 64*z = 164*z. Determine i, given that 0 + 0*i**3 - 2/17*i**4 + 0*i**2 + z*i = 0.
0
Let o(f) be the third derivative of -f**5/10 - f**4/6 + f**3/3 - f**2 + 7*f. Factor o(d).
-2*(d + 1)*(3*d - 1)
Let c be 4/6*((-18)/42 + 108/56). Factor c - 3*a + 5/4*a**2.
(a - 2)*(5*a - 2)/4
Let o = 149 - 146. Suppose -8*v**3 - 35*v**4 + 17*v**4 + 6 - 7*v**2 + 5*v + o*v**3 + 19*v**4 = 0. Calculate v.
-1, 1, 6
Let n(v) = v**3 - 5*v**2 - 6*v + 5. Let s be n(6). Suppose 0 = -0*x - x + s. Factor d**2 + 2*d**3 + 2*d**4 + d**5 - 3*d**x - 2*d**2 - d**2.
-2*d**2*(d - 1)**2*(d + 1)
Suppose 8*m - 26 = -2. Determine c, given that 1 - 3*c**4 + 5*c + 10*c**2 - 13*c**2 - 9*c**m + 4*c + 5 = 0.
-2, -1, 1
Let u(c) = 3*c**2 + 3*c - 6. Let k(d) = -2*d**2 - 2*d + 4. Let t(m) = -8*k(m) - 5*u(m). Let q be t(-3). Factor 3/5*x**3 + 2/5 - 1/5*x**2 - 3/5*x - 1/5*x**q.
-(x - 2)*(x - 1)**2*(x + 1)/5
Let h(y) = y. Let l(f) = 5*f**2 + 7*f. Let k(v) = -6*h(v) + l(v). Find o such that k(o) = 0.
-1/5, 0
Let n(d) be the third derivative of -d**5/30 - d**4/6 + 5*d**3 + 2*d**2 + 45*d. Factor n(f).
-2*(f - 3)*(f + 5)
Let r(a) be the first derivative of a**8/84 - 8*a**7/105 + 2*a**6/15 - a**2 + 3. Let q(j) be the second derivative of r(j). Let q(f) = 0. What is f?
0, 2
Factor 12/5*d + 9/5 + 3/5*d**2.
3*(d + 1)*(d + 3)/5
Let h(b) be the second derivative of -b**4/27 + 16*b**3/27 + 126*b + 2. Factor h(k).
-4*k*(k - 8)/9
Let o = -3 + 6. Let j = o - 1. Suppose -s + s + 2*s**j + 2*s**3 = 0. What is s?
-1, 0
Let w be ((-32)/(-14) - 2) + (-1272)/140. Let p = w + 9. Find o such that 0 + 0*o + p*o**2 = 0.
0
Let l(k) be the first derivative of 0*k + 24/5*k**5 + 0*k**2 - 5/3*k**6 - 9/2*k**4 + 11 + 4/3*k**3. Find f such that l(f) = 0.
0, 2/5, 1
Solve 376*q**5 - 755*q**5 + 16*q**2 + 8*q - 28*q**4 + 395*q**5 - 6*q**3 - 18*q**3 + 12*q**2 = 0 for q.
-1, -1/4, 0, 1, 2
Suppose g - 2*w + 12 = 2*w, 2*g = -5*w + 28. Let -9*s**g + 8 - 8 + 5*s**4 + 2*s**5 = 0. What is s?
0, 2
Let s = -63 + 63. Let l(u) be the second derivative of s*u**3 + 1/14*u**7 + 3/20*u**5 + 1/5*u**6 + 0*u**2 + 0*u**4 + 0 + 3*u. Factor l(j).
3*j**3*(j + 1)**2
Let q be 72/(-30)*((-102)/272)/((-18)/(-8)). Suppose 0 = 2*r + 3*r - 15. Factor q*x**5 + 4/5*x**2 + 8/5*x**4 + 2*x**r + 0 + 0*x.
2*x**2*(x + 1)**2*(x + 2)/5
Let c = -603 - -1147. Let x be c/221*2/8. Suppose x - 6/13*s**3 - 24/13*s + 22/13*s**2 = 0. Calculate s.
2/3, 1, 2
Suppose 11*l + 7*l - 19*l = 0. Let g(r) be the second derivative of l + 4/15*r**3 - 19/60*r**4 + 2/5*r**2 + 3*r + 7/100*r**5. What is z in g(z) = 0?
-2/7, 1, 2
Factor -61 - 30 + 45*x - 71 + 10*x**2 - 7*x**2.
3*(x - 3)*(x + 18)
Let m(k) = -4*k**3 + 13*k**2 - 3*k + 3. Let z(b) = 2*b**3 - b**2 + b - 1. Let a(t) = 2*m(t) + 6*z(t). Factor a(g).
4*g**2*(g + 5)
Let q(v) be the third derivative of -1/15*v**4 + 0*v + 0 - 4/15*v**3 + 7*v**2 - 1/150*v**5. Let q(k) = 0. What is k?
-2
Let y(r) be the second derivative of r**5/4 - 5*r**4/4 - 5*r**3/6 + 15*r**2/2 + 27*r. Suppose y(g) = 0. What is g?
-1, 1, 3
Let v(z) = 10*z**5 - 16*z**4 - 18*z**3 + 21*z**2 + 13*z. Let x(o) = -o**2 - o. Let y(d) = 2*v(d) + 10*x(d). Find i, given that y(i) = 0.
-1, -2/5, 0, 1, 2
Suppose -5*o - 4 - 6 = 0. Let n be (3/2 + o)*(-20)/25. Find q, given that 1/5*q**2 + n*q - 3/5 = 0.
-3, 1
Let b = 599 + -597. Let l(p) be the first derivative of 16/15*p**3 + 7/5*p**b + 4/5*p + 1/5*p**4 - 1/15*p**6 + 12 - 4/25*p**5. Factor l(s).
-2*(s - 2)*(s + 1)**4/5
Let i(b) be the third derivative of -5*b**8/28 - 153*b**7/70 - 73*b**6/40 + 139*b**5/20 + 93*b**4/8 + 7*b**3 - 24*b**2 - 4*b. Solve i(v) = 0.
-7, -1, -2/5, -1/4, 1
Let h(u) be the second derivative of 5/12*u**4 + 0*u**3 - 2*u + 0 + 0*u**2 + 1/4*u**5. Solve h(d) = 0.
-1, 0
Suppose -2 = -31*z + 65 + 57. Factor 3/2*b**3 - 7/2*b**2 + 19/6*b - 1 - 1/6*b**z.
-(b - 6)*(b - 1)**3/6
Let h(v) = 6*v**4 + 24*v**3 - 64*v**2 + 45*v - 11. Let p(k) = -k**4 - 5*k**3 + 13*k**2 - 9*k + 2. Let t(y) = 2*h(y) + 11*p(y). Find s, given that t(s) = 0.
0, 1, 3
Let f(l) be the second derivative of l**7/1260 - 23*l**6/1080 - 2*l**5/45 - 2*l**4/3 - 16*l. Let b(m) be the third derivative of f(m). Factor b(p).
2*(p - 8)*(3*p + 1)/3
Let j(d) be the first derivative of -5*d**3/3 - 115*d**2/2 + 250*d - 189. Factor j(r).
-5*(r - 2)*(r + 25)
Let b(v) = -2*v**2 - 8*v - 12. Let y(x) = -2. Let h(t) = 28*t**3 + 2*t**2 - t. Let a be h(1). Let f = a + -23. Let o(q) = f*y(q) - 2*b(q). Factor o(s).
4*(s + 1)*(s + 3)
Factor 19 - 18*r**2 + 9*r + 16 + 19 - 3*r**3 + 0*r**3 + 6*r**2.
-3*(r - 2)*(r + 3)**2
Suppose 0 = -5*f - 7 + 77. Factor f*b**5 - 5*b**3 + 4*b**4 - 3*b**3 - 10*b**5.
4*b**3*(b - 1)*(b + 2)
Factor 61/4*c**3 + 0*c + 0 - 31/4*c**2 - 29/4*c**4 - 1/4*c**5.
-c**2*(c - 1)**2*(c + 31)/4
Let l(m) be the first derivative of m**9/2016 - m**7/560 + 10*m**3 + 35. Let d(w) be the third derivative of l(w). Factor d(p).
3*p**3*(p - 1)*(p + 1)/2
Let j(s) = 9*s**2 - 39*s + 130. Let o(g) = 7*g**2 - 46*g + 130. Let r(c) = 3*j(c) - 4*o(c). Factor r(a).
-(a - 65)*(a - 2)
Suppose -5*z = 0, z + 48 = 3*a + 3*z. Let u = -14 + a. Find q, given that 2/9*q**4 + 0 + 16/9*q + 4/3*q**3 + 8/3*q**u = 0.
-2, 0
Suppose 64*q - 152 = -12*q. Factor -1/2*i - 1/4*i**q - 1/4.
-(i + 1)**2/4
Let i(b) be the second derivative of -b**5/40 + b**4/24 + b**3/12 - b**2/4 - 69*b - 2. Find q, given that i(q) = 0.
-1, 1
Solve -61*i**2 - 14*i**2 - 275*i**3 - 190*i**4 + 10*i**2 + 15*i**5 - 5*i**2 = 0 for i.
-1, -1/3, 0, 14
Let n(f) be the first derivative of -f**5/5 - 7*f**4/6 - f**3 - f - 1. Let w(a) be the first derivative of n(a). Factor w(m).
-2*m*(m + 3)*(2*m + 1)
Suppose 0 = d + 2*d + 3. Let u be d + 5 + 128/8. Factor -16 - b + u + 3*b - 2*b**2.
-2*(b - 2)*(b + 1)
Let p(t) be the second derivative of 0 + 1/50*t**6 + 3/25*t**5 + 1/10*t**4 - 28*t - 9/10*t**2 - 2/5*t**3. Factor p(m).
3*(m - 1)*(m + 1)**2*(m + 3)/5
Determine b so that 1095*b**2 - 2100*b - 108*b**3 + 249 - 16 + 287 + 935*b**2 + 33*b**3 = 0.
2/5, 2/3, 26
Let k(x) be the second derivative of -1/10*x**5 + 7/3*x**3 - 4*x**2 - 1/3*x**4 + 0 + 14*x. Find y such that k(y) = 0.
-4, 1
Solve -400 + 400 - 8*t**2 - 16*t - t**3 = 0 for t.
-4, 0
Factor 2*o**2 - 106*o - 6 + 56*o - o**3 + 55*o.
-(o - 3)*(o - 1)*(o + 2)
Let d(t) be the second derivative of -t**7/42 - t**6/15 + t**5/20 + t**4/6 - t + 5. Find m, given that d(m) = 0.
-2, -1, 0, 1
Let f(v) = v + 22. Let a be f(14). Let j = 39 - a. Let -15*z + 3*z**3 - 5*z**2 + 11*z**3 + 4*z**3 - j*z**3 + 5*z**4 = 0. Calculate z.
-3, -1, 0, 1
Let i(w) be the third derivative of w**7/525 - w**6/10 + 193*w**5/150 + 8*w**4 + 256*w**3/15 + w**2 + 48*w. Let i(p) = 0. What is p?
-1, 16
Find i such that 0 - 3/2*i**5 + 111/4*i**2 - 63/2*i**3 + 51/4*i**4 - 15/2*i = 0.
0, 1/2, 1, 2, 5
Suppose -85*n = -84*n - 4. Factor 3*h**2 + 4*h**2 + 8 - 11*h**2 - n.
-4*(h - 1)*(h + 1)
Let b = 65 + -83. Let n(v) = 8*v**3 - 8*v**2 - 7*v. Let a(i) = 2*i**3 - 2*i**2 - 2*i. Let m(p) = b*a(p) + 4*n(p). Solve m(l) = 0.
-1, 0, 2
Let k(a) = 15*a**4 - 45*a**3 + 50*a**2 - 30*a. Let s(u) = 7*u**4 - 22*u**3 + 25*u**2 - 14*u. Let w(o) = -2*k(o) + 5*s(o). Find r, given that w(r) = 0.
0, 1, 2
Suppose -3*w + 12 = 5*b - 4, -b = -5*w + 8. Let j = w + 3. Factor -16*y**2 - 4*y**j - 24*y**3 - 3*y - y + 0*y - 16*y**4.
-4*y*(y + 1)**4
Suppose -2*q = 3*q - 125. Suppose 28*y + 5*y**3 + 7*y - 5*y - 20 + 10*y - q*y**2 = 0. What is y?
1, 2
Let r(i) be the first derivative of 2*i**5/45 + 8*i**4/9 + 20*i**3/3 + 200*i**2/9 + 250*i/9 - 187. Find b, given that r(b) = 0.
-5, -1
Suppose -2*l + 10 = -0*l, 3*b - 4*l = -5. Find d such that -9*d + 23*d + 1 + 4*d - b - 8*d**2 = 0.
1/4, 2
Let h = 3/215 + 137/43. Find s such that -144/5*s - h - 324/5*s**2 = 0.
-2/9
Suppose t = -i - t + 6, t = 2*i - 2. Let s be (-2 - (-1)/i)*(-6)/18. What is f in 5/2*f**2 + 4*f + 2 + s*f**3 = 0?
-2, -1
Factor 2*k**4 + 12*k**3 + 4*k**2 + 10*k**4 + 0*k**3 + 4*k**5.
4*k**2*(k + 1)**3
Let g(v) = -8*v + 34. Let a be g(4). Suppose -s = -3*q - 9, s - 6 = -a*s + 2*q. Factor s*h + 2/11*h**2 - 2/11.
2*(h - 1)*(h + 1)/11
Let d = 2864 + -2864. Find c, given that 0 + 4/7*c**2 + d*c - 2/7*c**3 = 0.
0, 2
Let i be (30/8)/((-20)/(-48)). Suppose -10 = -5*a + d, 2*a - a - 23 = -4*d. Find h, given that a + h - 3*h**4 + i - 10*h - 15*h + 9*h**2 + 6*h**3 = 0.
-2, 1, 2
Let z(a) be the second derivative of -a**5/4 