*4 + 30*q**3 + 5*q + 5. Let h(a) = -5*a**4 + 28*a**3 + 6*a + 6. Let k(j) = -5*h(j) + 6*m(j). Factor k(w).
-5*w**3*(w - 8)
Let d(v) be the second derivative of -8*v + 0*v**2 - 1/21*v**7 + 0*v**6 + 0*v**3 + 0 + 1/10*v**5 + 0*v**4. Determine x, given that d(x) = 0.
-1, 0, 1
Let i(g) be the first derivative of g**6/24 + g**5/6 - 5*g**4/8 - 33*g**2/2 - 34. Let t(c) be the second derivative of i(c). Factor t(h).
5*h*(h - 1)*(h + 3)
Let f be -7*(-18)/(-9)*(-9)/42. Find x such that 0*x + 2/15*x**f + 0*x**4 - 2/15*x**5 + 0 + 0*x**2 = 0.
-1, 0, 1
Let s = 39/184 - -385/1656. Factor 4/3*g - 8/9 - s*g**3 + 0*g**2.
-4*(g - 1)**2*(g + 2)/9
Solve -138 + 15*h**3 + 50*h**3 - 305*h**2 - 5*h**4 - 1688*h + 2303*h - 312 = 0 for h.
2, 3, 5
Let m(x) = x - 21. Let c(k) = k - 21. Let j(s) = -3*c(s) + 4*m(s). Let a be j(21). Factor 2/3*d + a*d**2 - 1/3 - 2/3*d**3 + 1/3*d**4.
(d - 1)**3*(d + 1)/3
Let z(a) be the first derivative of 1/3*a**6 + 3*a**4 + 1 + a**2 + 8/5*a**5 + 0*a + 8/3*a**3. Factor z(o).
2*o*(o + 1)**4
Let c(t) be the first derivative of t**6/2 + 3*t**5 - 3*t**4/4 - 5*t**3 + 139. Factor c(f).
3*f**2*(f - 1)*(f + 1)*(f + 5)
Let y = -3 + -4. Let z(h) = -h**3 - 7*h**2 - h + 2. Let n be z(y). Factor 7*j - 2 + 2*j - n*j**3 + 7*j**4 - 61*j**2 + 56*j**2.
(j - 1)**2*(j + 1)*(7*j - 2)
Solve 28*d - 17*d**2 - 24 + 25*d**3 - 29*d**3 - 15*d**2 - 80*d = 0.
-6, -1
Let c(p) be the first derivative of -1/15*p**2 + 0*p - 12 - 8/75*p**5 - 8/45*p**3 - 1/5*p**4 - 1/45*p**6. Find i such that c(i) = 0.
-1, 0
Let a(w) be the second derivative of -13*w**5/40 + 47*w**4/8 + 89*w**3/6 + 6*w**2 + 895*w. Factor a(l).
-(l - 12)*(l + 1)*(13*l + 2)/2
Let d = 19 - 17. Factor -4*b**d + 22*b - 6*b - 12 + 0*b.
-4*(b - 3)*(b - 1)
Let a(o) be the first derivative of -o**9/2016 - o**8/280 - o**7/112 - o**6/120 - 6*o**3 - 22. Let x(n) be the third derivative of a(n). Factor x(k).
-3*k**2*(k + 1)**2*(k + 2)/2
Let j(n) be the second derivative of -n**7/7 - 7*n**6/10 + 42*n**5/5 + 47*n**4/2 - 255*n**3 + 675*n**2/2 - 507*n. Suppose j(c) = 0. What is c?
-5, 1/2, 3
Factor 3/8*z**3 - 111/4*z + 0 - 219/8*z**2.
3*z*(z - 74)*(z + 1)/8
Factor 2*t**2 + 0 + t + 3/4*t**3.
t*(t + 2)*(3*t + 2)/4
Factor 5 + 4568*f - 5*f**2 - 4569*f + 1.
-(f - 1)*(5*f + 6)
Let v(a) be the first derivative of 2*a**6 - 51*a**5/5 + 27*a**4/4 + 34*a**3 - 30*a**2 - 72*a - 9. Suppose v(t) = 0. What is t?
-1, -3/4, 2
Let w be (-56)/(-98)*(-14)/(-2). Solve -7*k**4 + k**w - 2*k**2 - k**5 - 5*k**5 - 6*k**3 + 4*k**5 = 0 for k.
-1, 0
Let s = 43 + -39. Let d(l) = l**2 + 134*l + 849. Let m(p) = 4*p**2 + 401*p + 2546. Let g(w) = s*m(w) - 11*d(w). Factor g(c).
5*(c + 13)**2
Let o(m) = 2*m**2 - m + 1. Let r(a) = 5*a**2 + 15*a - 78. Let j(x) = 3*o(x) - r(x). Factor j(z).
(z - 9)**2
Let v(g) = 4*g**2 + 2*g - 4. Let q(l) = 9*l**2 + 5*l - 9. Let x(k) = -3*q(k) + 7*v(k). Let y(f) = -2*f**2 + 2*f + 5. Let w(t) = x(t) - y(t). Factor w(z).
3*(z - 2)*(z + 1)
Let i(d) be the third derivative of -7/30*d**6 + 0*d + 0*d**4 - 14*d**2 - 2/15*d**5 - 2/21*d**7 + 0*d**3 + 0. Let i(x) = 0. What is x?
-1, -2/5, 0
Let p(m) be the first derivative of -9 + 4*m**3 + 87/4*m**4 - 6*m**2 + 63/5*m**5 + 0*m. Let p(n) = 0. What is n?
-1, -2/3, 0, 2/7
Let i = 31 + -27. Factor -33*n**2 - 43 - 99*n**2 - i*n**4 - 17 - 4 - 40*n**3 - 160*n.
-4*(n + 1)**2*(n + 4)**2
Suppose 6*x = 7*x - d - 1, 3*d + 9 = 5*x. Suppose 3*l - 3*t + 23 = 7*l, -t = -x*l + 1. Solve -3 - 65/2*g**l - 9/2*g**4 + 45/2*g**3 + 35/2*g = 0 for g.
1/3, 2/3, 1, 3
Let w(q) = 12*q - 40. Let p be w(8). Let z = 59 - p. Find l, given that 1/3*l**z + 8*l - 3*l**2 - 16/3 = 0.
1, 4
Let z = 349/450 + -18/25. Let p(q) be the third derivative of 0*q + z*q**3 + 0*q**6 + 0 + 0*q**4 - q**2 + 1/630*q**7 - 1/90*q**5. Factor p(l).
(l - 1)**2*(l + 1)**2/3
Let y(m) = 65*m + 975. Let k be y(-15). Let a(h) be the third derivative of -1/160*h**6 + 0 + k*h**4 + 0*h**3 + 1/40*h**5 + 0*h + 12*h**2. Solve a(u) = 0.
0, 2
Determine t so that 0*t - 2/7*t**3 - 64/7 + 12/7*t**2 = 0.
-2, 4
Factor 3/5*y**2 - 24/5*y - 27/5.
3*(y - 9)*(y + 1)/5
Let p(q) = -2*q**3 + 5*q**2 - 44*q + 228. Let n be p(4). Suppose 0*i**2 + 3/2*i**n - 1/2*i**5 + 0*i**3 + 0*i + 0 = 0. What is i?
0, 3
Find c such that 0*c - 2/7*c**5 + 0 - 2/7*c**4 + 0*c**3 + 0*c**2 = 0.
-1, 0
Let b(p) be the second derivative of p**7/42 + p**6/6 + 3*p**5/10 - p**4/6 - 7*p**3/6 - 3*p**2/2 - 46*p + 5. Determine j so that b(j) = 0.
-3, -1, 1
Let o(a) = 4*a - 24. Let x be o(5). Let g(l) = -65*l + 180. Let n(j) = -j**2 + 64*j - 180. Let k(m) = x*g(m) - 5*n(m). Find b such that k(b) = 0.
6
Let d(m) = m**2 + 5*m + 7. Let p be d(5). Factor -57*j + 10*j**3 + 5*j**2 + 5*j**4 + p*j.
5*j**2*(j + 1)**2
Let k(c) be the third derivative of -5*c**2 - 1/84*c**8 + 0*c - 2/15*c**5 + 0*c**3 + 1/10*c**6 + 0*c**4 + 0*c**7 + 0. Factor k(a).
-4*a**2*(a - 1)**2*(a + 2)
Find y such that 0*y**4 - 1 - 1/2*y**5 + y**2 - 3/2*y + 2*y**3 = 0.
-1, 1, 2
Let r(d) = -15*d**2 + 210*d - 5. Let w(s) = -19*s**2 + 211*s - 6. Let p(a) = 6*r(a) - 5*w(a). Determine f, given that p(f) = 0.
-41, 0
Suppose -90725 = 3*g - 90749. Solve f + 77/4*f**3 + 49/4*f**4 + 0 + g*f**2 = 0 for f.
-1, -2/7, 0
Suppose u - 3*j - 6 = 0, -81*u - 4*j = -85*u + 16. Let y(b) be the first derivative of 16/3*b - 4/3*b**2 + 1/9*b**u - 7. Solve y(d) = 0 for d.
4
Suppose 3 = -3*n - 3*k - 0, 4*n - 2*k = 26. Factor j**2 - 45*j**n + 43*j**4 + 3*j**2 - 2*j**3.
-2*j**2*(j - 1)*(j + 2)
Let h be 4/((0 - 2)/10). Let v be h/(-6) + (-8)/24. Find u such that 0 + 2/7*u + 2/7*u**v + 4/7*u**2 = 0.
-1, 0
Let w(v) be the second derivative of 0*v**2 + 10*v - 1/3*v**4 + 0 + 1/3*v**3 + 1/10*v**5. Factor w(m).
2*m*(m - 1)**2
Let 0 + 7/3*m**2 + 1/3*m**4 + 5/3*m**3 + m = 0. What is m?
-3, -1, 0
Let q(a) be the third derivative of -a**8/560 + a**7/140 + a**6/15 + 43*a**3/6 + 9*a**2. Let x(h) be the first derivative of q(h). Factor x(c).
-3*c**2*(c - 4)*(c + 2)
Let p(b) be the third derivative of -3*b**7/175 - 13*b**6/25 + 64*b**5/75 + 92*b**4/15 + 48*b**3/5 + 4*b**2 - 22*b. Determine c so that p(c) = 0.
-18, -2/3, 2
Let o(q) = 2*q**3 + 2*q**2 - 3*q - 2. Let f be o(-2). Let w be (-2)/(-4) - (-3 - 14/f). Factor w - 1/2*d**2 - 1/2*d.
-d*(d + 1)/2
Suppose -42 = 2*z - 5*z. Suppose -23*c + z = 14. Solve c*o**3 + 2/7*o**4 + 0*o - 2/7*o**2 + 0 = 0 for o.
-1, 0, 1
Let b(o) = 6*o**3 + 37*o**2 - 65*o - 5. Let z(m) = 20*m**3 + 112*m**2 - 196*m - 16. Let p(k) = -16*b(k) + 5*z(k). Factor p(l).
4*l*(l - 5)*(l - 3)
Suppose 0*v - 3*v = 14*v + 2*v. Determine j, given that 5/6*j**3 - 1/6*j + 2/3*j**2 + v = 0.
-1, 0, 1/5
Let c be 27/(-3)*20/(-12). Find u, given that 4*u - 37*u - c*u**2 + 9*u + 14*u + 5*u**4 = 0.
-1, 0, 2
Let g be (-42414)/36 + 2/(-15). Let p = g - -1180. Suppose -21/10*x**4 + 49/10*x**5 - 73/10*x**3 + 12/5*x + 2/5 + p*x**2 = 0. Calculate x.
-1, -2/7, 1
Factor -25*u**4 - 4*u**2 + 5*u**5 + 257*u**3 + u**2 - 5*u**2 - 222*u**3 - 7*u**2.
5*u**2*(u - 3)*(u - 1)**2
Let r(i) be the second derivative of i**5/200 + i**4/40 - i**2/5 + 65*i - 2. Suppose r(h) = 0. What is h?
-2, 1
Let q be -51*(2/(-1) + 3 + 0). Let v = q + 53. Factor -3/2*j + 1 - 5/2*j**v.
-(j + 1)*(5*j - 2)/2
Determine d so that 4/19*d**3 - 10/19*d**2 + 0 - 4/19*d + 10/19*d**4 = 0.
-1, -2/5, 0, 1
Let a(m) be the first derivative of 0*m - 18 + 4/5*m**5 - 39/8*m**4 - 49/8*m**2 + 28/3*m**3 - 1/24*m**6. Suppose a(r) = 0. Calculate r.
0, 1, 7
Let l be 1032/52 - (-6)/39. Let 184*k**3 + l*k**2 + 45*k**5 + 55*k**5 - 32*k + 28*k**2 - 300*k**4 = 0. What is k?
-2/5, 0, 2/5, 1, 2
Let m be -25*-6*7/210. Factor -1/3*p**m - p**3 + p**4 + 1/3*p**2 + 0 + 0*p.
-p**2*(p - 1)**3/3
Factor 24/7 + 18/7*w**2 - 40/7*w - 2/7*w**3.
-2*(w - 6)*(w - 2)*(w - 1)/7
Let b(u) = 2*u**2 - 19*u - 16. Let m be b(11). Suppose 9 = 3*c + 5*w - m, -4*c - 3*w = -20. Suppose 0*p - 1/2*p**2 + c = 0. What is p?
-2, 2
Let j(r) = -r - 4. Let m be j(3). Let a be (3 + m)*(3 - 4). Suppose 1 - 8*t**a - 3*t**5 - 3*t**2 - 9*t**3 - 1 - t**4 = 0. Calculate t.
-1, 0
Determine s, given that -20*s + 303 + 4*s**2 + 841 + 12 + 156*s = 0.
-17
Let x(y) = 4*y**2 + 2*y - 14. Let b(i) = -17*i**2 - 7*i + 55. Let z(s) = 4*b(s) + 18*x(s). Let z(w) = 0. What is w?
-4, 2
Let k(i) = -1 + 13 + 5*i**2 - 2*i - 3. Let z(h) be the second derivative of -h**4/4 + h**3/6 - 3*h**2 + 2*h. Let c(t) = 5*k(t) + 8*z(t