*x**2 - 5*x**f - 5*x**4 + 19*x**4 + x**3 - 9*x**4 = 0.
-1, 0, 1
Let d(n) be the second derivative of -5/42*n**7 - 5/6*n**4 + 5/6*n**3 + 1/3*n**6 + 0 + 0*n**2 + 0*n**5 + 18*n. Factor d(y).
-5*y*(y - 1)**3*(y + 1)
Let m(v) = 2*v**3 - 50*v**2 - 221*v - 324. Let c(g) = -3*g**3 + 99*g**2 + 441*g + 648. Let a(x) = -5*c(x) - 9*m(x). Let a(z) = 0. What is z?
-6, -3
Suppose 0 = 2*x + 4*d - 46, -5*x + 27 + 33 = -d. Factor 12 + 14*u**2 - 5*u**2 - 10*u + x - 8*u**2.
(u - 5)**2
Let h(u) be the third derivative of -u**10/7560 - u**9/756 - u**8/420 + 5*u**4/24 - 12*u**2. Let g(p) be the second derivative of h(p). Factor g(j).
-4*j**3*(j + 1)*(j + 4)
Let y(z) be the third derivative of z**7/210 - z**6/120 - 7*z**5/60 + 13*z**4/24 - z**3 + 79*z**2. Find q, given that y(q) = 0.
-3, 1, 2
Let d(x) = x**2 + 6*x - 5. Let w be d(-7). Let r = 745/4 - 5207/28. Let -2/7*k - 2/7 + r*k**3 + 2/7*k**w = 0. What is k?
-1, 1
Let h(z) be the third derivative of -1/50*z**5 - 1/150*z**6 + 1/15*z**4 + 0*z + 1/525*z**7 - 17*z**2 + 0 + 4/15*z**3. Suppose h(j) = 0. Calculate j.
-1, 2
Suppose -2*k + 9*k - 35 = 0. Let d(r) be the first derivative of 4 + 2*r**4 + 0*r + 4/5*r**k + 5/3*r**3 + 1/2*r**2. Factor d(q).
q*(q + 1)*(2*q + 1)**2
Let v be 2 + -6 + (5301/(-133))/(-9). Factor 6/7*u**3 + 9/7*u**4 - 3/7 - 9/7*u + v*u**5 - 6/7*u**2.
3*(u - 1)*(u + 1)**4/7
Let v(s) be the first derivative of -s**3/12 - 4*s**2 - 286. Factor v(n).
-n*(n + 32)/4
Let q(b) be the first derivative of -b**6/120 + 3*b**5/20 - 9*b**4/8 - b**3/3 - 3. Let f(c) be the third derivative of q(c). Factor f(m).
-3*(m - 3)**2
Let r be (-1 + 6)/((-5)/(-2)). Factor 73*s + 70*s + 6*s**r - 3*s**3 - 143*s.
-3*s**2*(s - 2)
Suppose 5*i - 15 = -b, 4*b = -4*i - 9 + 21. Determine c so that -1/5*c**4 + 4/5*c**2 + 1/5*c**i + 0 - 4/5*c = 0.
-2, 0, 1, 2
Let c(d) be the first derivative of -1/8*d**2 + 1/2*d - 1/12*d**3 + 5. Determine a so that c(a) = 0.
-2, 1
Let x(a) = 3*a**4 + a**2 + 1. Let v(k) = 11*k**4 + 8*k**3 + 57*k**2 + 40*k + 5. Let n(q) = v(q) - 5*x(q). Suppose n(z) = 0. Calculate z.
-2, -1, 0, 5
Let b(w) = 2*w**3 + 16*w**2 - 4*w + 4. Let c(p) = 2*p**2 + p - 1. Let z(v) = -b(v) - 4*c(v). What is s in z(s) = 0?
-12, 0
Let a(t) be the first derivative of -t**6/39 + 4*t**5/65 + t**4 - 72*t**3/13 + 135*t**2/13 - 108*t/13 + 364. Find v, given that a(v) = 0.
-6, 1, 3
Factor 8/3*l**3 + 0 + 4/9*l - 22/9*l**2 + 2*l**4.
2*l*(l + 2)*(3*l - 1)**2/9
Let m be 858/(-1638)*(-12)/44. Find s such that m*s - 1/7*s**3 + 4/7*s**2 - 4/7 = 0.
-1, 1, 4
Let p(i) = 20*i**2 - 69*i + 13. Let h(j) = 18*j**2 - 69*j + 12. Let d(c) = -5*h(c) + 6*p(c). Suppose d(q) = 0. Calculate q.
3/10, 2
Let f be 7/((-21)/92) - (3 + -1). Let i = -680/21 - f. Let 0 + 0*y + i*y**2 = 0. Calculate y.
0
Suppose -3*h = -a + 12, 7*a + 48*h + 4 = 47*h. Factor 20/3 + a*t - 5/3*t**2.
-5*(t - 2)*(t + 2)/3
Let c = -1/4 - -71/280. Let q(p) be the third derivative of c*p**6 + 1/84*p**4 - 1/84*p**5 + 0 + 5*p**2 + 0*p**3 + 1/1470*p**7 + 0*p - 1/2352*p**8. Factor q(t).
-t*(t - 1)**3*(t + 2)/7
Let h be -15*4/(-20) - (-26)/(-10). Determine b, given that 0*b**2 + 2/5*b + 0 - h*b**3 = 0.
-1, 0, 1
Let b(o) be the second derivative of 1/30*o**3 + 1/40*o**4 + 27*o - 1/300*o**6 + 0*o**2 + 0 + 0*o**5. Determine v, given that b(v) = 0.
-1, 0, 2
Let m be (5 - 4)/3*-9. Let c(h) = 7*h**2 - 3*h + 5. Let k(q) = 4*q**2 - 2*q + 3. Let y(n) = m*c(n) + 5*k(n). Factor y(a).
-a*(a + 1)
Let h(z) be the second derivative of 3*z**7/77 - 19*z**6/55 + 10*z**5/11 - 34*z**4/33 + 16*z**3/33 - z - 27. Solve h(c) = 0.
0, 2/3, 1, 4
Let h(f) be the first derivative of -7*f**5/10 - 29*f**4/4 - 107*f**3/6 - 17*f**2 - 6*f + 74. Suppose h(i) = 0. Calculate i.
-6, -1, -2/7
Let a(b) = 5*b**4 + 58*b**3 - 937*b**2 + 3126*b - 2916. Let l(k) = -11*k**4 - 116*k**3 + 1872*k**2 - 6251*k + 5832. Let o(u) = -13*a(u) - 6*l(u). Factor o(i).
(i - 27)**2*(i - 2)**2
Let o(z) be the second derivative of 0 - 56/33*z**3 + 49/22*z**2 - 25*z + 29/132*z**4 - 1/110*z**5. Factor o(u).
-(u - 7)**2*(2*u - 1)/11
Suppose 2 = 9*z - 7. Let f be 0 + -3 + 14/3 + z. Find r such that 0 + 2/3*r**4 + 10/3*r**3 + f*r + 16/3*r**2 = 0.
-2, -1, 0
Suppose 14 = 2*k + 2*k - 2*r, 23 = 4*k - 5*r. Factor 3*y**3 - 23*y + 17*y - 3*y**2 + 6*y**k.
3*y*(y - 1)*(y + 2)
Let k(q) = -2*q**2 - q - 1. Let u(c) = -2*c**3 - 2*c**2 - 5*c + 5. Let m(j) = -5*k(j) - u(j). Determine y so that m(y) = 0.
-5, -1, 0
Suppose -3*f + 3/5*f**3 - 1/5*f**4 + 0 + 13/5*f**2 = 0. What is f?
-3, 0, 1, 5
Let l(d) be the second derivative of d**5/90 - d**4/9 + d**3/3 + 224*d. Factor l(z).
2*z*(z - 3)**2/9
Factor -14*g + g**2 + 2*g + 8*g**2 - 6*g**2.
3*g*(g - 4)
Let i(p) be the first derivative of -p**4/24 + 5*p**3/9 - 23*p**2/12 + 7*p/3 - 11. Factor i(m).
-(m - 7)*(m - 2)*(m - 1)/6
Let c(q) be the third derivative of -q**5/30 + q**4/12 + 2*q**3/3 - 589*q**2. Find w such that c(w) = 0.
-1, 2
Suppose -11 - 23 = -2*r - 5*i, 4 = i. Let x = r - 3. Let 19*c**2 - 3 + 3 + 39*c + 6 + 62*c**2 + 21*c**x + 69*c**3 = 0. Calculate c.
-1, -2/7
Solve 0 - 33*m**3 - 12*m**4 + 45/2*m + 21/2*m**5 + 12*m**2 = 0.
-1, 0, 1, 15/7
Let k(t) be the third derivative of -1/90*t**5 + 1/9*t**4 - 1/180*t**6 + 24*t**2 + 0 + 4/9*t**3 + 0*t. Factor k(j).
-2*(j - 2)*(j + 1)*(j + 2)/3
Let a be 6/(-4)*36/(-27). Let h be 10/(-15)*(-9)/a. Find r such that 4*r**2 + 12*r**4 - 3*r**2 + 3*r**5 + 15*r**h + 5*r**2 = 0.
-2, -1, 0
Let v = 6251/34562 - -3/3142. Let 0*d**2 + 0 - 2/11*d**3 + v*d = 0. What is d?
-1, 0, 1
Let b(d) be the second derivative of d**7/126 + 2*d**6/45 - d**5/20 - 5*d**4/18 + 4*d**3/9 - 19*d. Factor b(x).
x*(x - 1)**2*(x + 2)*(x + 4)/3
Let a(i) = i**3 + 2*i**2 - 6*i - 8. Let u be a(-2). Factor u*b**3 - 2*b**3 - 25*b**2 + 27*b**2.
2*b**2*(b + 1)
Let n(y) be the second derivative of -49/6*y**2 - 1/36*y**4 - 7/9*y**3 + 0 + 9*y. Find h such that n(h) = 0.
-7
Let m = -15347 + 15349. Find v, given that 0*v**3 + 2/11*v**4 - 6/11*v**m + 4/11*v + 0 = 0.
-2, 0, 1
Let v be ((-80)/21)/(-4)*((-35)/(-10) - 2). Determine z so that v*z - 2*z**2 + 4/7 = 0.
-2/7, 1
Find u such that -112/19*u**2 + 32/19 - 10/19*u**5 + 26/19*u**4 + 32/19*u + 32/19*u**3 = 0.
-2, -2/5, 1, 2
Let k(p) be the first derivative of p**3/8 + 21*p**2/8 + 9*p - 123. Solve k(w) = 0.
-12, -2
Suppose -1 = 4*g - 4*j + 7, -4*j + 22 = 3*g. Factor 3/7*h**3 + 72/7*h - 48/7 - 27/7*h**g.
3*(h - 4)**2*(h - 1)/7
Let t be (-4)/(-10) + 13/(125 + 5). Find k such that -t*k**4 + 0*k**3 + 0 + 0*k + 0*k**2 - 1/4*k**5 = 0.
-2, 0
Let i(w) = w**2 - w. Let c(q) = 5*q**4 - 15*q**3 - 36*q**2 + 46*q. Let o(v) = c(v) + 6*i(v). Factor o(d).
5*d*(d - 4)*(d - 1)*(d + 2)
Let a(y) be the first derivative of y**6/24 + 13*y**5/20 - 29*y**4/16 + 5*y**3/4 - 169. Factor a(n).
n**2*(n - 1)**2*(n + 15)/4
Let q be -6*2*2/(-12). Suppose q*v - 7 = 3*r, -3*r + 1 = -v + 6. Find h such that -5*h**2 + h**2 + 2*h**2 - h**v = 0.
0
Let i(f) be the second derivative of 1/140*f**5 + 0 + 34*f + 0*f**2 + 1/42*f**3 + 1/42*f**4. Determine g, given that i(g) = 0.
-1, 0
Let m(h) be the first derivative of -5*h**4/4 + 15*h**3 + 5*h**2/2 - 45*h + 274. Determine q so that m(q) = 0.
-1, 1, 9
Let s(d) be the first derivative of -5*d**4/4 - 210*d**3 - 19845*d**2/2 + 507. Factor s(k).
-5*k*(k + 63)**2
Let i = 195 - 192. Let o(c) be the first derivative of -2/9*c**2 + 2/27*c**i + 5 + 2/9*c. Let o(s) = 0. Calculate s.
1
Let j(h) = -2*h**2 + 170*h - 192. Let f(v) = v + 5. Let r(p) = -4*f(p) - j(p). Let r(x) = 0. What is x?
1, 86
Let z(w) be the third derivative of -w**8/1680 + w**7/350 - w**6/600 - w**5/100 + w**4/60 - 2*w**2 - 67*w. Suppose z(p) = 0. Calculate p.
-1, 0, 1, 2
Let u be (7*(-14)/(-539))/(-2*3/(-66)). Solve 2/3*f**3 + 16/3*f + 10/3*f**u + 8/3 = 0.
-2, -1
Let g be 116/3*(7 - 4). Let x = g + -114. Find z such that -1/4*z**5 + 0*z**4 + 0 + 1/2*z**3 + 0*z**x - 1/4*z = 0.
-1, 0, 1
Let j(n) = n**3 - 11*n**2 - 6*n - 18. Let c be j(11). Let v = c + 94. Suppose 24*m**3 + 0 + v*m**5 - 53/2*m**4 - 17/2*m**2 + m = 0. What is m?
0, 1/4, 2/5, 1
Let g(h) = 2*h**3 + 17*h**2 + 10*h + 18. Let s(q) = -q - 14. Let a be s(-6). Let i be g(a). Factor -4/9*x**i + 2/9*x + 0 + 2/9*x**3.
2*x*(x - 1)**2/9
Let g(v) be the second derivative of 0*v**2 + 4/9*v**3 - 11/15*v**5 - 5/9*v**4 - 8/45*v**6 + 0 - 5*v. Find f such that g(f) = 0.
-2, -1, 0, 1/4
F