nd w such that d(w) = 0.
2, 3
Let t(k) be the first derivative of k**3/3 + 4*k**2 - 2*k - 1. Let w(i) = i**2 + 17*i - 5. Let m(s) = -5*t(s) + 2*w(s). Factor m(r).
-3*r*(r + 2)
Let n(j) = -j**2 - 326*j + 26904. Let f(t) = -4*t**2 - 977*t + 80716. Let p(l) = 2*f(l) - 7*n(l). Factor p(u).
-(u - 164)**2
Let h = -29121 - -58569/2. Find b such that -h*b**4 + 9/2*b**5 + 2241*b**3 - 13851*b**2 + 67797/2*b - 19683/2 = 0.
1/3, 9
Let u(m) be the second derivative of 2*m**7/21 - 82*m**6/15 + 542*m**5/5 - 2542*m**4/3 + 3094*m**3 - 5202*m**2 + 17*m. Suppose u(o) = 0. What is o?
1, 3, 17
Let i(x) be the second derivative of -x**7/455 - x**6/78 - 5*x**5/156 + 3*x**4/2 - 19*x. Let t(a) be the third derivative of i(a). Factor t(z).
-2*(6*z + 5)**2/13
Suppose -l = -5*l + 16, -2*l = -x + 10. Suppose 4*p + 3*y - 20 = 0, -2*p - 3*y + x = p. Factor -7*d**p - 1 + d**3 + d**4 - 2*d + 7*d**2 + d**3.
(d - 1)*(d + 1)**3
Let d(q) = -q**2. Let a(y) = 2*y**2. Let s = 34 - 22. Let f = s + -6. Let l(p) = f*d(p) + 2*a(p). Let l(t) = 0. What is t?
0
Let r be 160/48*5/((-150)/(-8)). Factor -2/9*l**2 - r*l + 0.
-2*l*(l + 4)/9
Suppose 0 = -1503*i + 1513*i. Factor 0*c**2 + 1/4*c**3 + i + 0*c - 1/4*c**4.
-c**3*(c - 1)/4
Let t be 13/(-26)*-2*2. Let m(v) be the second derivative of 0*v**t + 10*v - 1/60*v**6 + 1/12*v**3 + 1/24*v**4 + 0 - 1/40*v**5. Suppose m(h) = 0. What is h?
-1, 0, 1
Let h be 4/16 - (-4)/(-20). Let o(v) be the first derivative of -1/6*v**3 + 0*v**2 + 0*v**4 + 4 + 1/4*v + h*v**5. Factor o(t).
(t - 1)**2*(t + 1)**2/4
Let p(z) be the first derivative of 40*z + 10/3*z**3 - 15/4*z**4 + 30*z**2 + 1 - z**5. Solve p(h) = 0.
-2, -1, 2
Let k(p) be the first derivative of -p**4/2 - 10*p**3 + p**2 + 30*p - 664. Find y such that k(y) = 0.
-15, -1, 1
Suppose 2*h + 3*h = 35. Factor -29*p**4 - 5*p**2 - 27*p**3 + h*p**3 + p**2 + 13*p**4.
-4*p**2*(p + 1)*(4*p + 1)
Let w be (3 - 117/3)/(-1). Suppose 0 = -0*s - s + w. Solve s - 36 - 3*v + 3*v**2 + 0*v = 0 for v.
0, 1
Let z(d) be the third derivative of -d**6/1080 - 7*d**5/540 - d**4/36 - 48*d**2 + 2*d. Factor z(u).
-u*(u + 1)*(u + 6)/9
Let h = -89 + 98. Suppose -h - 6 = -5*q. Determine y so that 2*y - 7/2*y**5 - 10*y**2 + 0 + y**4 + 21/2*y**q = 0.
-2, 0, 2/7, 1
Let q be (2 + 93/(-42))*(-368)/69. Factor -2/7 - 6/7*v**2 + q*v.
-2*(v - 1)*(3*v - 1)/7
Let c(o) be the first derivative of 15/2*o**4 - 5/6*o**6 + 28 + o**5 - 70/3*o**3 - 15*o + 55/2*o**2. Factor c(a).
-5*(a - 1)**4*(a + 3)
Let p(r) be the first derivative of -r**4/2 - 26*r**3/3 - 10*r**2 + 48*r - 171. Determine z, given that p(z) = 0.
-12, -2, 1
Let n(z) = -z**3 + 4*z**2 + 3*z - 2. Let h be n(4). Suppose 12 = h*f - 8. Factor 0 + 4/9*s - 2/3*s**3 - 2/9*s**f.
-2*s*(s + 1)*(3*s - 2)/9
Let l(p) = -p**5 - p**4 - p**2 - p + 1. Let a(u) = 4*u**5 - 4*u**3 + 10*u**2 + 12*u - 4. Let x(s) = -a(s) - 6*l(s). Factor x(j).
2*(j - 1)*(j + 1)**4
Let r(c) = -3*c - 1. Let n be r(3). Let p be (-1)/((n/(-5))/(-4)). Let -f + 2 - f**3 + 4*f**2 - f + p*f**3 + 7*f = 0. Calculate f.
-2, -1
Let m = -102 + 105. Factor -87*u + 39*u + m*u - 200*u - 60 - 20*u**2.
-5*(u + 12)*(4*u + 1)
Solve -201*v**3 - 3*v**5 - 106*v**4 + 22*v**4 - 387*v**3 = 0 for v.
-14, 0
Suppose 3*b = 2*f + 19, 6*f - 2*f = -8. Let i(w) be the second derivative of -5*w + 0*w**2 + 7/15*w**6 + 0*w**3 - 12/25*w**b + 0 + 2/15*w**4. Solve i(y) = 0.
0, 2/7, 2/5
Factor 2316/5*i + 664/5 - 28/5*i**2.
-4*(i - 83)*(7*i + 2)/5
Suppose -2 = 42*k + 194*k - 2. What is b in 0*b**2 + 0 + k*b + 1/3*b**3 - 1/6*b**4 = 0?
0, 2
Let u = 24 - 41/2. Let g be (-2 - -1)/((-10)/20). Factor 5/2*l**g + 2*l**3 - 1 - u*l.
(l - 1)*(l + 2)*(4*l + 1)/2
Let b(n) be the first derivative of 5 + 0*n**2 - 6*n - 2/15*n**4 + 1/25*n**5 + 2/15*n**3. Let a(w) be the first derivative of b(w). Factor a(f).
4*f*(f - 1)**2/5
Let w be (-22 - -21)/((-2)/8). Let z(m) be the second derivative of 1/18*m**3 - m + 0*m**2 + 0 - 1/36*m**w. Factor z(h).
-h*(h - 1)/3
Let u = -149 - -86. Let w = u + 67. Solve 0 + b**5 + 1/2*b**2 + 0*b + 13/4*b**w + 11/4*b**3 = 0.
-2, -1, -1/4, 0
Let t(r) be the first derivative of -r**6/360 - r**5/30 - r**4/6 - 5*r**3 - 12. Let k(w) be the third derivative of t(w). Determine z, given that k(z) = 0.
-2
Factor 3581*i**2 + 2*i - 2*i - 5*i**4 - 3661*i**2 + i**4 - 84*i**3.
-4*i**2*(i + 1)*(i + 20)
Let 2 - 2*f + 1/2*f**3 - 1/2*f**2 = 0. What is f?
-2, 1, 2
Factor -115/8 + 29/2*s - 1/8*s**2.
-(s - 115)*(s - 1)/8
Let j(t) = -6*t - 2*t**2 + 0*t**2 + 3*t**2 + 2 - 6. Suppose -2*f = -f - 2. Let c(u) = 3*u**2 - 13*u - 8. Let b(q) = f*c(q) - 5*j(q). Find r such that b(r) = 0.
-2
Let 4/5*v**2 - 101/5*v + v**3 + 4 = 0. What is v?
-5, 1/5, 4
Let r(u) be the second derivative of 5*u**7/42 + u**6/2 - 5*u**5/4 - 5*u**4/4 + 10*u**3/3 - 73*u. Factor r(g).
5*g*(g - 1)**2*(g + 1)*(g + 4)
Let f(p) be the third derivative of p**6/120 + p**5/15 + p**4/8 - 55*p**2 - 6*p. Factor f(l).
l*(l + 1)*(l + 3)
Let z(f) be the first derivative of f**8/1120 + f**7/840 - f**6/240 - f**5/120 + 10*f**3 - 51. Let d(b) be the third derivative of z(b). Factor d(c).
c*(c - 1)*(c + 1)*(3*c + 2)/2
What is x in 9*x**4 + 1154*x**5 + 636*x + 216 + 285*x**3 + 40*x**4 + 666*x**2 - 1157*x**5 - 13*x**4 = 0?
-2, -1, 18
Factor -1/9*q**4 + 0*q + 0 - 2/3*q**3 + 1/9*q**5 + 0*q**2.
q**3*(q - 3)*(q + 2)/9
Let i be (-6 - -13)/(-3 + 2). Let q be i/7 + 2 + (-14)/(-18). Find n, given that -32/9 - 2/9*n**2 - q*n = 0.
-4
Let o(a) be the third derivative of a**5/20 - a**4/8 - 10*a**3 + 2*a**2 - 1. What is v in o(v) = 0?
-4, 5
Let s(f) be the first derivative of 5*f**3/3 - 55*f**2/2 - 96*f - 7. Let m(p) = -p**2 + 9*p + 16. Let k(u) = 34*m(u) + 6*s(u). Factor k(o).
-4*(o + 2)*(o + 4)
Suppose -3*t - t + 2*f = -6, -f + 5 = 2*t. Suppose 4*q**t - 57*q**4 - 5*q**5 - 5*q + 10*q**3 + 55*q**4 + 0*q**2 - 2 = 0. What is q?
-1, -2/5, 1
Let c(d) = 2*d**4 - 10*d**3 - 16*d**2 - 12*d - 3. Let n(y) = 5*y**4 - 21*y**3 - 32*y**2 - 24*y - 7. Let g(v) = 7*c(v) - 3*n(v). Let g(f) = 0. What is f?
-3, -2, 0
Let n(j) = j**2 - j + 3. Let r be n(3). Suppose 2*a = -v + r, 3*a + v + 4 = 3*v. Factor 3/5 + 0*x - 3/5*x**a.
-3*(x - 1)*(x + 1)/5
What is y in -176/7*y + 2/7*y**2 + 3872/7 = 0?
44
Let s(w) be the first derivative of -w**6/15 - 16*w**5/25 - 8*w**4/5 - 4*w**3/15 + 17*w**2/5 + 4*w - 147. Suppose s(l) = 0. Calculate l.
-5, -2, -1, 1
Suppose 2*p + 22 = 5*u, 2*p + 379*u - 381*u + 4 = 0. Factor 0 - 8/11*s - 24/11*s**2 - 2/11*s**5 - 26/11*s**3 - 12/11*s**p.
-2*s*(s + 1)**2*(s + 2)**2/11
Let q be (-2)/(-4)*(191 - -1)/3. Let a be 2*-5*(q/(-70))/4. Determine s so that -26/7*s**2 + 32/7*s - a + 6/7*s**3 = 0.
1/3, 2
Let f(m) be the second derivative of 0*m**2 + 6*m + 0 - 1/3*m**4 - 1/5*m**3 - 3/50*m**5. Let f(b) = 0. Calculate b.
-3, -1/3, 0
Solve -28/3 + 25/3*y - 3/2*y**2 = 0 for y.
14/9, 4
Let w = 1362 - 8117/6. Let v = 10 - w. Factor v*s**2 + 1/3 + 7/6*s.
(s + 1)*(5*s + 2)/6
Suppose 14*f + 37 = 65. Suppose 0 = 5*t - 4*z - 22, 4*t + 3*z - 11 = 4*z. Factor 2*c - f*c + c**2 - 3*c**t.
-2*c**2
Factor 144*i + 19*i**2 - 192 - 2*i**2 + 2*i**2 + 2*i**2.
3*(i + 8)*(7*i - 8)
Let t = 15/13 + 549/65. Factor 24/5*f + 3/5*f**2 + t.
3*(f + 4)**2/5
Let v(u) be the second derivative of -4*u**6/35 + u**5/7 + u**4/3 - 10*u**3/21 - 2*u**2/7 + 4*u + 1. Suppose v(m) = 0. What is m?
-1, -1/6, 1
Let j(h) = -56*h - 280. Let r be j(-5). Factor -20/3*x**4 + r*x - 28/3*x**5 + 0*x**2 + 8/3*x**3 + 0.
-4*x**3*(x + 1)*(7*x - 2)/3
Let t be 75/216 - ((-9)/(-8))/9. Let c(r) be the second derivative of 0*r**2 + t*r**3 + 5*r + 1/2*r**4 + 2/15*r**5 + 0. Factor c(p).
2*p*(p + 2)*(4*p + 1)/3
Let u(c) = c**3 - 110*c**2 - 326*c - 1467. Let o be u(113). Let 20/7*p**o - 4/7*p**3 + 0 - 24/7*p = 0. What is p?
0, 2, 3
Find s such that 84*s**3 + 84 - 96*s - 153*s**3 + 66*s**3 + 33*s**2 = 0.
2, 7
Let j(r) be the second derivative of -r**4/4 - 107*r**3/2 - 176*r. Let j(i) = 0. Calculate i.
-107, 0
Let u(l) be the first derivative of -4/7*l**3 + 0*l - 40 - 1/14*l**4 - 9/7*l**2. Suppose u(v) = 0. What is v?
-3, 0
Let p(t) = 4*t**2 + 4*t - 16. Let d(z) = -4*z**2 - 4*z + 18. Let q(s) = 4*d(s) + 3*p(s). Suppose q(x) = 0. What is x?
-3, 2
Let o(m) = -10*m**2 + 14*m. Let g(x) = 69*x**3 - 11*x**2 + 20*x**2 - 68*x**3 + 11*x**2 - 29*x. Let t(k) = -2*g(k) - 5*o(k). Factor t(i).
-2*i*(i - 3)*(i - 2)
Let x(p) = 75*p**2 + 