(m - 1)
Let v(h) = -3 - h**2 + 0 + 2 + 2*h + 7. Let y be v(3). Suppose 3*x**2 - 32*x**4 - 40*x**y - 13*x + 17*x - 7*x**2 = 0. What is x?
-1, -1/2, 0, 1/4
Suppose 3*q = -w + 18, -5*w + 0*q = -2*q - 107. Let k = 24 - w. Factor 1/4*i**3 - k*i**2 - 1/2 - 11/4*i + i**4.
(i - 2)*(i + 1)**2*(4*i + 1)/4
Let w(h) be the third derivative of h**8/840 + 2*h**7/525 - h**6/100 - 2*h**5/75 + h**4/15 + 2*h**2 - 20*h. What is s in w(s) = 0?
-2, 0, 1
Let b(y) be the third derivative of -y**5/300 + y**4/30 + 2*y**3/5 + 23*y**2 - 2. Factor b(j).
-(j - 6)*(j + 2)/5
Let n(d) be the first derivative of 2 + 0*d - 1/18*d**4 + 0*d**2 - 2/27*d**3. Let n(a) = 0. What is a?
-1, 0
Solve 1/6*h**4 + 4 + 5/6*h**3 - 10/3*h - 5/3*h**2 = 0.
-6, -2, 1, 2
Factor 114/7*g**2 - 3/7*g**3 + 0 - 1083/7*g.
-3*g*(g - 19)**2/7
Suppose 6 + 8 = 7*b. Let -2*l**b - 70*l - 215 - 3*l**2 - 29 - 1 = 0. Calculate l.
-7
Let g(l) be the first derivative of l**6/420 - l**4/28 - 2*l**3/21 + l**2/2 + 12. Let u(m) be the second derivative of g(m). Factor u(f).
2*(f - 2)*(f + 1)**2/7
Let h(z) be the second derivative of -20/3*z**3 + 0 - 33*z - 40*z**2 - 5/12*z**4. Factor h(o).
-5*(o + 4)**2
Factor 219501 + 87*p**2 + 1/3*p**3 + 7569*p.
(p + 87)**3/3
Let f(r) be the third derivative of -1/5*r**5 + 0*r + 8*r**2 + 0 - 1/6*r**4 + 4/3*r**3 + 2/105*r**7 + 1/30*r**6. Factor f(b).
4*(b - 1)**2*(b + 1)*(b + 2)
Let i(b) be the third derivative of 1/6*b**3 - 1/30*b**5 - 11/80*b**6 + 45*b**2 + 0*b + 25/144*b**4 + 0. Factor i(c).
-(3*c + 1)**2*(11*c - 6)/6
Suppose -4*a + 8*a - 32 = 0. Let m be -40*(-3)/273 + a/(-52). Solve -4/7*o**2 + 2/7*o**3 + 0 + m*o = 0.
0, 1
Let x(b) be the second derivative of b**5/140 + 61*b**4/84 + 899*b**3/42 - 961*b**2/14 - 19*b + 4. Find r, given that x(r) = 0.
-31, 1
Let i(o) = 3*o**2 + o - 2. Let w(q) = -6*q**2 - 3*q + 4. Let z(b) = 5*i(b) + 2*w(b). Let u(y) = -2*y**2 + 2. Let j(x) = 5*u(x) + 4*z(x). Factor j(a).
2*(a - 1)**2
Find a such that 394*a**3 + 174*a**2 + 3698 - 1178*a - 2692*a - 201*a**3 - 195*a**3 = 0.
1, 43
Let z(t) be the second derivative of 2*t**7/105 - t**6/15 - t**5/5 + 4*t**4/3 - 8*t**3/3 - 7*t**2 + 28*t. Let l(v) be the first derivative of z(v). Factor l(c).
4*(c - 2)*(c - 1)**2*(c + 2)
Let h(x) be the first derivative of x**4/4 - 3*x**3 - 15*x - 7. Let p(a) be the first derivative of h(a). Solve p(r) = 0.
0, 6
Suppose u + 7 = 11. Factor -4*l**u + 9*l**3 + 0*l**4 - 4*l**2 - 17*l**3.
-4*l**2*(l + 1)**2
Let r(g) be the third derivative of g**6/180 + 19*g**5/90 + 20*g**4/9 - 100*g**3/9 - 79*g**2. Factor r(k).
2*(k - 1)*(k + 10)**2/3
Let r(u) be the second derivative of u**7/126 + 5*u**6/18 + 28*u**5/15 - 146*u**4/9 + 56*u**3/9 + 392*u**2/3 + u - 238. Find h such that r(h) = 0.
-14, -1, 2
Factor -11*u**3 + 0*u**2 - u**3 - 4*u**4 - 4*u - 12*u**2.
-4*u*(u + 1)**3
Let r(a) be the first derivative of -3*a**4/8 + a**3 + 38. Solve r(o) = 0 for o.
0, 2
Factor 11264*n - 14355*n**4 - 113*n**3 + 7744 + 14357*n**4 + 4558*n**2 - 57*n**3 - 1210*n**2.
2*(n - 44)**2*(n + 1)*(n + 2)
Factor -14*f**2 + 4*f**3 - 3*f - 2*f**3 - 12*f + 15*f.
2*f**2*(f - 7)
Factor -252*c**2 + 120*c**3 - 272*c**4 + 86*c + 42*c - 265*c**4 + 541*c**4.
4*c*(c - 1)**2*(c + 32)
Let u(x) be the first derivative of -1 + 1/9*x**4 + 6*x + 0*x**2 + 0*x**3. Let k(a) be the first derivative of u(a). Determine p so that k(p) = 0.
0
Let v be 3168/224 + (-10 - 3). Let y be 1/(0 + 7/2). Factor y*x**2 - v*x + 8/7.
2*(x - 2)**2/7
Factor 8*m**4 + 3*m**3 + 2*m**4 + 21*m**3 + 2*m**4 - 96*m**2 + 128*m - 14*m**4.
-2*m*(m - 4)**3
Find b such that -21/8*b**3 + 3/4*b**5 + 3/8*b**4 - 3/4 + 15/8*b + 3/8*b**2 = 0.
-2, -1, 1/2, 1
Let b(q) be the third derivative of -q**7/560 + q**6/40 - 9*q**5/80 + q**4/4 + 22*q**3/3 - 42*q**2. Let v(k) be the first derivative of b(k). Factor v(c).
-3*(c - 4)*(c - 1)**2/2
Let r be (15/35)/((-12)/(-21)). Let w(j) be the second derivative of r*j**4 - 5*j - 3*j**2 + 21/20*j**5 - 3/2*j**3 + 3/10*j**6 + 0. Factor w(b).
3*(b + 1)**3*(3*b - 2)
Let k = 11725 + -11722. Solve 1/8*l**4 - 1/8*l**2 + 0 + 3/8*l**k - 3/8*l = 0.
-3, -1, 0, 1
Let h be (-2 - (-10)/15)/(264/(-36)). Find y, given that -6/11*y**2 + 8/11 - h*y**3 + 0*y = 0.
-2, 1
Let h(y) = 3*y**3 - 2*y - 3. Let i be h(-1). Let c be (-15)/(-42)*i*(-1)/5. Solve 2/7*w + 0 + c*w**2 = 0.
-1, 0
Let l(o) be the first derivative of o**6/540 + o**5/90 - o**4/12 - 17*o**3/3 + 2*o - 17. Let q(p) be the third derivative of l(p). Factor q(a).
2*(a - 1)*(a + 3)/3
Let m(w) be the second derivative of 0*w**3 + 0 + 2/5*w**5 + 15*w + 1/3*w**4 + 0*w**2. Factor m(v).
4*v**2*(2*v + 1)
Let g(w) be the first derivative of -4*w**2 + 21 + 0*w + 10/3*w**3 - 1/2*w**4. Factor g(q).
-2*q*(q - 4)*(q - 1)
Suppose 5*t = -2*p + 17, -2*t - 6 = -0*p + 4*p. Suppose 16 = 3*j + t*j. Determine o so that 2/9 + 4/9*o**j + 2/3*o = 0.
-1, -1/2
Let t = -67 + 87. Factor t*s**2 - 16*s**3 - 6*s + 3*s - s.
-4*s*(s - 1)*(4*s - 1)
Let y(r) be the first derivative of -r**5/720 + 7*r**4/288 + 12*r**2 - 36. Let f(j) be the second derivative of y(j). Suppose f(i) = 0. What is i?
0, 7
Let h = -114 + 128. Let n be (-56)/(-21)*(h/10 - -1). Let -8/5 - n*k - 14/5*k**2 = 0. Calculate k.
-2, -2/7
Let p be 1/(1/3) + -6 + -105. Let i be (p/132)/((-9)/6*1). What is j in -2/11*j + 0 - 6/11*j**3 - i*j**2 - 2/11*j**4 = 0?
-1, 0
Let o = 111 + -106. Let j(b) be the first derivative of 9/5*b**o - 5*b**3 - 12*b + 6*b**4 - b**6 + 8 - 18*b**2. Determine q, given that j(q) = 0.
-1, -1/2, 2
Let d(n) be the second derivative of n**7/105 - n**6/10 + n**5/6 + 20*n**2 + 31*n. Let k(f) be the first derivative of d(f). Determine j, given that k(j) = 0.
0, 1, 5
Let t(s) = -16 - 13*s + 8*s**2 - 7*s**3 + 8*s**3 + 2*s. Let q be t(-9). Factor 1/3*l**2 + 3 + q*l.
(l + 3)**2/3
Suppose -23 = -5*j + 22. Let a(n) = 15*n**2 + 6*n - 3. Let p(h) = 7*h**2 + 3*h - 2. Let t(o) = j*p(o) - 4*a(o). Let t(q) = 0. What is q?
-2, 1
Let g(r) be the second derivative of -6*r**6/5 + 24*r**5/5 + 44*r**4/3 + 32*r**3/3 - r + 9. Find h such that g(h) = 0.
-2/3, 0, 4
Solve 36 + 3*n**2 + 3/2*n**3 - 30*n = 0 for n.
-6, 2
Determine p so that p - 5*p + 39*p - 8*p - 3*p**2 - 28 + 4*p**2 = 0.
-28, 1
Let b(x) = -8*x**2 - 10*x - 9. Suppose 10*s + 42 = 3*s. Let a(z) = 7*z**2 + 9*z + 8. Let w(j) = s*b(j) - 7*a(j). Factor w(h).
-(h + 1)*(h + 2)
Suppose -224 - 2/7*r**2 - 16*r = 0. Calculate r.
-28
Factor -60 + 0*y - 5*y + 10283*y**2 - 10278*y**2.
5*(y - 4)*(y + 3)
Let j(h) be the first derivative of 2/3*h**3 + 12 + 8/5*h**5 + 0*h - 1/2*h**6 + 0*h**2 - 7/4*h**4. Solve j(q) = 0 for q.
0, 2/3, 1
Let t be (-9)/30*2 + 1638/455. Factor 0 + 0*b**2 - 2/7*b + 2/7*b**t.
2*b*(b - 1)*(b + 1)/7
Factor -64/11*p + 2/11*p**2 - 136/11.
2*(p - 34)*(p + 2)/11
Factor 2*m**2 - 1309 - m**2 + 1066 - 54*m - 4*m**2.
-3*(m + 9)**2
Let d(s) = -22*s - 66. Let f be d(-3). Let b(z) be the second derivative of -1/30*z**5 - 3*z - 2/9*z**3 + 0*z**2 + f - 1/6*z**4. Factor b(u).
-2*u*(u + 1)*(u + 2)/3
Let x(s) be the first derivative of 2*s**6 - 201*s**5/5 + 321*s**4/4 - 29*s**3 - 45*s**2/2 + 346. Find l such that x(l) = 0.
-1/4, 0, 1, 15
Let m(i) be the first derivative of -i**5/10 + 5*i**4/8 + 13*i**3/6 + 7*i**2/4 + 42. Find c such that m(c) = 0.
-1, 0, 7
Let g be 4/(-18) - 658/(-126). Let f = 4 - 0. Factor -4/7*n**3 + 0 + 2/7*n + 0*n**f + 0*n**2 + 2/7*n**g.
2*n*(n - 1)**2*(n + 1)**2/7
Let q(t) be the second derivative of t**4/4 - 2*t**3 + 6*t**2 - 78*t. Find b such that q(b) = 0.
2
Let o(g) be the second derivative of -17*g**4/6 - 17*g**3/3 + 7*g**2 + 5*g. Let c(w) = -3*w + 4*w - 3 + 6*w + 7*