t r(l) = -22*l**2 - 184*l + 8. Let g(c) = 8*b(c) - 3*r(c). Factor g(m).
2*m*(m + 32)
Let t(u) be the second derivative of 2*u**2 - 4*u + 0 + 0*u**4 + u**3 - 1/10*u**5. Factor t(f).
-2*(f - 2)*(f + 1)**2
Factor -20*i - 16/3 - 3*i**3 + 52/3*i**2.
-(i - 4)*(i - 2)*(9*i + 2)/3
Suppose 0 = -2*o + o + 3. Let -44*p**o + p + 7*p**2 - 9 + 45*p**3 + 2*p - 2*p**2 = 0. Calculate p.
-3, 1
Let f be ((-1785)/150 - -12) + 2/5. Determine v, given that -v**5 + v**3 + 1/2*v**4 + 0 + 0*v - f*v**2 = 0.
-1, 0, 1/2, 1
Let u(b) be the third derivative of 0*b - b**2 + 1/15*b**5 - 3/2*b**4 + 16/3*b**3 - 14. What is t in u(t) = 0?
1, 8
Let k(q) = -q**4 + 13*q**3 - 10*q**2 + 6*q + 6. Let u(o) = o**4 - 3*o**3 - o - 1. Let i(t) = k(t) + 6*u(t). Let i(h) = 0. Calculate h.
-1, 0, 2
Suppose -15*b + 1 + 74 = 0. Suppose 0 = 2*u - 5*u. Determine j so that -5/8*j**3 + 0 + u*j - 1/8*j**2 - 7/8*j**4 - 3/8*j**b = 0.
-1, -1/3, 0
Find m such that 3/2*m + 1/2*m**2 + 1 = 0.
-2, -1
Let 0*p**3 - 1/4*p**4 + 0*p + 0 + p**2 = 0. Calculate p.
-2, 0, 2
Let a(y) = -6*y + 19. Let d be a(8). Let g = -29 - d. Factor 0 + 1/4*p**3 + g*p - 1/2*p**2.
p**2*(p - 2)/4
Let v = -3/20 + 23/120. Let d(u) be the second derivative of -1/2*u**3 + 9/4*u**2 + 0 + v*u**4 + u. Factor d(r).
(r - 3)**2/2
Suppose -116 = -75*s + 34. Let c(z) be the first derivative of 1/4*z**4 + 0*z**s + 0*z + 0*z**3 + 1/5*z**5 - 8. Find r such that c(r) = 0.
-1, 0
Let d(h) be the third derivative of h**5/5 + 43*h**4/12 - 5*h**3 - 92*h**2. Factor d(a).
2*(2*a + 15)*(3*a - 1)
Suppose -2*r - 10 = -3*r. Suppose -3*a + r = -5. What is d in -3 + 2*d - 9*d**2 + a*d**2 + d**2 + 4*d = 0?
1
Let m(f) be the second derivative of 0 + 0*f**2 + 3*f + 1/6*f**4 + 1/3*f**3. Determine g so that m(g) = 0.
-1, 0
Let w = -46 - -49. Factor -4*t**3 + 0*t**3 - 8*t**3 + 3*t**3 + w*t**4 + 6*t - 3*t**2 + 3*t**5.
3*t*(t - 1)**2*(t + 1)*(t + 2)
Let v = 4050 - 4047. Let 4/5*a**5 + 8/5*a**2 + 8/5 - 16/5*a**4 - 4*a + 16/5*a**v = 0. What is a?
-1, 1, 2
What is s in 48*s**4 - 1575*s**2 + 540 - 205*s**3 + 20*s**5 - 1755*s - 37*s**4 + 48*s**4 + 36*s**4 = 0?
-3, 1/4, 4
Let b(g) = -2*g**3 - g**2 + 3*g - 4. Let y(p) = -p**3 + p - 1. Let t be 4 + 0*1/3. Let m(s) = t*y(s) - b(s). Factor m(f).
-f*(f - 1)*(2*f + 1)
Let t be 752/329 - (-2)/(-1). Factor -t*m + 2/7*m**2 - 2/7 + 2/7*m**3.
2*(m - 1)*(m + 1)**2/7
Let z(f) be the first derivative of f**4/20 + 9*f**3/5 + 243*f**2/10 + 729*f/5 + 114. Factor z(n).
(n + 9)**3/5
Let c(z) = 20*z**4 - 15*z**3 - 25*z**2 + 15*z + 5. Let j(k) = -k**4 + k**3 + k**2 - k. Let l(h) = -c(h) - 25*j(h). Suppose l(d) = 0. What is d?
-1, 1
Suppose -4*i - 107 = -4*c - i, -5*c + 125 = 5*i. Suppose -x - 2*x - 5*y = -c, y = 4. Factor 5*k**3 - 17*k**3 - 9*k**3 + 6*k**2 + 0*k**x.
-3*k**2*(7*k - 2)
Let -16*j - 173*j + 49*j - 65*j**2 - 57*j - 5*j**3 - 375 - 78*j = 0. What is j?
-5, -3
Let t be (-3 + (-11)/(-5))*2/(44/(-55)). Solve 0 + 3/4*q**t + 9/4*q = 0.
-3, 0
Factor 1/3*j**2 + 16/3*j - 17/3.
(j - 1)*(j + 17)/3
Let s(l) be the third derivative of -l**5/45 - 125*l**4/9 - 31250*l**3/9 - 312*l**2. Factor s(y).
-4*(y + 125)**2/3
Let o be (-1 - -2) + (-7)/9. Let f(k) = -3059*k - 36708. Let d be f(-12). Find r, given that d + o*r**4 + 4/9*r**5 + 0*r - 4/9*r**3 - 2/9*r**2 = 0.
-1, -1/2, 0, 1
Let o be ((-5950)/(-260))/17 - 2/(-13). Determine l so that -o*l**2 + 0 - 3*l = 0.
-2, 0
Let b = 2071/249 - -278/83. Let -12 + 1/3*d**4 - 4*d + 4*d**3 + b*d**2 = 0. What is d?
-6, -1, 1
Solve 0 - 1/8*c**2 - 37/8*c = 0.
-37, 0
Let c(j) be the first derivative of 1/22*j**4 + 0*j - 2 - 2/55*j**5 + 0*j**3 + 0*j**2. Solve c(z) = 0 for z.
0, 1
Let 2/3*u**4 + 0*u - 5/6*u**3 + 0 - u**2 = 0. What is u?
-3/4, 0, 2
Let 65*w**4 - 1455*w**3 + 12015 + 6*w**4 + 7825*w**2 - 5*w**5 + 64*w**4 + 10485 - 18833*w - 2167*w = 0. Calculate w.
5, 6
Let i(m) = m**3 - 5*m**2 - m + 5. Let s be i(5). Suppose 4*p + j = 7, s*j + 4*j = -20. Factor 2*u - 4*u**3 - 11*u**2 + 6*u**2 - p*u**3 + 0*u**2.
-u*(u + 1)*(7*u - 2)
Let i(n) be the third derivative of -n**5/30 + 13*n**4/3 - 676*n**3/3 + 80*n**2. What is w in i(w) = 0?
26
Let r(h) = h**2 - 2*h. Let s be r(-4). Suppose -3*j - j + s = 0. Factor 3 + 18*k**3 - 15*k**3 - 3*k + 3*k**2 - j.
3*(k - 1)*(k + 1)**2
Let i(c) = c**2 + 14*c. Let b be i(-14). Suppose b = z + 2*m - 11, z - 3*m = -1 + 7. Factor 4 + 16*j**3 + 6*j**4 - 9*j**5 - 8*j**2 - z*j**5 - 4.
-2*j**2*(j + 1)*(3*j - 2)**2
Suppose -i + 2*d + 7 = 0, -3 = 4*i - 4*d - 23. Let j(k) = 3*k**3 + 4*k**2 - 12. Let o be j(i). Factor 78*p - o*p**2 - 12 - 147/2*p**3.
-3*(p + 2)*(7*p - 2)**2/2
Let f be 5 - 8/12*6. Let d be (f - 237)/(42/(-24)). Suppose 720/7*h**3 + d*h**2 + 162/7*h**4 + 32/7 + 320/7*h = 0. What is h?
-2, -2/9
Let z(x) be the second derivative of -1/98*x**7 + 0 + 0*x**2 + 3/70*x**6 - 3/140*x**5 + 1/7*x**3 + 12*x - 3/28*x**4. Find u, given that z(u) = 0.
-1, 0, 1, 2
Let m = 152 - 148. Let s(x) be the second derivative of 1/30*x**m - 2/15*x**3 + 0*x**2 + 0 - 4*x. Factor s(h).
2*h*(h - 2)/5
Suppose p + 3*y - 4 = -p, -4 = -2*p + 4*y. Let 25/8*z + 5/2*z**p + 0 + 1/2*z**3 = 0. Calculate z.
-5/2, 0
Factor 654*i - 80*i**2 - 59 - 253 + 4*i**3 - 162*i - 712 + 20*i.
4*(i - 8)**2*(i - 4)
Let r be (-3)/9 - (-4)/12. Let x be 4/4*(-18)/(-6). Find j such that j**4 + 5/3*j**x + 2/3*j**2 + r + 0*j = 0.
-1, -2/3, 0
Suppose -2*x + d = -20, -2*d = 6 - 2. Let w be (3 + (-45)/25)*x. Find g such that -54/5*g + 0 - w*g**2 - 18/5*g**3 - 2/5*g**4 = 0.
-3, 0
Suppose 0 = 4*d + 27*r - 24*r + 16, -3*d - 18 = 3*r. Suppose 0 + 3/4*g - 1/4*g**3 - 1/2*g**d = 0. What is g?
-3, 0, 1
Determine b, given that 1/11 - 4/11*b**3 + 4/11*b - 1/11*b**2 = 0.
-1, -1/4, 1
Let q be (1*(3 + -4) - -3) + 2. Suppose -7 + 4*s**3 + 14*s**3 - 17 - 14*s**q + 12 + 22*s + 66*s**2 = 0. Calculate s.
-1, 2/7, 3
Let j(p) = -3*p**2 + 7*p. Let m(o) = 8*o**2 - 22*o. Let i = -8 + 1. Let a(l) = i*j(l) - 2*m(l). Solve a(k) = 0 for k.
0, 1
Suppose -5*w - 4*n = -12 - 11, 0 = 2*w - 2*n - 2. Let l(b) be the third derivative of 2*b**2 + 0*b**w + 0*b + 1/210*b**5 - 1/21*b**4 + 0. Factor l(k).
2*k*(k - 4)/7
Let a = 1229/540 + -7/270. Suppose 3/4*o**5 + 3/4*o**2 + 0 + 9/4*o**4 + a*o**3 + 0*o = 0. Calculate o.
-1, 0
Let w(r) = 10*r**3 - 16*r**2 + 20*r - 2. Let s(x) = -32*x**2 + 19*x**3 + 8*x + 10*x - 5 + 22*x. Let j(b) = -6*s(b) + 11*w(b). Let j(i) = 0. Calculate i.
1, 2
Let o(i) be the second derivative of i**4/8 + 67*i**3/4 - 51*i**2 - 2*i + 65. Factor o(t).
3*(t - 1)*(t + 68)/2
Let q(o) be the first derivative of -o**4 + 4*o**3/3 + 2*o**2 - 4*o - 139. Factor q(p).
-4*(p - 1)**2*(p + 1)
Let k(t) be the second derivative of 0*t**4 - 1/30*t**5 + 0 + 39*t - 1/90*t**6 + 1/9*t**3 + 1/6*t**2. Find v such that k(v) = 0.
-1, 1
Let k(g) = -2*g**2 + 11*g - 9. Let f be k(4). Determine j so that -6*j + 2*j + 6*j + f*j**2 - 20*j = 0.
0, 6
Let w(m) = m**3 - m. Let c(b) be the second derivative of -13*b**5/20 + 7*b**4/12 + b**3 + b. Let l = -104 - -128. Let h(p) = l*w(p) + 3*c(p). Factor h(z).
-3*z*(z - 1)*(5*z - 2)
Let c(m) be the third derivative of 0 + 0*m - 11*m**2 + 0*m**3 + 0*m**4 - 1/200*m**6 - 1/50*m**5. Let c(i) = 0. Calculate i.
-2, 0
Let r(n) be the first derivative of -n**5/15 + n**4/4 + n**3/3 - 11*n**2/6 + 2*n + 140. Solve r(p) = 0 for p.
-2, 1, 3
Let u(z) = -z**5 + z**4 - z**3 + z**2 + z - 1. Let w(g) = -5*g**5 - 8*g**3 + 4*g**2 + 4*g - 4. Let q(t) = 4*u(t) - w(t). Factor q(r).
r**3*(r + 2)**2
Let k(d) be the second derivative of d**5/35 - d**4/28 - d**3/42 - 83*d. Factor k(x).
x*(x - 1)*(4*x + 1)/7
Suppose -k = -13 - 3. Suppose 0 = -w - 3*w + k. Determine a, given that -4*a + 4*a**3 - 3*a**2 + 2*a**w + 5*a**4 - 4*a**4 - 4*a**4 + 4 = 0.
-1, 1, 2
Let r(z) = z + 7. Let g be r(-4). Let x be 1/((-1)/(2 - 7)). Suppose 3*p - g*p**3 - 7*p**3 - 9*p**2 - x*p - 5*p**4 - 2*p**3 = 0. Calculate p.
-1, -2/5, 0
Suppose 0 = 5*r - 8 - 17, -4*r + 20 = -3*o. Let x be 3 + o/2 + -1. Determine n, given that -9*n + 7*n + 7*n**5 + 15*n**3 - x*n**2 + 19*n**4 - n**2 + 4*n**2 = 0.
-1, 0, 2/7
What is j in -2/9*j**2 + 0 + 4/9*j = 0?
0, 2
Let z(s) = s - s**2 + s**3 + 3*s**2 - 3*s**2. Suppose 0 = 7*f - 4*f + 15. Let j(w) = 2*w**3 - 4*w**2 + 8*w - 1. Let l(t) = f*z(t) + j(t). Factor l(d).
-(d - 1)*(d + 1)*(3*d - 1)
Let k(r) be the second derivative of 1/42*r**7 - 1/18*r**5 + 0*r**6 + 0*r**2 + r + 1/54*r**3