3. Find c such that p(c) = 0.
3
Let o = 437/4 - 109. Factor -1/4*t**2 + 1/4*t + 0 - o*t**3 + 1/4*t**4.
t*(t - 1)**2*(t + 1)/4
Let r(k) be the first derivative of -k**3/3 + k**2/2 - 1. Let u(v) = -2*v**3 + 2*v**2. Let i be 2/(-7) - (-18)/14. Let y(m) = i*u(m) + 2*r(m). Factor y(f).
-2*f*(f - 1)*(f + 1)
Let u be ((-3)/15)/((-2)/5). Suppose -4*x + 5 = -2*z + x, 2*z + 5*x = 5. Factor 0*f**2 + z - u*f + 1/2*f**3.
f*(f - 1)*(f + 1)/2
Let f be 1/2 - -3*2/9. Let a(i) be the second derivative of -f*i**3 + 0 + 5/12*i**4 + i + i**2. Factor a(d).
(d - 1)*(5*d - 2)
Factor 0 - 1/3*w**2 + 1/6*w**5 - 1/6*w**3 + 1/3*w**4 + 0*w.
w**2*(w - 1)*(w + 1)*(w + 2)/6
Let o(q) be the second derivative of q**8/1440 + q**7/756 - 2*q**6/135 + q**5/45 - q**4/6 - 3*q. Let u(v) be the third derivative of o(v). Solve u(l) = 0 for l.
-2, 2/7, 1
Factor 1/4 - 1/8*u**2 + 1/8*u.
-(u - 2)*(u + 1)/8
Let 12*t**2 + 36*t - t**2 - 2*t**4 + 18 - 4*t**3 + 5*t**2 = 0. What is t?
-3, -1, 3
Let z(f) be the second derivative of -f**7/210 - f**6/40 - f**5/60 + f**4/8 + f**3/3 + 2*f**2 - 6*f. Let x(b) be the first derivative of z(b). Factor x(c).
-(c - 1)*(c + 1)**2*(c + 2)
Suppose -35 = -4*w - 3. Let g(j) = j**3 - 7*j**2 - 6*j - 8. Let d be g(w). Find f, given that -1/4*f**4 - 4 + 2*f**3 - 6*f**2 + d*f = 0.
2
Let q = 153/8 + -135/8. Let f(t) be the first derivative of 3*t - 15/2*t**2 + q*t**4 + 13/4*t**3 - 5. Find g, given that f(g) = 0.
-2, 1/4, 2/3
Let r(x) = 2*x**2 + 4*x + 12. Let t(k) = 2 - 5 + 4. Suppose -p + 0 = 1. Let s(o) = p*r(o) + 10*t(o). Factor s(j).
-2*(j + 1)**2
Let x(n) be the first derivative of -n**7/126 + n**6/90 + n**5/60 - n**4/36 + 7*n - 5. Let c(u) be the first derivative of x(u). What is m in c(m) = 0?
-1, 0, 1
Let x(d) = -d**3 + 8*d**2 - 8*d + 10. Let g be x(7). Factor 6 + 3*y**2 + 3*y - 6 - 3 - g*y**3.
-3*(y - 1)**2*(y + 1)
Factor 2*o + 2/5*o**3 + 8/5*o**2 + 4/5.
2*(o + 1)**2*(o + 2)/5
Suppose -6 = -4*u - 5*o, 0*u + u - 12 = 4*o. Solve 2/9*i**u + 0*i**3 + 0*i + 0 - 2/9*i**2 = 0 for i.
-1, 0, 1
Let g be (-2)/(-9) + (-160)/(-9). Let x be (-2)/9 + 94/g. Determine o, given that 2*o**5 + 0*o**3 + 2*o**3 - 4*o**x - 2*o**4 + 2*o**2 = 0.
-1, 0, 1
Factor 28*f**2 - 3*f + f - 16*f**3 - 4*f**3 - 6*f**2.
-2*f*(f - 1)*(10*f - 1)
Suppose -8 = -2*u - u - 2*w, -5*w = 2*u + 2. Suppose -12 = -u*l - 0*l. Determine m, given that 5*m - 10*m + 7 + l*m**2 - 4*m - 1 = 0.
1, 2
Solve -12/5 + 14*f - 148/5*f**2 + 2*f**5 + 144/5*f**3 - 64/5*f**4 = 0.
2/5, 1, 3
Let r = 550 - 6048/11. Factor -8/11*q**2 - 10/11*q - 4/11 - r*q**3.
-2*(q + 1)**2*(q + 2)/11
Let g(h) be the first derivative of -h**7/126 + h**6/90 - 4*h - 2. Let x(w) be the first derivative of g(w). Factor x(q).
-q**4*(q - 1)/3
Let w(k) be the second derivative of -k**4/6 - 5*k**3/3 - 6*k**2 - 10*k. Determine j so that w(j) = 0.
-3, -2
Factor 0*x**2 + 0 + 0*x - 2/7*x**3 + 1/7*x**4.
x**3*(x - 2)/7
Suppose 0 = z - 0*z. Factor -n**2 + 2 - 2 + z.
-n**2
Factor -4/15*c + 0 - 2/15*c**2.
-2*c*(c + 2)/15
Let o(d) = -12*d**5 + 51*d**4 - 51*d**3 + 12*d**2. Let s(z) = 11*z**5 - 51*z**4 + 52*z**3 - 12*z**2. Let k(v) = -4*o(v) - 3*s(v). Suppose k(u) = 0. What is u?
0, 2/5, 1, 2
Let i(t) be the first derivative of t**5 - 15*t**4/4 - 35*t**3/3 + 75*t**2/2 + 90*t - 9. Factor i(m).
5*(m - 3)**2*(m + 1)*(m + 2)
Let d be 16/1468*(-3)/6. Let m = 2930/1101 - d. Solve 5/3*t**3 + 2/3 + 1/3*t - m*t**2 = 0.
-2/5, 1
Let b(r) be the second derivative of -1/15*r**6 - 2/3*r**3 + 0*r**2 + r + 1/14*r**7 - 9/20*r**5 + r**4 + 0. Let b(p) = 0. Calculate p.
-2, 0, 2/3, 1
Let h(d) be the first derivative of d**6/60 + 2*d**5/25 + d**4/10 - d**3/15 - d**2/4 - d/5 - 5. Factor h(u).
(u - 1)*(u + 1)**3*(u + 2)/10
Determine t so that 9*t**5 + 0*t - 8 - 32*t**2 + 2*t**5 - 8*t**3 - 7*t**5 + 8*t**4 - 28*t = 0.
-1, 2
Let r(s) be the second derivative of 1/42*s**4 - 5*s + 0 + 0*s**3 - 1/7*s**2. Find v, given that r(v) = 0.
-1, 1
Find i such that i + i + i**2 - 6*i**2 + 4*i**2 = 0.
0, 2
Let z(f) = -f**2 - 7*f - 7. Let d be z(-5). Let p = d + -1. Let -4 - 10*o**p + 0*o + 4*o**2 + 14*o = 0. What is o?
1/3, 2
Let k be (14/(-21))/((-2)/9). Solve 8*j**4 + 2*j - j**3 - 12*j**4 - 3*j**k + 2*j + 4*j**2 = 0 for j.
-1, 0, 1
Let t(z) be the second derivative of -1/42*z**7 + 0*z**3 - 1/12*z**4 + 3*z + 1/20*z**5 + 0*z**2 + 1/30*z**6 + 0. Factor t(l).
-l**2*(l - 1)**2*(l + 1)
Suppose 64/9*i - 4/3*i**2 - 20/9 = 0. Calculate i.
1/3, 5
Let s(o) be the third derivative of -1/3*o**3 + 0*o**5 + 0*o + 1/1440*o**6 + o**2 + 0 - 1/96*o**4. Let t(g) be the first derivative of s(g). Factor t(k).
(k - 1)*(k + 1)/4
Let b(p) be the first derivative of -3*p**4/4 + 3*p**3 - 3*p**2 + 26. Determine t, given that b(t) = 0.
0, 1, 2
Let f(z) be the first derivative of -14/15*z**3 + 4/5*z + z**2 - 5. Factor f(r).
-2*(r - 1)*(7*r + 2)/5
Let k(m) = m**3 - 6*m**2 - 7*m + 4. Let i be k(7). Find r such that 4*r - i*r + r**2 + 1 - 2*r**2 = 0.
-1, 1
Let a(q) = q**5 - q**2 - q - 1. Let c(m) = 6*m**5 + 2*m**4 + m**3 - 5*m**2 - 5*m - 5. Let s(l) = 10*a(l) - 2*c(l). Factor s(j).
-2*j**3*(j + 1)**2
Let z(y) = 4*y**3 - 4*y**2 + 12*y - 4. Let f(q) = q**3 + q - 1. Let w(g) = -8*f(g) + z(g). Factor w(n).
-4*(n - 1)*(n + 1)**2
Let z(l) = -l**5 - l**4 + l**3 + l**2 + 1. Let b(r) = 4 + 3*r**5 + 5*r**2 + 4*r**3 - 8*r**5 - 3*r**3 - r**4. Let h(c) = 3*b(c) - 12*z(c). Factor h(f).
-3*f**2*(f - 1)**3
Suppose 0*l + 12 = 3*l - 3*x, 4*l + 2*x + 8 = 0. Factor -2*d**4 - 1/2*d**3 + d**2 + 3/2*d**5 + 0*d + l.
d**2*(d - 1)**2*(3*d + 2)/2
Factor 0 - 1/2*v + 1/2*v**2.
v*(v - 1)/2
Let y(z) be the third derivative of z**5/570 + z**4/114 + 19*z**2. What is q in y(q) = 0?
-2, 0
Let t(u) be the first derivative of 6 - 1/15*u**3 - 1/10*u**2 + 0*u. Determine v, given that t(v) = 0.
-1, 0
Factor -8*q**5 - 4*q**4 - 9*q**5 - q**4 + 12*q**5.
-5*q**4*(q + 1)
Let y(b) be the second derivative of -b**6/600 + b**5/150 - 7*b**2/2 + b. Let u(h) be the first derivative of y(h). Determine j so that u(j) = 0.
0, 2
Determine s, given that 10*s**2 - 4*s**3 - 3*s**2 + 5*s**3 = 0.
-7, 0
Factor 1/4*y**3 + 0*y - y**5 + 0*y**2 + 3/4*y**4 + 0.
-y**3*(y - 1)*(4*y + 1)/4
Let d be ((-40)/(-5) + -2 + -2)/10. Factor d*m - 2/5*m**5 + 0 - 4/5*m**2 + 0*m**3 + 4/5*m**4.
-2*m*(m - 1)**3*(m + 1)/5
Let k = -638/5 - -128. Determine z, given that -2/5*z + 0 + 2/5*z**2 - 4/5*z**5 + 6/5*z**3 - k*z**4 = 0.
-1, 0, 1/2, 1
Let q(x) be the second derivative of -x**7/70 + 2*x**6/25 - 9*x**5/100 - x**4/5 + 2*x**3/5 - 17*x. Find s, given that q(s) = 0.
-1, 0, 1, 2
Let h = 38/7 + -134/35. Let p(i) be the first derivative of 4/9*i**3 + 0*i**2 - 3/2*i**4 - 5/9*i**6 - 3 + 0*i + h*i**5. Factor p(v).
-2*v**2*(v - 1)**2*(5*v - 2)/3
What is s in 7*s - 24*s**4 - 7*s + 36*s**3 - 3*s**5 + 7*s**5 - 16*s**2 = 0?
0, 1, 4
Factor -i**4 + 6*i**3 + 3*i**5 + i**4 + 9*i**4.
3*i**3*(i + 1)*(i + 2)
Let h(l) be the second derivative of -l**7/63 + 2*l**6/45 - l**4/9 + l**3/9 + 23*l. Factor h(m).
-2*m*(m - 1)**3*(m + 1)/3
Solve -4*u**3 - 16*u + 15*u**2 - u**3 + u - 3 + 8 = 0 for u.
1
Let q = -5012 + 130289/26. Let g = q + 18/13. Solve 1/2*h**2 + g - h = 0.
1
Let s(p) = -3*p**3 - 12*p**2 - 5*p + 1. Let k be (-16)/(-6)*(-45)/12. Let u = k + 13. Let b(r) = r**3 - r**2 - 1. Let g(v) = u*b(v) - 3*s(v). Factor g(m).
3*(m + 1)*(m + 2)*(4*m - 1)
Let k be (13 - 10)*3/9 + -1. Factor -4/3*w**3 + 0*w**2 + k + 0*w + 4/3*w**4.
4*w**3*(w - 1)/3
Let c(v) be the first derivative of v**7/2100 + v**6/450 - v**3 + 3. Let w(g) be the third derivative of c(g). Factor w(s).
2*s**2*(s + 2)/5
Let c(w) = 3*w - 1. Let f be c(1). Factor -f*n**4 + 5*n + 4 - 2 + 3*n - 4*n**3 - 4*n.
-2*(n - 1)*(n + 1)**3
Find n, given that -3/5*n**4 + 0*n + 0*n**2 - 6/5*n**3 + 0 = 0.
-2, 0
Let i(k) be the second derivative of -1/30*k**6 - 1/3*k**4 + k + 1/6*k**5 - k**2 + 1/3*k**3 + 0. Let d(t) be the first derivative of i(t). Factor d(r).
-2*(r - 1)**2*(2*r - 1)
Let d(n) = n**3 + 5*n**2 + n + 7. Let s be d(-5). Factor s*k + 3*k**2 + 2*k - k**2.
2*k*(k + 2)
Let p be ((-8)/(-24))/(2/12). Let w(t) be the second derivative of 0 + 1/12*t**4 + 1/30*t**6 + 1/10*t**5 + 0*t**3 + t + 0*t**p. Solve w(g) = 0.
-1, 0
Let b(h) be the first derivative of 2 + 1/12*h**4 + 0*h**2 + 0*h**3 - 2*h. Let g(m) be the first derivative of b(m). Determine n, given that g(n) = 0.
0
Let l(u) = -u**3 + 5*u