Let u(p) be the second derivative of -7/12*p**4 + 5/2*p**3 + 0 - 9/2*p**2 - 46*p + 1/20*p**5. Determine k, given that u(k) = 0.
1, 3
Let j = 133 + -130. Suppose j*w - 5*w = 0. Let -1/4*p**2 + w - 1/4*p + 1/4*p**4 + 1/4*p**3 = 0. Calculate p.
-1, 0, 1
Let t(j) = -80*j**4 - 195*j**3 - 190*j**2 - 70*j + 5. Let l(b) = b**5 - b**4 - b**2 - 2*b + 1. Let x(s) = 5*l(s) - t(s). Factor x(c).
5*c*(c + 1)**3*(c + 12)
Let y(p) be the second derivative of -1/10*p**5 + 1/60*p**6 + 0*p**2 - 1/6*p**3 + 5/24*p**4 + 0 + 28*p. Let y(s) = 0. What is s?
0, 1, 2
Let n(c) be the second derivative of -c**4/9 + 14*c**3/9 - 49*c**2/6 + c - 3. Factor n(k).
-(2*k - 7)**2/3
Determine y so that -2/5*y**2 + 0*y + 2/5 = 0.
-1, 1
Let v(h) be the second derivative of 0*h**3 + 0*h**2 - 1/12*h**4 + 0 - 5*h. What is d in v(d) = 0?
0
Let u(b) be the third derivative of -b**5/270 + 7*b**4/6 - 147*b**3 - 6*b**2 - 69*b. Factor u(z).
-2*(z - 63)**2/9
Let m be 750/(-625) + (3 - 1). Let s be 4/14 - 3/35. Determine k, given that 2/5*k**2 + 2/5 - 4/5*k**4 - s*k**5 + k - m*k**3 = 0.
-2, -1, 1
Factor 620/3*j**2 + 100/3*j**3 + 112/3 - 544/3*j.
4*(j + 7)*(5*j - 2)**2/3
Let a be 4/14 - (-18)/(-14). Let s(p) = p**2 + p + 1. Let n(g) = g + 3*g - 3 - 10*g. Let m(v) = a*n(v) - 3*s(v). Suppose m(d) = 0. What is d?
0, 1
Suppose z - 2 = 2*s, -2*z + 2*s = 2*z - 14. Factor 10*g**3 + 5*g**3 - 9*g**3 + 3*g**z + 3*g**2.
3*g**2*(g + 1)**2
Suppose -9 = -6*m + 3. Factor 20 - 13*p**2 + 5*p**2 + 3*p**m.
-5*(p - 2)*(p + 2)
Let j(z) be the second derivative of z**6/30 + 2*z**5/5 - z**4/12 - 4*z**3/3 + 35*z - 1. Suppose j(p) = 0. What is p?
-8, -1, 0, 1
Suppose 32*u = 7*u + 50. Factor 27/8*a**3 + 3/2*a**u + 9/4*a**4 + 0 + 3/8*a**5 + 0*a.
3*a**2*(a + 1)**2*(a + 4)/8
Let h = 31 - 31. Suppose 3*z - 14 + 2 = h. Factor -1/4*p**3 - 1/2*p**5 + 0*p + 3/4*p**z + 0 + 0*p**2.
-p**3*(p - 1)*(2*p - 1)/4
Let h(w) be the third derivative of 0 + 0*w - 2/7*w**3 - 1/15*w**5 - 29*w**2 + 1/140*w**6 + 17/84*w**4. Factor h(q).
2*(q - 3)*(q - 1)*(3*q - 2)/7
Let b(f) be the third derivative of -f**6/120 + f**5/60 + 15*f**2. Let k(z) = -5*z**3 - 5*z - 2. Let j(v) = -4*b(v) + k(v). Let j(l) = 0. Calculate l.
-2, -1
Let q(p) be the third derivative of p**6/30 - p**5/60 - 3*p**4/2 + 3*p**3/2 - 499*p**2. Determine o so that q(o) = 0.
-3, 1/4, 3
Let h(j) be the third derivative of -11*j**6/360 + 7*j**5/36 - 7*j**4/18 + 2*j**3/9 - 2*j**2 + 26*j. Factor h(d).
-(d - 2)*(d - 1)*(11*d - 2)/3
Let w be 52/14 + 4 + 156/(-42). Let j(p) be the first derivative of 5/2*p**4 + 6 + 3*p**2 - 3/5*p**5 - p - w*p**3. Solve j(s) = 0.
1/3, 1
Suppose 10*j**2 + 0 + 50/3*j + 2/3*j**4 - 6*j**3 = 0. What is j?
-1, 0, 5
Let p = -2054 - -2056. Determine f, given that -8/7 - 24/7*f + 10/7*f**3 - 6/7*f**p = 0.
-1, -2/5, 2
Let f(l) be the third derivative of l**6/720 - 11*l**5/360 + l**4/8 + 193*l**2. What is i in f(i) = 0?
0, 2, 9
Let j(w) = -2*w**2 - 12*w - 3. Let k be j(-8). Let o be k/(-21) - (-2)/6. Factor -1 - 3*z**2 + z**2 - o*z + z**2 + 0*z.
-(z + 1)**2
Factor -8 + 4/3*c**4 - 37/3*c**3 + 19/3*c + 38/3*c**2.
(c - 8)*(c - 1)**2*(4*c + 3)/3
Let b be (-26)/22 + 1 + (-6027)/(-6468). Let z(g) = 2*g**2 - g - 1. Let q be z(-1). Determine l, given that -l - 1/4*l**q - b = 0.
-3, -1
Let h(o) be the first derivative of o**5/40 - 43*o**4/32 - 11*o**3/6 - 370. Suppose h(l) = 0. Calculate l.
-1, 0, 44
Let f(r) be the second derivative of r**5/100 + 7*r**4/30 + 5*r**3/6 + 6*r**2/5 + 8*r. Let f(j) = 0. What is j?
-12, -1
Let v(b) be the second derivative of 23*b**7/2100 - 4*b**6/75 + 9*b**5/100 - b**4/30 - 19*b**3/6 - 25*b. Let d(n) be the second derivative of v(n). Factor d(y).
2*(y - 1)**2*(23*y - 2)/5
Let t be (17/(-2))/(3/6). Let b = 26 + t. Let q(s) = 16*s**2 - 33*s - 1. Let f(i) = 4*i**2 - 8*i. Let j(x) = b*f(x) - 2*q(x). Solve j(u) = 0 for u.
1/2, 1
Let d(c) be the third derivative of -3*c**8/560 - c**7/14 - 2*c**6/5 - 6*c**5/5 - 2*c**4 - 8*c**3/5 + 2*c**2 + 78*c. Factor d(l).
-3*(l + 2)**4*(3*l + 1)/5
Let c(k) be the third derivative of 0*k + 0 - 1/90*k**6 + 1/315*k**7 + 0*k**5 + 9*k**2 + 0*k**3 + 1/168*k**8 + 0*k**4. Factor c(t).
2*t**3*(t + 1)*(3*t - 2)/3
Suppose 0 = 2*j + 1 - 7. Find d, given that -5*d + 8*d - j*d + 5*d**2 = 0.
0
Let n(y) = 4. Let f(t) = -5*t**2 + 65*t + 54. Let o(s) = f(s) + 4*n(s). Factor o(m).
-5*(m - 14)*(m + 1)
Let s(c) = -c + 1. Let a(l) = 4*l - 5. Let g(k) = -a(k) - 5*s(k). Let q(x) = -x**3 - 3*x**2 + 2*x. Let z(f) = 4*g(f) - q(f). Find b, given that z(b) = 0.
-2, -1, 0
Suppose 5*v = 3*a + 16, -3*v - 2*a = 2*v - 31. Suppose -19*u = -18*u - v. Factor 4*j**5 + 5 + 5*j**4 - u*j**5 + 10*j**2 - 4 - 10*j**3 - 5*j.
-(j - 1)**5
Let g(s) be the first derivative of s**2/2 + 10. Let a be g(2). Let -8 + 3 + 1 + 8*h - 4*h**a = 0. Calculate h.
1
Factor 207*u**5 - 32*u**3 + 4*u**4 - 40 + 10*u**4 - 203*u**5 + 2*u**4 + 92*u - 40*u**2.
4*(u - 1)**3*(u + 2)*(u + 5)
Suppose b + 5*f = 17, 0 = 2*f - 4 - 2. Let -126*v**4 - 12*v**3 - 2*v**2 + 5*v**b + 135*v**4 = 0. Calculate v.
0, 1/3, 1
Suppose -105/4*j - 69/4*j**2 - 3 + 6*j**3 = 0. What is j?
-1, -1/8, 4
Let m be 18/(-20)*(-136)/153. Factor 0*b + 0 - m*b**5 + 4/5*b**3 + 0*b**2 + 0*b**4.
-4*b**3*(b - 1)*(b + 1)/5
Suppose 0*w + 12 = 3*w. Suppose -w*z - 1/3*z**4 - 4/3 - 2*z**3 - 13/3*z**2 = 0. What is z?
-2, -1
Let l = -214 - -1502/7. Suppose 11*g - 12*g = -2. Factor 0 - 6/7*i**3 + l*i**g - 10/7*i**4 + 0*i.
-2*i**2*(i + 1)*(5*i - 2)/7
Let i(u) be the third derivative of 5/12*u**4 + 0*u**5 + 0 - 5/6*u**3 + 1/42*u**7 + 0*u - 33*u**2 - 1/12*u**6. What is z in i(z) = 0?
-1, 1
Factor 75/2*o + 5/6*o**4 - 25/6*o**3 - 45 - 5/2*o**2.
5*(o - 3)**2*(o - 2)*(o + 3)/6
Let u(h) be the second derivative of 0*h**4 + 0 + 13*h + 0*h**2 + 0*h**3 - 1/40*h**5. Suppose u(i) = 0. Calculate i.
0
Let t(a) be the second derivative of a**5/30 + 2*a**4/3 + 7*a**3/3 + 10*a**2/3 - 268*a. Factor t(n).
2*(n + 1)**2*(n + 10)/3
Let r(u) be the first derivative of -u**3 - 5*u**2/2 - 2*u + 1. Let t(b) = -13 + 26 + b - 12. Let w(q) = -r(q) - 4*t(q). Factor w(k).
(k + 1)*(3*k - 2)
Let w(m) be the second derivative of m**5/50 + m**4/15 - m**3/3 - 6*m**2/5 - 7*m + 3. Solve w(t) = 0 for t.
-3, -1, 2
Let f(z) = 2*z**3 + z**2 + z - 1. Let t(v) = v**3 - 42*v**2 + 83*v - 48. Let n(d) = -2*f(d) - t(d). Factor n(p).
-5*(p - 5)*(p - 2)*(p - 1)
Let z be 85 + (-1 - (4 + -4)). Find i such that z*i - 25 - 100*i - 10*i**2 + 71*i = 0.
1/2, 5
Let f(m) be the second derivative of m**4/18 - m**3/9 + 6*m + 9. Factor f(r).
2*r*(r - 1)/3
Let b(r) be the third derivative of 0 - 1/100*r**5 + 1/525*r**7 - 47*r**2 + 0*r**4 - 1/600*r**6 + 0*r**3 + 0*r. Find y, given that b(y) = 0.
-1, 0, 3/2
Let r(j) be the second derivative of -j**7/7560 + j**6/216 - 5*j**5/72 + 2*j**4/3 - 19*j. Let z(a) be the third derivative of r(a). Factor z(i).
-(i - 5)**2/3
Let p(i) be the first derivative of -i**3/2 + 27*i**2 - 105*i/2 - 513. Determine l, given that p(l) = 0.
1, 35
Let i(y) = 63*y - 187. Let f be i(3). Factor -3 + f*s - 1/3*s**2.
-(s - 3)**2/3
Let z(n) be the second derivative of -n**4/60 + 31*n**3/30 - 29*n**2/5 - 2*n + 27. Find a such that z(a) = 0.
2, 29
Let q = 1694 + -25406/15. What is c in 2/15*c**4 + 2/5*c**3 - q + 2/15*c**2 - 2/5*c = 0?
-2, -1, 1
Let q(n) be the third derivative of -n**7/140 + 91*n**6/240 - 101*n**5/20 - 28*n**4 + 128*n**3/3 + 10*n**2 + 20*n. Let q(i) = 0. What is i?
-2, 1/3, 16
Let q(i) be the second derivative of i**7/4200 - i**5/150 - 19*i**3/6 + 19*i. Let j(m) be the second derivative of q(m). Find b such that j(b) = 0.
-2, 0, 2
Let r(f) be the first derivative of 1/3*f**3 + 6*f + 7/2*f**2 - 6. Suppose r(n) = 0. What is n?
-6, -1
Let r(f) be the second derivative of 7*f**5/5 - 26*f**4/3 + 26*f**3/3 + 12*f**2 + f + 6. Factor r(j).
4*(j - 3)*(j - 1)*(7*j + 2)
Let v(x) = -15*x**4 - 46*x**3 - 41*x**2 - 8*x + 1. Let m(w) = -w**4 - w**2 + 1. Suppose -3 = 9*r - 6*r. Let j(o) = r*m(o) + v(o). Factor j(i).
-2*i*(i + 1)*(i + 2)*(7*i + 2)
Let r(h) be the third derivative of h**6/120 + 7*h**5/30 - 31*h**4/24 + 8*h**3/3 - h**2 + 31*h. Determine n so that r(n) = 0.
-16, 1
Factor 5 - 2*z**2 - 17*z**2 + 85*z - 71*z**2 + 0.
-5*(z - 1)*(18*z + 1)
Let h = 950/63 + -110/9. Let -4/7*y**2 + 0 - h*y = 0. What is y?
-5, 0
Let u be (-2 + 3)*(-5)/(-1). Suppose 3*q - 3 = 2*q. Solve -22/