- 7. Let d(g) = 7*m(g) + 6*s(g). Solve d(f) = 0 for f.
0, 2
Determine y so that -3/7*y**2 + 15/7*y**4 + 3*y**3 + 3/7*y**5 - 12/7 - 24/7*y = 0.
-2, -1, 1
Suppose 0 = 7*o - 10*o. Let u(n) be the second derivative of n**2 + 0 + o*n**3 + n - 1/6*n**4. Factor u(d).
-2*(d - 1)*(d + 1)
Let p = 9 + -5. Suppose -p*o**2 + 2*o + 25 - 14*o - 25 = 0. Calculate o.
-3, 0
Factor 2/5*g**2 - 2/5 + 0*g.
2*(g - 1)*(g + 1)/5
Let g be 50/20*(-4)/(-20). Factor -g - 9/4*w - 3*w**2 - 5/4*w**3.
-(w + 1)**2*(5*w + 2)/4
Let n(j) = j**2. Let s be (-19)/(-7) + 4/14. Suppose -s*w + w - 2 = 0. Let l(i) = -4*i**3 - 7*i**2. Let k(g) = w*l(g) - 6*n(g). Factor k(v).
v**2*(4*v + 1)
Let k(m) be the first derivative of 7*m**4/18 - 20*m**3/9 + 4*m**2 - 16*m/9 - 21. Suppose k(p) = 0. What is p?
2/7, 2
Let t be 6/324*(-2)/2*-3. Let x(r) be the second derivative of t*r**4 - 2/3*r**2 - 3*r + 1/9*r**3 + 0. Factor x(q).
2*(q - 1)*(q + 2)/3
Let y(c) be the second derivative of 0 + 0*c**2 - 1/12*c**4 + 0*c**3 + c + 0*c**5 + 1/30*c**6. Factor y(w).
w**2*(w - 1)*(w + 1)
Let 46/13*k + 12/13 + 14/13*k**2 = 0. Calculate k.
-3, -2/7
Let d(s) be the first derivative of -6*s**6 + 24*s**5 - 28*s**4 + 32*s**3/3 + 44. Factor d(w).
-4*w**2*(w - 2)*(3*w - 2)**2
Factor 64*m**4 - 412*m**3 + m**5 + 2*m**5 - 7*m**5 + 156*m**3.
-4*m**3*(m - 8)**2
Let n(f) be the third derivative of 0*f**4 - 1/840*f**7 - 3/80*f**5 + 0*f + 0*f**3 + 0 - 1/80*f**6 + 3*f**2. Suppose n(l) = 0. What is l?
-3, 0
Let n = 487 - 1445/3. Factor 14*k**2 - 8/3 + n*k.
2*(3*k + 2)*(7*k - 2)/3
Let f = 1 + 2. Factor -4*q**2 + 2*q + 2 + f*q**2 - 3.
-(q - 1)**2
Suppose 3*a + 10 - 1 = f, -2*a = 0. Find n such that 9*n - f*n + 3*n**5 + 3*n**4 - 3*n**2 - 3*n**3 = 0.
-1, 0, 1
Let r(c) = 3*c**3 + 2*c**2 + 5*c + 2. Let q(x) = -7*x**3 - 5*x**2 - 11*x - 4. Let w(t) = 4*q(t) + 9*r(t). Factor w(p).
-(p - 1)*(p + 1)*(p + 2)
Let i(d) be the first derivative of -d**3 + 9*d**2/2 - 6*d - 46. Find u, given that i(u) = 0.
1, 2
Let -1/4*b - 1/4*b**4 - 3/4*b**3 - 3/4*b**2 + 0 = 0. Calculate b.
-1, 0
Find z such that 12/11*z**2 + 0*z - 6/11*z**3 + 0 - 6/11*z**4 = 0.
-2, 0, 1
Factor 111*l**2 + 537*l + 23*l**4 + 96*l**3 - 507*l - 8*l**4.
3*l*(l + 1)*(l + 5)*(5*l + 2)
Let -18 - 56*u + 520*u**4 - 522*u**4 - 14*u**3 - 60*u**2 - 10*u**3 = 0. What is u?
-9, -1
Let g(x) be the first derivative of -x**4/2 - 10*x**3/3 - 7*x**2 - 6*x + 3. Factor g(z).
-2*(z + 1)**2*(z + 3)
Let a = -960 - -960. Let -1/3*x**5 + 1/3*x**3 + 1/3*x**2 - 1/3*x**4 + 0*x + a = 0. Calculate x.
-1, 0, 1
Let k(g) be the first derivative of 2*g**3/27 - g**2/3 + 4*g/9 + 8. Factor k(c).
2*(c - 2)*(c - 1)/9
Let w = 4 + -3. Suppose -w - 3 = -z. Determine n so that 0 + 2/3*n**3 - 2/3*n - 2/3*n**2 + 2/3*n**z = 0.
-1, 0, 1
Let n(y) = y + 3. Let d be n(-2). Suppose b - 2 = d. Factor -7*c - b*c**2 + 9*c - 1 + 2*c**2.
-(c - 1)**2
Solve 1/3*q**3 - 1/3*q**5 - 1/3*q**2 + 1/3*q**4 + 0*q + 0 = 0.
-1, 0, 1
Suppose o + 5 = 0, -3*k - 5 = 5*o - 37. Suppose 5*c - 1 = k. Find x such that 4*x - x - x - 2*x**3 + 2*x**2 - 2*x**c = 0.
-1, 0, 1
Let w = -343 + 345. Factor -2/9*j**4 + 0 + 0*j**3 + 0*j + 2/9*j**w.
-2*j**2*(j - 1)*(j + 1)/9
Let i(j) be the third derivative of j**8/3024 - j**7/270 + 2*j**6/135 - 2*j**5/135 - 2*j**4/27 + 8*j**3/27 - 5*j**2. Factor i(y).
(y - 2)**4*(y + 1)/9
Suppose 6*q = 3*q + 6. Suppose 2*v - 6*v = -8. Let 8*o - q*o**2 - 8 + v*o - 2*o = 0. Calculate o.
2
Let f = -72 + 74. Factor 0*g**f + 3/4*g - 1/4*g**3 + 1/2.
-(g - 2)*(g + 1)**2/4
Factor -6/11*c**4 - 24/11*c + 18/11*c**2 - 24/11 + 12/11*c**3.
-6*(c - 2)**2*(c + 1)**2/11
Let q(c) be the third derivative of -c**5/270 + 5*c**4/108 - 4*c**3/27 + 31*c**2. Solve q(a) = 0 for a.
1, 4
Suppose 20*m**2 - 31 - 22*m**2 + 14*m + 11 = 0. What is m?
2, 5
Let k(v) be the second derivative of 0 - v - 1/15*v**3 + 0*v**5 - 2/75*v**6 + 1/15*v**4 + 0*v**2 + 1/105*v**7. Let k(j) = 0. Calculate j.
-1, 0, 1
Let r(v) be the third derivative of v**7/5040 - v**6/1440 - v**4/6 + 4*v**2. Let g(o) be the second derivative of r(o). Solve g(x) = 0 for x.
0, 1
Let t(n) be the third derivative of -n**6/720 + 7*n**5/360 - 38*n**2. Find h, given that t(h) = 0.
0, 7
Let p(n) be the second derivative of -n - 1/3*n**3 + 0*n**2 + 1/6*n**4 + 0. Suppose p(x) = 0. Calculate x.
0, 1
Let a(p) be the first derivative of 2/7*p - 4/7*p**2 + 2/35*p**5 - 2/7*p**4 + 4/7*p**3 - 3. Factor a(i).
2*(i - 1)**4/7
Factor 6/11*i**2 - 2/11 + 4/11*i.
2*(i + 1)*(3*i - 1)/11
Let z be (-68)/6 + (-1)/(-3). Let s = -9 - z. Factor -26/3*c**s + 8/3 + 10/3*c**3 + 8/3*c.
2*(c - 2)*(c - 1)*(5*c + 2)/3
Suppose 0 = -4*f + 4*d + 28, -3*f - 4 = -f + 4*d. Suppose 0 = -3*a + f*a - 2. Factor 1/4 + 0*i - 1/4*i**a.
-(i - 1)*(i + 1)/4
Let -2/5*c**2 - 12/5*c - 2 = 0. What is c?
-5, -1
Suppose -y = 5*n - 40, n + n + 3*y - 16 = 0. Let t = n + -6. Factor 7*k**2 - 3*k**2 - t*k - 3*k**2.
k*(k - 2)
Let s(a) = -4*a**3 + 12*a**2 - 6*a + 2. Let v(b) = 7*b**3 - 25*b**2 + 13*b - 5. Suppose -3*d + 14 = -1. Let c(f) = d*s(f) + 2*v(f). Factor c(k).
-2*k*(k - 1)*(3*k - 2)
Let z = -76 + 80. Let y(q) be the first derivative of 0*q**2 - 1/3*q**6 - 4/5*q**5 + 0*q**3 - 2 - 1/2*q**z + 0*q. Let y(w) = 0. Calculate w.
-1, 0
Let u(k) be the third derivative of -k**8/1680 + k**7/1050 + k**6/600 - k**5/300 + 9*k**2. Factor u(c).
-c**2*(c - 1)**2*(c + 1)/5
Let p(h) = -3*h**3 - 9*h**2 + 5*h + 7. Let n(u) = -u**3 - 5*u**2 + 3*u + 3. Let m(y) = -7*n(y) + 3*p(y). Let m(a) = 0. Calculate a.
0, 1, 3
Suppose -3*r + 3 = -2*l, -r = -2*l - 3 + 2. Suppose 1 - j - j**2 + l*j + j = 0. Calculate j.
-1, 1
Let d = 12 + -10. Let c = 2 - 0. Factor d*i**2 + i - 3*i**2 + i**5 - 4*i**4 + 6*i**3 - 3*i**c.
i*(i - 1)**4
Let y(m) = -m + 1. Let d be y(1). Suppose a = 5 - d. Suppose 0 + 0*f + 0*f**3 + 0*f**2 + 0*f**4 + 1/4*f**a = 0. Calculate f.
0
Let v = 19/30 + -2/15. Let b(l) be the first derivative of -v*l**4 + 2 + 4/3*l**3 - 4*l + l**2. Factor b(t).
-2*(t - 2)*(t - 1)*(t + 1)
Let o(g) = -g**3 + 30*g**2 - 31*g + 70. Let m be o(29). Let w(c) be the first derivative of -21/4*c**4 + 18*c**2 + 9*c**3 - m*c + 1. Factor w(h).
-3*(h - 2)*(h + 1)*(7*h - 2)
Let c = 1/402 + 1601/2814. Factor c*x**3 - 2/7 - 2/7*x**5 - 2/7*x**4 - 2/7*x + 4/7*x**2.
-2*(x - 1)**2*(x + 1)**3/7
Factor -4/5*a**4 - 1/5*a**2 - a**3 + 0 + 0*a.
-a**2*(a + 1)*(4*a + 1)/5
Let d = 418 + -835/2. Let p = -3 + 5. Factor v - 1/2*v**p - d.
-(v - 1)**2/2
Suppose 0 = b - 4*b - 6. Let r be 16/60*(-5)/b. Factor r - 1/3*j**3 - 5/3*j + 4/3*j**2.
-(j - 2)*(j - 1)**2/3
Let c(m) be the third derivative of m**8/336 + 11*m**7/630 - m**6/40 - 19*m**5/180 + m**4/12 + 4*m**3/9 + 67*m**2. Solve c(i) = 0 for i.
-4, -1, -2/3, 1
Factor 58*p**2 - 6 - 12*p**3 - 2*p - 13*p - 25*p**2 + 0*p.
-3*(p - 2)*(p - 1)*(4*p + 1)
Let y = -308/15 + 64/3. Factor y*a + 0 - 6/5*a**4 - 8/5*a**3 + 2/5*a**2.
-2*a*(a + 1)**2*(3*a - 2)/5
Let p(j) = -4*j**4 - 8*j**3 + 6. Let y(l) = -3*l**4 - 7*l**3 + 5. Suppose -3*a - 8 - 7 = 0. Let u be (a/(-2))/(4/8). Let n(w) = u*p(w) - 6*y(w). Factor n(b).
-2*b**3*(b - 1)
Let d be 4/(-18) + 2 + 0. Let r be 4*(-1)/54*-39 - 2. Factor 10/9*a**3 - 2/9*a**5 - d*a - 2/9*a**4 + 2/9*a**2 + r.
-2*(a - 1)**3*(a + 2)**2/9
Let h(u) = 6*u**5 + 29*u**4 - 94*u**3 + 101*u**2 - 11*u - 11. Let x(d) = d**5 + 6*d**4 - 19*d**3 + 20*d**2 - 2*d - 2. Let w(v) = 6*h(v) - 33*x(v). Factor w(q).
3*q**2*(q - 3)**2*(q - 2)
Let d(z) = z**3 - 5*z**2 + 4*z. Let m be d(3). Let n(f) = 5*f**2 + 9*f - 2. Let w(x) = 9*x**2 + 17*x - 4. Let c(p) = m*w(p) + 11*n(p). Factor c(t).
(t - 2)*(t - 1)
Factor -1/3*q**2 + 1/3*q**4 + 1/3*q**3 - 1/3*q + 0.
q*(q - 1)*(q + 1)**2/3
Let f(o) be the second derivative of -o**4/42 - o**3/7 - 2*o**2/7 + 6*o. Factor f(d).
-2*(d + 1)*(d + 2)/7
Let y(g) be the second derivative of -g**5/180 - g**4/72 + g**3/9 - g**2/2 + 4*g. Let s(c) be the first derivative of y(c). Suppose s(o) = 0. Calculate o.
-2, 1
Factor -10*s**2 + 50/3*s**3 - 2/3 - 6*s.
2*(s - 1)*(5*s + 1)**2/3
Let d(l) be the third derivative of 0*l**3 + 0*l + 5*l**2 - 3/20*l**5 + 0 - 1/40*l**6 - 1/4*l**4. Factor d(c).
-3*c*(c + 1)*(c + 2)
Let s(o) be the third derivative of o**6/420 + 2*o**5/105 + o**4/21 - o**2. Factor s(r).
2*r*(r + 2)**2/7
Let m(f) be the second derivative of -1/24*f**4 + 0*f**2 + 1/12*f**3 + 0 + 3*f. Factor m(z).
-z*(z - 1)/2
Let l(d) be the third derivativ