hat c(q) = 0.
-1, 0, 103
Let s be 3/(-3) - (3 + -7). Factor 52 - 151*j + 205*j**2 + 20*j**s + 73 + 701*j.
5*(j + 5)**2*(4*j + 1)
Let r(z) = 5*z + 12. Let n be r(-2). Solve -96*m - 12 - 489*m**n - 1361*m**2 - 204*m - 25*m**2 = 0.
-2/25
Let j(p) be the third derivative of 0 + 1/120*p**5 - 14*p**2 + 0*p - 1/24*p**4 + 0*p**3. Determine d so that j(d) = 0.
0, 2
Let w = 29521 - 29519. Factor j + 0 - 1/2*j**4 + 0*j**3 + 3/2*j**w.
-j*(j - 2)*(j + 1)**2/2
Let p(x) be the second derivative of -x**5/110 - 7*x**4/66 - 16*x**3/33 - 12*x**2/11 + 101*x - 2. Factor p(y).
-2*(y + 2)**2*(y + 3)/11
Let f be 3 - ((-275)/308)/(-5)*(1 - -11). Suppose -f*j + 4/7 + 2/7*j**2 = 0. Calculate j.
1, 2
Let g(y) be the third derivative of -1/90*y**6 + 0*y + 0 + 1/3*y**4 + 34/315*y**7 - 17/45*y**5 + 0*y**3 - y**2 - 5/252*y**8. Determine s so that g(s) = 0.
-1, 0, 2/5, 1, 3
Let m(w) be the second derivative of -1/270*w**6 - w + 1/36*w**4 + 2/9*w**2 + 0 - 4/27*w**3 + 1/90*w**5. Factor m(k).
-(k - 2)*(k - 1)**2*(k + 2)/9
Suppose -41 = 6*g - 971. Let z = g - 1084/7. Factor -z*p**3 + 0 + 0*p + 1/7*p**2.
-p**2*(p - 1)/7
Let r = 3777 - 11321/3. Factor 2/9*v**3 + 50/3*v + 250/9 + r*v**2.
2*(v + 5)**3/9
Let w be ((-2)/4)/(8/(-32)). Factor -6*p - 7*p**2 - 6*p**2 + 13*p**2 - w*p**2.
-2*p*(p + 3)
Factor 45*g**2 - 33*g**3 + 103 - 110*g + 38*g**3 - 103.
5*g*(g - 2)*(g + 11)
Let v be 19/2 + (1 - 2)/2. Let p be ((-1)/v)/(16/(-72)). Factor 3/2*l**2 + p*l**3 - 1/2*l**4 - 1 - 1/2*l.
-(l - 2)*(l - 1)*(l + 1)**2/2
Let u(v) = 212*v**2 + 2. Let z(m) = -m**3 - 207*m**2 - 3. Let f(g) = 3*u(g) + 2*z(g). What is k in f(k) = 0?
0, 111
Let u(b) be the second derivative of 4/5*b**6 + 19/2*b**4 + 1/14*b**7 + 15/4*b**5 + 3*b + 14*b**3 + 0 + 12*b**2. Factor u(r).
3*(r + 1)**2*(r + 2)**3
Let p(m) be the second derivative of -4/3*m**2 - 61/90*m**5 - 3*m + 61/54*m**4 - 1/63*m**7 - 8/27*m**3 + 23/135*m**6 + 0. What is t in p(t) = 0?
-1/3, 1, 2, 3
Let t be 12/18*(-78)/4. Let h = -9 - t. Factor h*n**2 - 4*n - 2 + 7*n**3 - 3*n**3 - 2.
4*(n - 1)*(n + 1)**2
Solve 15*c**3 + 30*c**4 + 4*c**5 - 4*c**5 - 5*c**5 + 12*c**3 + 8*c**3 = 0 for c.
-1, 0, 7
Let r = -10238/5 - -2048. Factor r - 3/5*n - 12/5*n**2 - 7/5*n**3.
-(n + 1)**2*(7*n - 2)/5
Let k(j) = j**3 + 3*j**2 - j - 1. Let c(h) = -9*h - 17. Let x be c(-2). Let b be k(x). Factor 0 - s**b - 2/5*s + 2/5*s**3 + s**4.
s*(s - 1)*(s + 1)*(5*s + 2)/5
What is f in -3*f**2 + 111 + 106*f + 258 + 5*f**2 - 69 = 0?
-50, -3
Let f(z) be the second derivative of z**5/510 - z**4/204 - z**2/2 + 47*z. Let q(y) be the first derivative of f(y). Factor q(g).
2*g*(g - 1)/17
Let p(y) = 2*y**4 - 8*y**3 - 6*y**2 + 36*y - 28. Let r(i) = -4*i**4 + 15*i**3 + 14*i**2 - 73*i + 55. Let g(t) = -7*p(t) - 4*r(t). Factor g(s).
2*(s - 2)**2*(s - 1)*(s + 3)
Let v = -676 + 676. Let b(r) be the first derivative of 2/9*r**3 + 1/4*r**4 + 3 + 0*r + v*r**2 + 1/15*r**5. Suppose b(z) = 0. What is z?
-2, -1, 0
Let i(a) be the second derivative of a**7/63 + 7*a**6/15 + 4*a**5 + 50*a**4/9 + 7*a. Determine o so that i(o) = 0.
-10, -1, 0
Let w be ((-7)/(35/4))/((-23)/(1265/66)). Let 0 - w*h**2 + 0*h - 7/3*h**3 = 0. What is h?
-2/7, 0
Let d = 45/199 + 178188/1393. Let r = d + -128. Factor 3/7 - r*h**2 - 2/7*h.
-(h - 1)*(h + 3)/7
Let i(j) = -j**2 - 5*j. Let n be i(-5). Suppose 1 + n*w**2 - 6*w - 3*w**2 - 4 = 0. What is w?
-1
Determine i so that 2/3*i**4 + 2/3*i**3 - 2/3*i**5 - 2/3*i**2 + 0 + 0*i = 0.
-1, 0, 1
Let i(q) = 3*q**3 - q**2 + 9*q - 19. Let c(k) = 2*k**3 + 9*k - 21. Let p(u) = 4*c(u) - 3*i(u). Suppose p(s) = 0. What is s?
-3, 3
Factor 9/2 + 21/2*w + 3/2*w**3 + 15/2*w**2.
3*(w + 1)**2*(w + 3)/2
Let u(p) = -p**3 - 15*p**2 - 30*p - 224. Let w be u(-14). Suppose w + 2*m + 5/2*m**4 - 3/2*m**3 - 5/2*m**2 - 1/2*m**5 = 0. Calculate m.
-1, 0, 1, 4
Factor -8*w**4 - 5*w**2 - 15*w**3 - 16*w + w**3 + 37*w**2 + 4*w**5 + 2*w**3.
4*w*(w - 2)*(w - 1)**2*(w + 2)
Let f(n) be the second derivative of 4/9*n**3 - 2/3*n**2 - 1/12*n**4 + 0 - 9*n. Determine z, given that f(z) = 0.
2/3, 2
Let m(r) be the second derivative of r**4/12 + 5*r**3/6 - 7*r**2 + 153*r. Let m(h) = 0. What is h?
-7, 2
Factor 3/7*u**2 + 0*u - 12/7.
3*(u - 2)*(u + 2)/7
Suppose -f = -a, 4*f - 9 - 5 = -3*a. Factor -2*t**3 + 2*t + 3/2*t**f - 2 + 1/2*t**4.
(t - 2)**2*(t - 1)*(t + 1)/2
Let n(u) be the first derivative of -u**6/60 + u**5/25 + 7*u**4/40 - 2*u**3/3 + 3*u**2/5 - 626. Solve n(m) = 0 for m.
-3, 0, 1, 2
Let u(h) be the first derivative of -h**5/15 + 2*h**4/3 - 8*h**3/3 - 11*h**2/2 + 9. Let q(z) be the second derivative of u(z). Factor q(j).
-4*(j - 2)**2
Let a(r) be the first derivative of r**5/140 - r**4/42 - r**3/42 + r**2/7 - 9*r + 3. Let o(j) be the first derivative of a(j). Factor o(t).
(t - 2)*(t - 1)*(t + 1)/7
Suppose -5*z - 390 = z. Let x = 196/3 + z. Determine g, given that 1/3*g**2 - 1/3*g - x + 1/3*g**3 = 0.
-1, 1
Let r(w) be the third derivative of -w**6/780 - w**5/65 - 5*w**4/156 - 229*w**2. Factor r(l).
-2*l*(l + 1)*(l + 5)/13
Determine u so that 968/5 + 88/5*u + 2/5*u**2 = 0.
-22
Find w such that -1479*w**3 + 1470*w**3 + 0*w**5 - 6*w**4 + 3*w**5 = 0.
-1, 0, 3
Let y(j) be the first derivative of -j**3/30 - j**2/4 - 3*j/5 - 46. Suppose y(z) = 0. Calculate z.
-3, -2
Suppose -3*s - s = -44. Let y(c) be the first derivative of c**4/4 - 7*c**2/2 + 5. Let a(p) = 2*p**3 - 13*p. Let d(v) = s*y(v) - 6*a(v). Solve d(l) = 0.
-1, 0, 1
Factor -36/11*w**2 + 2/11*w**3 + 34/11*w + 0.
2*w*(w - 17)*(w - 1)/11
Suppose 0 = -3*k - 2*k + 70. Let g = k + -11. Factor g*a - 10*a**2 - 3*a**3 + 17*a**2 - 10*a**2 + 3.
-3*(a - 1)*(a + 1)**2
Let i = -26/11 + 141/55. Factor 0*d**3 + 0 + 0*d + 1/5*d**2 - i*d**4.
-d**2*(d - 1)*(d + 1)/5
Let u(n) = 4*n + 5. Let x be u(-1). Let b be x/(-4) + (-36)/(-16). Determine s, given that 2/7 + 4/7*s + 2/7*s**b = 0.
-1
Let m(c) = -4 + 7*c**2 + 3 - 4*c**2 + c - 2*c**2. Let o(y) = 10*y**3 + 12*y**2 + 2*y - 6. Let j(f) = 6*m(f) - o(f). Solve j(b) = 0.
-1, 0, 2/5
Let i be (8/(-2088))/((-4)/294). Let n = i + 3/58. Factor 4/3 + 4/3*q + n*q**2.
(q + 2)**2/3
Let h be 25 + -28 - (-2 - (1 + 2)). Let r(q) be the first derivative of 1/3*q**3 - 7 + 4*q + h*q**2. Solve r(a) = 0 for a.
-2
Let f(i) be the third derivative of i**7/210 - 31*i**6/120 + 59*i**5/60 - 29*i**4/24 - 5*i**2 + 2. Find u such that f(u) = 0.
0, 1, 29
Factor -297*f**3 + 134*f**3 + 145*f**3 - 21*f**2 - 3*f.
-3*f*(f + 1)*(6*f + 1)
Let l = 117551/3 - 39183. Solve -1/6*g**3 + 5/6*g**2 - 4/3*g + l = 0 for g.
1, 2
Let n = 33000 + -32998. Factor 0 + 50/9*p - n*p**3 + 10/3*p**2 + 2/9*p**4.
2*p*(p - 5)**2*(p + 1)/9
Let l(k) be the third derivative of k**6/192 - 11*k**5/160 + 23*k**4/96 + k**3/2 + 3*k**2 - 6*k. Determine j so that l(j) = 0.
-2/5, 3, 4
Let n(q) = 7*q**4 - 17*q**3 - 2*q**2 + 8*q. Let r(g) = g**4 - 3*g**3 + g**2 + g. Let i(f) = -n(f) + 8*r(f). Factor i(z).
z**2*(z - 5)*(z - 2)
Let z = 12/19 + -125/228. Let v(j) be the first derivative of 0*j**2 + 5 - z*j**3 + 0*j. Find s, given that v(s) = 0.
0
Let q be ((0 + -3)/(-9))/((-1)/3). Let s be q/4 - 21/40*-2. Factor -8*n**2 - s - 18/5*n**3 - 26/5*n.
-2*(n + 1)**2*(9*n + 2)/5
Let a be -2*(-1 - 3) + -2. Find x, given that -128*x - 315*x**4 - 72*x**3 + 1640*x**3 + 38 - 336*x**2 - 371*x**4 - a = 0.
-2/7, 2/7, 2
Factor -9*i**2 + 21*i**2 - 14*i**2 + 2.
-2*(i - 1)*(i + 1)
Let f(a) be the first derivative of 5*a**3/3 - 115*a**2/2 + 210*a - 820. Factor f(k).
5*(k - 21)*(k - 2)
Let v = 21 - 5. Solve -10*h**2 - 11*h**4 + 5 + 0 + v*h**4 = 0.
-1, 1
Let u = 12 - 19. Let w(r) = -r**3 - 6*r**2 + 5*r - 8. Let s be w(u). Determine f so that 3 + 4*f**2 + 12*f + 0*f**2 + s - f**2 = 0.
-3, -1
Suppose d - 12 = -5*i + i, -5*i = -5*d + 10. Let n(a) = a + 3. Let l be n(0). Factor 2 + 2*k**l - 2 + 2*k - k**3 - 3*k**i.
k*(k - 2)*(k - 1)
Let g(o) be the first derivative of 15 - 11/4*o**2 - 7/3*o + 5/18*o**3. Determine s so that g(s) = 0.
-2/5, 7
Let k(r) be the first derivative of 1/4*r**4 - 1/2*r**2 + 2*r - 2/3*r**3 + 17. Factor k(y).
(y - 2)*(y - 1)*(y + 1)
Suppose 2*k - 4 = 4*w, -4*k - 4*w + 41 = -w. Let p(x) be the first derivative of 2/3*x**2 + k - 1/12*x**4 + 0*x + 0*x**3. Solve p(q) = 0 for q.
-2, 0, 2
Factor 36/7*p**2 + 432/7 + 216/7*p + 2/7*p**3.
2*(p + 6)**3/7
Let -39/4*l**2 - 507/2*l - 1/8*l**3 - 2197 = 0. What is l?
-26
Suppose 0 = -7*d + 269 - 38. 