r**4 - 2*r**3 + r**4 + 12*r**2 - 68*r**2.
-r*(r - 4)**2*(3*r - 1)
Let f = 21/877 + 196343/4385. Factor -128/5 - f*m + 28/5*m**3 - 2/5*m**4 - 66/5*m**2.
-2*(m - 8)**2*(m + 1)**2/5
Let b = -2/169 - -682/507. Let u be (2/5)/((-9)/(-15)). Factor -2/3 - b*c + 4/3*c**3 + u*c**2.
2*(c - 1)*(c + 1)*(2*c + 1)/3
Suppose -3*c - 13 - 3 = -2*z, 5*c + 10 = -5*z. Factor -20*u - 11 - 59 + 20 - z*u**2.
-2*(u + 5)**2
Let 32/5*w + 4/5*w**3 + 4*w**2 + 16/5 = 0. Calculate w.
-2, -1
Let r(l) be the third derivative of l**5/12 - 115*l**4/24 - 20*l**3 + 406*l**2. Factor r(y).
5*(y - 24)*(y + 1)
What is j in 2/23*j**4 + 30/23*j**2 + 0*j - 2/23*j**5 + 34/23*j**3 + 0 = 0?
-3, -1, 0, 5
Let k(s) be the second derivative of -2/33*s**3 - s + 0 + 1/66*s**4 + 1/11*s**2. Solve k(p) = 0.
1
Let q(a) be the first derivative of -2*a**3/7 - 723*a**2/7 - 1440*a/7 + 468. Factor q(m).
-6*(m + 1)*(m + 240)/7
Suppose -5*z + 18 = g, -31*g + 33*g + z - 9 = 0. Factor -1/4*q**4 - 3/2*q**2 - 1/4 - q - q**g.
-(q + 1)**4/4
Let l(c) = -c**3 - 39*c**2 - 309*c - 9. Let s be l(-11). Solve 1/2 + 3/4*o + 1/4*o**s = 0 for o.
-2, -1
Suppose b + 2*b - 12 = 3*g, -1 = b. Let d be ((70/21)/g)/((-1)/3). Factor -3/7*h**d + 0*h + 3/7.
-3*(h - 1)*(h + 1)/7
Suppose 3*l + 10 = 16. Factor -p**l - 5*p + 0*p - 4 + 13*p - 3*p.
-(p - 4)*(p - 1)
What is q in -2/3*q**4 + 20/9*q + 0 + 6*q**2 - 20/9*q**3 = 0?
-5, -1/3, 0, 2
Determine i, given that 27/2 - 1/6*i**2 + 4*i = 0.
-3, 27
Let v(c) be the first derivative of 13 + 3*c**3 - 27/8*c**4 + 15*c**2 + 12*c. Solve v(s) = 0.
-2/3, 2
Let k = -10193 - -71375/7. Suppose k*j**2 + 2/7 - 2*j = 0. Calculate j.
1/4, 1/3
Let f(y) be the first derivative of 5*y**4/4 - 35*y**3/3 + 40*y**2 - 60*y - 105. Factor f(d).
5*(d - 3)*(d - 2)**2
Factor 15*q + 22*q**2 - 2*q**2 + 4*q**2 + q**3 - 7*q**2 - q**4.
-q*(q - 5)*(q + 1)*(q + 3)
Suppose 8 = -5*o - 3*r - 4, 5*o - 4 = r. Let q(n) = o*n + 0*n - n**2 + 0*n + n**3. Let x(j) = -3*j**3 + j**2. Let i(p) = 2*q(p) + x(p). Factor i(f).
-f**2*(f + 1)
Let z(j) be the second derivative of -7*j**5/100 - 43*j**4/30 + 67*j**3/30 + 13*j**2/5 + 24*j. Find v such that z(v) = 0.
-13, -2/7, 1
Suppose 21 = -0*b + 3*b. Solve -12 - c - 7*c - b*c - 3*c**2 = 0.
-4, -1
Let w(z) = z**5 - 5*z**4 - 6*z**3 - 2*z**2 - z + 1. Let k(y) = 2*y**5 + y**3 + y**2 - y + 1. Let n(l) = 2*k(l) - 2*w(l). Let n(i) = 0. Calculate i.
-3, -1, 0
Let i(z) be the third derivative of 0 + 4/3*z**3 + 1/6*z**4 - 1/30*z**5 + 37*z**2 + 0*z - 1/120*z**6. Factor i(p).
-(p - 2)*(p + 2)**2
Let m(n) be the third derivative of n**7/1260 - n**5/60 + n**4 - 21*n**2. Let j(r) be the second derivative of m(r). Factor j(b).
2*(b - 1)*(b + 1)
Let v be (-12)/(-16) - 25/(-20). What is f in 0 + 3/2*f**v + 3/2*f = 0?
-1, 0
Let d(o) = -6*o**2 + 23*o + 17. Let w(a) = -a**2 - 3 + 2 + 4*a + 4. Let m = -35 + 41. Let x(v) = m*d(v) - 34*w(v). Let x(i) = 0. Calculate i.
0, 1
Let r(n) = n**3 - 7*n**2 + 7*n + 14. Let a be r(7). Let c = -121/2 + a. Factor 0 + c*o**2 + o - 1/2*o**5 + 3/2*o**3 - 1/2*o**4.
-o*(o - 2)*(o + 1)**3/2
Let m = 14 - 15. Let p be ((-112)/(-40))/(m/(-5)). What is b in 3*b**5 + p*b**2 - 3*b**3 + 3*b**4 - 17*b**2 + 0*b**4 = 0?
-1, 0, 1
Let i = 37 - 40. Let c(s) = 3. Let j(d) = -d**2 + 6*d + 9. Let q(h) = -2*h**2 + 12*h + 19. Let b(y) = 5*j(y) - 3*q(y). Let v(r) = i*b(r) - 21*c(r). Factor v(f).
-3*(f - 3)**2
Let q(o) be the second derivative of o**4/20 - o**3 + 63*o**2/10 + 4*o - 23. Factor q(l).
3*(l - 7)*(l - 3)/5
Let y be 99/(-154) - 48/(-42). Suppose 1/2*d**5 - d**3 + 0 + y*d + 0*d**4 + 0*d**2 = 0. Calculate d.
-1, 0, 1
What is y in 1/4*y**4 - 3/2*y**3 + 5/4*y**2 + 6*y - 9 = 0?
-2, 2, 3
Let c be ((-8)/12 + 1)*6. Suppose c*b - 22 = -2*b + 2*f, -2*b - 5*f - 7 = 0. Let -z + z**b + z**3 + 0*z - 5*z**4 - 6*z**2 - 10*z**3 = 0. What is z?
-1, -1/4, 0
Let m(t) be the third derivative of 0 + 5/336*t**8 + 1/21*t**7 + 0*t**3 + 0*t**4 + 0*t**5 + 0*t + 7*t**2 - 1/8*t**6. Factor m(f).
5*f**3*(f - 1)*(f + 3)
Let s be (0 - -5)*(2 - (-24)/2). Let j be 2 - ((-4)/s)/(13/(-390)). Suppose -j*t**2 - 16/7*t - 32/7 = 0. What is t?
-4
Let i(o) = -3*o + 12. Let q be i(3). Suppose 5*x - 5*a = 0, -q + 18 = 5*a. What is r in -14*r**2 - 22/3*r - 4/3 - 34/3*r**x - 10/3*r**4 = 0?
-1, -2/5
Suppose 0 = -2*k + 7 - 3. Determine r so that 0*r**5 + 4*r**4 - 3*r**5 - 4*r**2 - 2*r**3 + 5*r**5 + 0*r**k = 0.
-2, -1, 0, 1
Suppose 0 - 1/8*d - 3/8*d**2 = 0. What is d?
-1/3, 0
Factor -6*g - 19*g**2 - 11*g**4 + 14*g**3 + 24*g - 11*g**2 - 9*g**4 + 18*g**4.
-2*g*(g - 3)**2*(g - 1)
Let -5*f - 3*f + 24*f + 5*f**2 - 40 + 19*f = 0. What is f?
-8, 1
Find s such that -5/3*s**4 - 25/3*s**2 + 20/3*s**3 + 0 + 10/3*s = 0.
0, 1, 2
Suppose 7*z + 56 = 11*z. Let c be 4/z*(27/15 + 1). Determine j, given that -2*j**2 + c + 2/5*j - 2/5*j**3 + 6/5*j**4 = 0.
-1, -2/3, 1
Let x(y) be the first derivative of -y**3/3 + 21*y**2/2 - 18*y + 31. Let g be x(20). Find i such that 0 + i**3 + 1/2*i**g - 1/2*i = 0.
-1, 0, 1/2
Let -3*z**2 + z**3 + 4*z + 7*z**2 - z**2 - 10*z**3 + 2*z = 0. Calculate z.
-2/3, 0, 1
Factor -17/6*t**2 - 8/3*t**4 + 1/3*t + 0 + 20/3*t**3.
-t*(t - 2)*(4*t - 1)**2/6
Let v(y) = 3*y**5 + y**3 - y**2 + y + 1. Let h(f) = -6*f**5 + 2*f**4 - 16*f**3 - 5*f**2 + f - 3. Let m(x) = h(x) + 3*v(x). Find a such that m(a) = 0.
-2, -1, 0, 1/3, 2
Let d be ((15/27)/5)/((-13 - 1)/(-28)). Let 0 - 2/9*o + d*o**2 = 0. Calculate o.
0, 1
Let u(j) = -2*j**2 + 13*j + 12. Let l be u(7). Factor 20*a - l*a**2 - 9 + 11*a**2 + 15.
2*(a + 3)*(3*a + 1)
Suppose 56 = 5*w - 5*r + r, 0 = w - 2*r - 10. Suppose 2 - 3*i**2 + i + 14*i - 2*i**2 - w = 0. Calculate i.
1, 2
Let u = -140/19 + 496/57. Determine j, given that u*j**2 + 0 - 1/3*j**3 + 5/3*j = 0.
-1, 0, 5
Let w be (-3)/6 + (-55)/(-10). Let a(x) = 8*x**3 + 12*x**2 + 6*x. Let s(j) = -j**4 + 15*j**3 + 23*j**2 + 12*j. Let r(f) = w*a(f) - 2*s(f). Factor r(d).
2*d*(d + 1)**2*(d + 3)
Let w(h) be the second derivative of 1/8*h**2 - 1/48*h**4 - 14*h + 0 + 0*h**3. Find n such that w(n) = 0.
-1, 1
Let z be 1*57/21 - 62/(-217). Let u(x) be the second derivative of 3/20*x**5 + 3*x**2 - 3*x + 0*x**4 + 0 - 3/2*x**z. Factor u(f).
3*(f - 1)**2*(f + 2)
Let l(r) be the first derivative of 6/5*r - 19 - 2/5*r**3 - 4/5*r**2 + 2/5*r**4. Suppose l(k) = 0. Calculate k.
-1, 3/4, 1
Let j(s) be the third derivative of s**6/24 - 3*s**5/2 + 135*s**4/8 - 90*s**3 + 4*s**2 + 18. What is v in j(v) = 0?
3, 12
Let j(t) = -t**4 + 26*t**2 + 2*t - 50. Let i(h) = h**4 - 53*h**2 - 5*h + 101. Let n(x) = 2*i(x) + 5*j(x). Factor n(y).
-3*(y - 2)**2*(y + 2)**2
Let i(a) = 5*a**2 + 160*a - 20. Let l(v) = v**2 - v - 2. Let o(y) = -i(y) + 10*l(y). Factor o(c).
5*c*(c - 34)
Let n(g) be the first derivative of 2*g**2 + 0*g + 4/3*g**3 - 2. Factor n(k).
4*k*(k + 1)
Let t(g) be the second derivative of g**9/68040 - g**8/30240 - g**4/4 + 9*g. Let y(r) be the third derivative of t(r). What is q in y(q) = 0?
0, 1
Let z(k) be the first derivative of 21*k**4/4 - k**3 + 217. Suppose z(l) = 0. What is l?
0, 1/7
Let j(c) be the second derivative of -15*c + 0 + 3/2*c**3 - 1/10*c**6 - 9/20*c**5 - 1/4*c**4 + 3*c**2. Find z such that j(z) = 0.
-2, -1, 1
Let z(d) be the second derivative of -d**7/21 - d**6/15 + 6*d**5/5 + 14*d**4/3 + 16*d**3/3 - 191*d. Suppose z(i) = 0. What is i?
-2, -1, 0, 4
Let f(p) be the first derivative of p**4 - 268*p**3/3 + 262*p**2 - 260*p - 172. Factor f(u).
4*(u - 65)*(u - 1)**2
Let g(z) be the third derivative of -z**5/15 - 7*z**4/3 - 22*z**3 - 755*z**2. Factor g(f).
-4*(f + 3)*(f + 11)
Let l(a) be the first derivative of a + 1/3*a**4 - 2/5*a**5 + 4*a**3 - 2 - 1/15*a**6 - 9*a**2. Let q(p) be the first derivative of l(p). Factor q(v).
-2*(v - 1)**2*(v + 3)**2
Let l(x) be the second derivative of x**5/160 + 5*x**4/48 - x**3/48 - 5*x**2/8 - 6*x + 22. Determine k, given that l(k) = 0.
-10, -1, 1
Let g(f) = 22*f**4 + 70*f**3 + 118*f**2 + 94*f + 24. Let j(o) = -31*o - 3 - 5 + 35*o**3 - 7*o**4 - 58*o**3 - 39*o**2. Let p(q) = 3*g(q) + 10*j(q). Factor p(b).
-4*(b + 1)**3*(b + 2)
Let s(d) be the second derivative of -21/20*d**5 + 3 + 3*d**2 + d - 11/2*d**3 + 4*d**4. Determine k so that s(k) = 0.
2/7, 1
Let f(p) = 10*p + 20. Let m be f(-2). Let u(r) be the third derivative of 0*r + 1/7*r**3 + 6*r**2 + 1/210*r**5 + 1/21*r**4 + m. Factor u(c).
2*(c + 1)*(c + 3)/7
Let k(s) be the se