k?
-1, 1
Let l be ((-14232)/(-9))/4 - 2. Let j = l - 390. Solve -20/3*i**2 - 10/3*i - 2/3*i**5 - 2/3 - j*i**4 - 20/3*i**3 = 0 for i.
-1
Let m = 1657/6 - 276. Determine i so that -1/6*i**3 + 0 - 1/3*i**2 - m*i = 0.
-1, 0
Let i = 2492/5 - 496. Factor i - 3/5*v**2 - 9/5*v.
-3*(v - 1)*(v + 4)/5
Solve -4*c**4 + 5*c**4 - 2*c**4 + c**3 = 0 for c.
0, 1
Let l(n) be the first derivative of 0*n + 1/5*n**2 + 3/5*n**3 + 1/5*n**5 + 2 + 3/5*n**4. Factor l(j).
j*(j + 1)**2*(5*j + 2)/5
Suppose 9*g = -0*g + 9. Factor -7/2*o + g + 1/2*o**4 - 5/2*o**3 + 9/2*o**2.
(o - 2)*(o - 1)**3/2
Suppose 0 + 4/7*q**2 + 8/7*q**3 + 4/7*q**4 + 0*q = 0. What is q?
-1, 0
Let g(t) = -3*t**2 - 4*t - 1. Let x(k) = 4*k**2 + 5*k + 1. Let y = -3 + 5. Suppose -3*n = 3*w - 15, n = 6*n - 10. Let s(i) = w*g(i) + y*x(i). Factor s(m).
-(m + 1)**2
Let 6/5*p + 3/5*p**4 + 0 - 21/5*p**2 + 18/5*p**3 - 6/5*p**5 = 0. What is p?
-2, 0, 1/2, 1
Suppose -25 = -6*u + u. Let d(j) be the first derivative of 7/25*j**u + 0*j**2 - 2 + 1/15*j**3 + 1/4*j**4 + 0*j + 1/10*j**6. Factor d(f).
f**2*(f + 1)**2*(3*f + 1)/5
Suppose 2/11*s**3 - 2/11*s**2 + 0*s + 0 = 0. Calculate s.
0, 1
Factor -11*p**3 - 20*p**2 + 9 + 12*p + 21*p**3 - 6*p**3 + 27.
4*(p - 3)**2*(p + 1)
Factor -3 - 1/3*z**2 - 2*z.
-(z + 3)**2/3
Let l(s) be the first derivative of -s**6/6 - 2*s**5 - 33*s**4/4 - 40*s**3/3 - 8*s**2 - 4. Determine d, given that l(d) = 0.
-4, -1, 0
Let a(y) = 2*y**5 - 20*y**4 - 7*y**3 + 57*y**2 + 45*y. Let l(v) = -v**5 + 20*v**4 + 6*v**3 - 56*v**2 - 45*v. Let z(o) = -4*a(o) - 3*l(o). Factor z(h).
-5*h*(h - 3)**2*(h + 1)**2
Let -8/7 - 16/7*j**2 - 4/7*j**3 - 20/7*j = 0. Calculate j.
-2, -1
Let v be (-25)/(-3) - (-6)/9. Let x = 11 - v. Factor 0*m - 3*m**2 + 2*m**2 + 2*m**x - m.
m*(m - 1)
Suppose 0 = -7*i + 14*i - 14. Factor -8/9*g**3 - 8/9*g**i - 2/9*g + 0.
-2*g*(2*g + 1)**2/9
Let r(h) be the third derivative of 8*h**2 + 0 + 1/6*h**3 - 1/60*h**6 - 1/240*h**5 - 1/280*h**7 + 0*h + 1/12*h**4. Determine a, given that r(a) = 0.
-2, -1, -2/3, 1
Factor 2/17*g**3 + 2/17*g**2 - 2/17*g - 2/17*g**4 + 0.
-2*g*(g - 1)**2*(g + 1)/17
Let i(m) be the second derivative of 1/2*m**2 - 1/12*m**4 + 1/6*m**3 + 0 - 1/20*m**5 + m. Factor i(u).
-(u - 1)*(u + 1)**2
Solve 0*x**3 + 0*x - 2/9*x**2 + 0 + 2/9*x**4 = 0.
-1, 0, 1
Let l = 7/17 + 71/34. Factor 7/2*y**4 + l*y**3 + 3/2*y**5 + 0 + 1/2*y**2 + 0*y.
y**2*(y + 1)**2*(3*y + 1)/2
Let x(p) be the third derivative of -3/4*p**4 + 0 + 2/3*p**3 + 0*p + p**2 + 1/3*p**5. Let x(j) = 0. What is j?
2/5, 1/2
Let h(l) = l**4 + l**2 + l - 1. Let t(r) = -2*r**4 + r**3 - 8*r**2 + 3. Let w(a) = -12*h(a) - 4*t(a). Solve w(i) = 0 for i.
-3, 0, 1
Let f = 7 - 4. Factor 2 - v - f - v**4 + 9*v**2 - 11*v**3 + v**4 + 4*v**4.
(v - 1)**3*(4*v + 1)
Let q(g) be the second derivative of -3/4*g**3 + 0 + 3/4*g**2 - 1/8*g**4 + 9/40*g**5 - 5*g. Suppose q(f) = 0. Calculate f.
-1, 1/3, 1
Suppose -2*b - z + 5 = b, -25 = -2*b - 5*z. Suppose 3*s - 3*x = -0*x - 6, b = -4*s - 5*x + 28. Factor -2*w + 0 - 1/2*w**3 - 2*w**s.
-w*(w + 2)**2/2
Let s(a) be the first derivative of 4*a**5/5 + 125*a**4/36 + 125*a**3/27 + 20*a**2/9 + 4*a/9 + 29. Let s(f) = 0. Calculate f.
-2, -1, -1/4, -2/9
Let x(l) be the first derivative of -l**7/280 - l**6/120 + l**5/20 - 8*l**3/3 + 3. Let o(f) be the third derivative of x(f). Find m such that o(m) = 0.
-2, 0, 1
Let a be ((-7)/((-14)/(-3)))/(-3). Determine m so that 0 - 1/2*m**2 + a*m = 0.
0, 1
Suppose 16 = 4*g, 0*g + 5*g = 4*u + 32. Let n = 5 + u. Factor 5 - 5 + 2*m - m**n.
-m*(m - 2)
Let s be (-76)/(-42) - 12/18. Determine n, given that 12/7*n**3 + s*n**2 + 8/7*n**4 + 0 + 2/7*n + 2/7*n**5 = 0.
-1, 0
Factor -2/13*p**2 + 10/13*p - 12/13.
-2*(p - 3)*(p - 2)/13
Suppose 0*f = 2*f - 2. Let o be (0/(f - -1))/2. Factor o*q**3 + 2*q - 2 + 3 - q**4 - 2*q**3.
-(q - 1)*(q + 1)**3
Suppose 3*x = 28 - 1. Suppose k**3 + x*k**2 + 0*k**3 + 4 - 12*k**2 = 0. What is k?
-1, 2
Let f be (-3)/(-2)*136/153. Factor -2/3 - f*l**3 + 2/3*l**2 + 4/3*l.
-2*(l - 1)*(l + 1)*(2*l - 1)/3
Let h(r) = -r**2 + 12*r + 30. Let s be h(14). Let w(b) be the first derivative of 2/3*b**3 + 3 + 2*b - 2*b**s. Solve w(z) = 0.
1
Let i(k) be the third derivative of 0 + 0*k + 0*k**3 - 1/80*k**5 - 2*k**2 + 0*k**4 + 1/160*k**6. Factor i(q).
3*q**2*(q - 1)/4
Factor 1/5*h**4 + 0 - 8/5*h + 2/5*h**2 + h**3.
h*(h - 1)*(h + 2)*(h + 4)/5
Suppose 5*t - z = 153, 0 = -0*t + t + 2*z - 35. Let j = t - 123/4. Solve -1/4*u**4 - j*u + 1/4*u**3 + 0 + 1/4*u**2 = 0.
-1, 0, 1
Let z(a) = a. Let r(b) be the first derivative of 1/2*b**2 - b**3 + 2*b - 1. Let h(j) = r(j) - 6*z(j). Factor h(c).
-(c + 2)*(3*c - 1)
Suppose 0 = 13*v - 10*v + 315. Let m be (-6)/(-30) + (-9)/v. Factor 8/7 + m*x**2 + 8/7*x.
2*(x + 2)**2/7
Let z be (-1)/1*(2 + -3). Factor -4*i + 3*i**2 - i**3 + z + 0*i**2 + 0*i**2 + i.
-(i - 1)**3
Let k be 7/(84/9)*(-1 + 5). What is s in 0*s + 0 + 2/7*s**k + 0*s**2 = 0?
0
Let s(b) be the third derivative of -b**6/840 + b**5/35 - 2*b**4/7 + 32*b**3/21 + 16*b**2. What is r in s(r) = 0?
4
Solve 32/3*o**2 - 76/3*o**3 + 28/3*o**4 + 16/3*o + 0 = 0 for o.
-2/7, 0, 1, 2
Solve -k**3 + 20*k**2 - 8*k**2 + 3*k**3 = 0 for k.
-6, 0
Let k(v) be the first derivative of v**4/3 + 4*v**3/3 + 8*v + 7. Let z(i) be the first derivative of k(i). Factor z(x).
4*x*(x + 2)
Suppose -9*i + 0 + 6*i**2 - 7 + 1 = 0. Calculate i.
-1/2, 2
Let c = -1 + 3. Suppose 5*h - 20 = 5*s, -4*h + 6 = -3*s - 6. Factor -2*y**2 + c*y + h + 4*y - 4.
-2*(y - 2)*(y - 1)
Let k(n) be the second derivative of 0*n**2 + 0 + 6*n + 1/36*n**3 + 1/72*n**4. Factor k(p).
p*(p + 1)/6
Let c(f) be the second derivative of -f**8/26880 + f**4/4 + 2*f. Let p(t) be the third derivative of c(t). Let p(i) = 0. Calculate i.
0
Let x(i) be the second derivative of 3*i**5/10 - 5*i**4/3 + 4*i**3/3 + 5*i**2/2 + i. Let v(s) be the first derivative of x(s). Suppose v(z) = 0. What is z?
2/9, 2
Let i(v) = -v**3 + 8*v**2 - 6*v - 1. Let t be i(7). Let p = 6 + t. What is b in 6*b**5 + 20*b**4 + p*b**2 + 2*b - 7*b**3 + 0*b**5 + 31*b**3 = 0?
-1, -1/3, 0
Suppose 0 = -5*x + 4 + 11. Let r = x + -3. Determine m, given that 6*m**2 - 2*m**2 + r*m**2 - 6*m**5 + 8*m**3 - 2*m - 4*m**4 = 0.
-1, 0, 1/3, 1
Let m(v) be the third derivative of -1/210*v**5 + 1/21*v**4 - 1/7*v**3 + 0 + 0*v - 3*v**2. Find x such that m(x) = 0.
1, 3
Let r(m) be the third derivative of m**5/300 + m**4/40 + m**3/15 - 11*m**2. Factor r(s).
(s + 1)*(s + 2)/5
Let h be -2 - ((4 - 3) + -3). Let t(g) be the third derivative of g**2 + 0*g + 1/60*g**6 - 1/12*g**4 + h - 1/35*g**7 + 1/10*g**5 + 0*g**3. Factor t(j).
-2*j*(j - 1)*(j + 1)*(3*j - 1)
Let l(f) = -6*f**5 + 6*f**4 - 36*f**2 + 39*f - 9. Let r(q) = 11*q**5 - 13*q**4 - q**3 + 71*q**2 - 77*q + 19. Let y(a) = 5*l(a) + 3*r(a). Factor y(h).
3*(h - 2)*(h - 1)**3*(h + 2)
Let l(s) be the first derivative of -s**8/2240 - s**7/840 - s**6/1440 + 4*s**3/3 - 1. Let r(i) be the third derivative of l(i). Suppose r(j) = 0. Calculate j.
-1, -1/3, 0
Let s(n) be the first derivative of 27*n**4/4 - 12*n**3 - 33*n**2/2 - 6*n + 4. Factor s(z).
3*(z - 2)*(3*z + 1)**2
Let s(q) be the first derivative of 2*q**7/147 - q**5/35 + 5*q + 6. Let u(w) be the first derivative of s(w). Let u(k) = 0. What is k?
-1, 0, 1
Factor 0*x + 0 + 1/4*x**3 - 1/4*x**2 + 1/4*x**4 - 1/4*x**5.
-x**2*(x - 1)**2*(x + 1)/4
Let w(s) = -s**3 + s**2 + 3*s + 4. Let q be w(3). Let o(n) = n**2 + 6*n + 5. Let i be o(q). Factor 0*j + 2/5*j**3 + i - 2/5*j**4 + 0*j**2.
-2*j**3*(j - 1)/5
Let p(t) be the second derivative of 1/16*t**4 + 1/60*t**5 + 0 + 1/12*t**3 - t - 1/2*t**2. Let x(h) be the first derivative of p(h). Let x(s) = 0. Calculate s.
-1, -1/2
Factor 9*l**2 + 38*l - 3*l**3 - 38*l.
-3*l**2*(l - 3)
Let i(x) be the third derivative of -3/8*x**4 + x**3 + 5*x**2 + 0*x + 3/40*x**6 + 0 - 1/20*x**5 - 1/70*x**7. Factor i(v).
-3*(v - 2)*(v - 1)**2*(v + 1)
Let i(l) = l**2 - 2*l - 8. Let n be i(6). Let k = n + -14. Solve -1/6*u**k + 1/6 + 0*u = 0.
-1, 1
Let r be ((-4)/(-5))/((-30)/(-75)). Suppose r - 2*c + 1/2*c**2 = 0. Calculate c.
2
Let t(o) be the second derivative of -o**8/4480 + o**7/840 - o**4/6 + 2*o. Let d(x) be the third derivative of t(x). Factor d(w).
-3*w**2*(w - 2)/2
Let t(z) be the second derivative of -4*z**6/75 - 9*z**5/50 - z**4/5 - z**3/15 - 2*z. Suppose t(w) = 0. What is w?
-1, -1/4, 0
Let z(p) = p*