-12)/8*(-12)/45. Factor 0 + 2/5*r**2 + d*r.
2*r*(r + 1)/5
Find t such that -22*t**3 - 21*t**4 - 5*t + 6 + 79*t**3 - 45*t**2 - 3*t + 11*t = 0.
-2/7, 1
Let r be (2/(-5))/(1 - (-44)/(-40)). Let o(y) be the third derivative of 0*y + 2/9*y**3 - 1/9*y**r + 0 - 2*y**2 - 1/36*y**5. Find h such that o(h) = 0.
-2, 2/5
Let y = -206/5 - -417/10. Let -3/2*z - z**2 + z**3 + 3/2*z**4 + y*z**5 - 1/2 = 0. Calculate z.
-1, 1
Let g be 1/(-2)*(-1)/(-3)*-4. Factor -1/3*y + g - 1/3*y**2.
-(y - 1)*(y + 2)/3
Let n(r) be the second derivative of 3*r**7/28 - 7*r**6/40 - 33*r**5/40 + 7*r**4/4 - r**3 + 5*r. Solve n(w) = 0.
-2, 0, 1/2, 2/3, 2
Find r, given that 1/3*r**5 + 2/3*r**2 + 1/3*r - 1/3 - 2/3*r**3 - 1/3*r**4 = 0.
-1, 1
Let r be (-6 + 8)/(1 + 0/2). Solve 0*z**4 + 0*z**r - 1/2*z**5 - 1/2*z + 0 + z**3 = 0 for z.
-1, 0, 1
Solve -3*m**3 + 8*m**3 + 3*m**2 - 2*m**3 + 3*m**4 + 3*m**3 = 0.
-1, 0
Let q(m) = -2*m - 6. Let f be 54/(-10) - 2/(-5). Let j be q(f). Factor 3*d**3 - 2*d**j + d**2 + 3*d**4 + 2*d**4 + d**5.
d**2*(d + 1)**3
Suppose 3/5*g**2 + 6/5*g + 3/5 = 0. What is g?
-1
Let n(h) be the second derivative of 5*h**4/36 - 20*h**3/3 + 120*h**2 - h + 38. Factor n(w).
5*(w - 12)**2/3
Let a = -3 + 2. Let s(q) be the first derivative of 2*q**5/5 - 3*q**4/2 + 4*q**3/3 - 5*q**2 + 1. Let r(l) = l. Let j(k) = a*s(k) - 10*r(k). Factor j(m).
-2*m**2*(m - 2)*(m - 1)
Let x(p) = -5*p - 5*p + p + 8*p**2 - p**2. Let a(m) = -5*m - m**2 - 8*m + 11*m**2. Let y(z) = 5*a(z) - 7*x(z). Determine g, given that y(g) = 0.
0, 2
Determine c, given that 92/3*c**2 + 40*c + 50/3 + 8*c**3 + 2/3*c**4 = 0.
-5, -1
Let c(f) = -f**3 + 5*f**2 + 9*f - 3. Let j be c(6). Let y be ((-12)/j)/((-2)/5). Factor 2*x + x**2 + y*x - 3*x.
x*(x + 1)
Let y(s) be the second derivative of -s**6/1260 + s**5/140 - s**4/42 + s**3/6 - 2*s. Let j(m) be the second derivative of y(m). What is a in j(a) = 0?
1, 2
What is d in 0*d - 2/9*d**2 + 0 = 0?
0
Suppose -13 - 3 = -8*i. Let a(q) be the second derivative of -3*q + 1/30*q**5 + 2/9*q**3 - 1/6*q**4 + 0*q**i + 0. Factor a(x).
2*x*(x - 2)*(x - 1)/3
Let g be 1/5 - (-236)/20. Find n such that 12*n**4 + 4*n - 13*n**5 - g*n**2 + 6*n**3 + 4*n**5 - n = 0.
-1, 0, 1/3, 1
Suppose 2*g + 4*s = 14, 4*g + 4*s + s = 22. Let u(m) = 2*m + 16. Let p be u(-7). Determine i so that 4*i**g - i**3 + i**p - 2*i**3 = 0.
-1, 0
Suppose 2*k - 16 = -4*n, -k - k = -4*n + 24. Let h(r) = r**2 - 4*r. Let j be h(n). Factor x - x + 7*x**j - 9*x**5 - 2*x + 4*x**3.
-2*x*(x - 1)**2*(x + 1)**2
Factor -1/7*s**5 + 0*s - 1/7*s**2 + 1/7*s**4 + 0 + 1/7*s**3.
-s**2*(s - 1)**2*(s + 1)/7
What is v in -16 + 16*v + 0*v**5 + 5*v**2 - v**5 + 7*v**4 - 16*v**3 + 3*v**2 = 0?
-1, 2
Determine n so that -4/5 + 0*n + 4/5*n**2 = 0.
-1, 1
Let f = 3 - 6. Let p(n) = n**4 - 24*n**3 + 36*n**2 - 19*n + 1. Let i(r) = -12*r**3 + 18*r**2 - 9*r. Let z(y) = f*p(y) + 5*i(y). Factor z(m).
-3*(m - 1)**4
Suppose 0 = -3*x + 1 + 5. Let h be (8/5 - 0)*x. Factor 8/5*f - 1/5 - h*f**2.
-(4*f - 1)**2/5
Let w(j) be the third derivative of -j**7/210 + j**6/72 + j**5/90 + 23*j**2. Factor w(t).
-t**2*(t - 2)*(3*t + 1)/3
Let k be 5/((-80)/(-24)) - (-13)/2. What is m in k*m**3 + 4/3*m**2 + 7*m**4 + 0*m + 0 - 49/3*m**5 = 0?
-2/7, 0, 1
Let b(d) be the second derivative of d**4/36 + 2*d**3/9 + 2*d**2/3 - 7*d. Factor b(o).
(o + 2)**2/3
Let h(w) be the second derivative of w**6/6 + 2*w. Solve h(d) = 0 for d.
0
Let f be -1*1/2*538. Let p = f - -2425/9. Factor 0 + 2/9*y**3 + p*y - 2/3*y**2.
2*y*(y - 2)*(y - 1)/9
Let w(p) = -p**2 + 3*p + 3. Let j be w(3). Determine z, given that 8*z - 1 + 4*z**j - 1 + 0 - 10*z**2 = 0.
1/2, 1
Factor -79*z + 5*z**2 - 2*z**2 + 85*z.
3*z*(z + 2)
Find u such that 6*u + 2*u + 16 - 16 - 4*u**2 = 0.
0, 2
Let f(z) be the third derivative of -z**9/60480 - z**8/6720 - z**7/1680 - z**6/720 + z**5/30 - 5*z**2. Let h(u) be the third derivative of f(u). Factor h(c).
-(c + 1)**3
Let w(h) be the third derivative of -h**6/420 - h**5/210 + h**4/84 + h**3/21 + 3*h**2. Factor w(v).
-2*(v - 1)*(v + 1)**2/7
Suppose 7*u**3 - 8*u**3 - 2*u - u**3 + 4*u**2 = 0. Calculate u.
0, 1
Let j = 33 + -31. Factor 0 + 0*b + 1/5*b**j.
b**2/5
Let k(b) = -12*b**3 - 6*b**2 + 3*b. Let n(r) = -2*r**2 - 7*r**2 + 2*r**3 + 3*r**2 + 3*r - 15*r**3. Let w(s) = -4*k(s) + 3*n(s). Factor w(p).
3*p*(p + 1)*(3*p - 1)
Let g = 2895/4 - 723. Solve 1/4*l + 3/4*l**2 + 0 + 1/4*l**4 + g*l**3 = 0.
-1, 0
Let k be (5/(-15))/(1/(-9)). Suppose 0 = 3*z - 7*z + 2*r + 20, 2*r - 8 = -k*z. Determine s so that -s**z - 2*s**3 + 16*s - 12*s - 6*s**2 + 6*s**3 - 1 = 0.
1
Let p be (-26)/(-8) + (-4)/16. Factor -2*b + 0*b**3 - 2*b + b + 2 + b**p.
(b - 1)**2*(b + 2)
Let l(v) = -v**2 + 17*v. Let j be l(17). Let k(d) be the second derivative of 0*d**2 + j*d**3 + 0 - 2*d + 1/24*d**4 + 7/80*d**5. Suppose k(c) = 0. What is c?
-2/7, 0
Let d(t) be the first derivative of t**5/90 + t**4/54 - 2*t + 2. Let x(w) be the first derivative of d(w). Factor x(f).
2*f**2*(f + 1)/9
Suppose o - 5*n - 12 = 0, 0*o - o = -4*n - 10. Determine r, given that 3 - 3 + 2*r**3 - o*r**2 = 0.
0, 1
Suppose -5*h - 2*v = v - 10, 0 = -3*h + 4*v + 6. Factor -6*q - 58 + 40 - 6*q**2 - h*q**3 + 16*q**2.
-2*(q - 3)**2*(q + 1)
Factor 10/7*o**2 - 4/7*o**4 - 8/7 - 1/7*o**5 + 4/7*o - 1/7*o**3.
-(o - 1)**2*(o + 2)**3/7
Let g be (-2)/(-1) + (-14)/8. Let s(u) = -u**2 + 5*u - 5. Let y be s(2). Factor -m - g*m**2 - y.
-(m + 2)**2/4
Find d such that 0*d - 2/17*d**5 + 0*d**4 + 0*d**2 + 2/17*d**3 + 0 = 0.
-1, 0, 1
Let q(s) be the second derivative of -2*s**2 + 1/6*s**4 + s + 0 - 1/3*s**3. Factor q(h).
2*(h - 2)*(h + 1)
Let h(b) be the first derivative of b**6/4 - 11*b**5/10 + 15*b**4/8 - 3*b**3/2 + b**2/2 + 50. Let h(n) = 0. What is n?
0, 2/3, 1
Let q(r) = -r**5 - 6*r**4 - r**3 + 8*r**2 - 8*r + 8. Let u(o) = -o**4 + o**2 - o + 1. Let b(g) = -3*q(g) + 24*u(g). Factor b(s).
3*s**3*(s - 1)**2
Suppose -4 = -o - o. Suppose 7 + 7 + 10 + s**o + 8*s - 8 = 0. What is s?
-4
Let w be 252/98 + (-6)/(-14). Let d(l) be the second derivative of 0*l**w - l + 0*l**2 + 0 - 1/20*l**5 - 1/12*l**4. Factor d(u).
-u**2*(u + 1)
Let k(y) be the first derivative of y**4/4 + y**3 + 4*y + 3. Let r(v) be the first derivative of k(v). Solve r(a) = 0 for a.
-2, 0
Suppose -5*i + 2*z - 4*z = -23, -5*i + 22 = 3*z. Factor -3*n + n**4 + i*n - 4*n + 5*n**2 - 4*n**3.
n*(n - 2)*(n - 1)**2
Let c(s) = 4*s**3 + 3*s**2 - 4*s - 1. Let u = 15 - 29. Let k(f) = 2 - 12*f**3 - 7*f - 10*f**2 + 1 + 19*f. Let x(z) = u*c(z) - 4*k(z). Let x(v) = 0. Calculate v.
-1, -1/4, 1
Let u(r) be the second derivative of 0 - 2/231*r**7 + 0*r**4 + 1/110*r**5 - 2*r + 0*r**3 - 1/165*r**6 + 0*r**2. Find y such that u(y) = 0.
-1, 0, 1/2
Suppose 0*o - 48 = 4*o. Let n = o + 15. Factor -1/4*c**n - 5/4*c - 1/2 - c**2.
-(c + 1)**2*(c + 2)/4
Let b be 222/36 - (-2)/(-12). Suppose -10 = -4*c + b. Suppose 8/9*s**3 + 8/9*s + 2/9*s**c + 4/3*s**2 + 2/9 = 0. What is s?
-1
Factor 0 + 0*q**2 - 3/2*q**3 + 1/2*q**4 + 2*q.
q*(q - 2)**2*(q + 1)/2
Suppose -4*w = 5*b - 189, -15 + 54 = w + 4*b. Solve -54 - 2*j - j**2 - 2*j + w = 0 for j.
-3, -1
Let x = 136/3 + -45. Let i(s) be the first derivative of -1/6*s**2 - x*s**3 - 1 + 0*s - 1/4*s**4 - 1/15*s**5. Factor i(c).
-c*(c + 1)**3/3
Let y be -2*((-11)/66 - 11/6). Factor -108*l**2 + 2/5*l**5 - 486/5 + 36*l**3 - 6*l**y + 162*l.
2*(l - 3)**5/5
Let j be (-294)/(-63)*(18/(-7))/(-3). Let 2/7*y**3 + 4/7 - 6/7*y**2 + 2/7*y**j - 2/7*y = 0. Calculate y.
-2, -1, 1
Let g(u) be the third derivative of u**8/112 - u**7/14 + u**6/4 - u**5/2 + 5*u**4/8 - u**3/2 + 7*u**2. Solve g(v) = 0.
1
Let u(l) = -8*l**4 + 6*l**3 + 2*l**2 - 14*l - 14. Let o(n) = 3*n**4 - 2*n**3 - n**2 + 5*n + 5. Let r(i) = 14*o(i) + 5*u(i). Find m, given that r(m) = 0.
-2, 0, 1
Determine p, given that 2/9*p**2 + 2/9*p**3 - 4/3*p + 0 = 0.
-3, 0, 2
Factor -1/2*f**4 + 0 + 0*f**3 + 1/4*f + 1/2*f**2 - 1/4*f**5.
-f*(f - 1)*(f + 1)**3/4
Let a = 1 + 2. Suppose -a*w - 2*w = -25. Factor -w*l**2 - l**3 - l**4 + l + 0*l**4 + 6*l**2.
-l*(l - 1)*(l + 1)**2
Let r(c) be the first derivative of c**7/840 + c**6/120 - c**5/30 - 10*c**3/3 + 3. Let x(o) be the third derivative of r(o). Find d, given that x(d) = 0.
-4, 0, 1
Let q = 1151/5 - 234. Let x = q + 23/5. What is d in x*d**2 - 2/5 - 7/5*d = 0?
-1/4, 2
Let b = -9749/30 + 325. Let k(y) be the first derivative of 0*y - b*y