.
-(s - 2)*(s + 10)/4
Let j(r) be the second derivative of 0 + 3/50*r**5 + r + 1/3*r**4 - 6/5*r**2 + 1/15*r**3. Factor j(q).
2*(q + 1)*(q + 3)*(3*q - 2)/5
Let v(y) = 4*y**2 - 8. Let i(k) = k**2 + k. Let x(l) = 5*i(l) - v(l). Let g be x(-4). Factor -9/4*j**2 - 9/4*j**3 - 3/4*j**g - 3/4*j + 0.
-3*j*(j + 1)**3/4
Suppose -3*q + 3*k = -0*k - 6, 4 = 2*q - 5*k. Let c(f) be the second derivative of 1/28*f**4 + 0*f**q + 0 - 1/14*f**3 - 6*f. Find h such that c(h) = 0.
0, 1
Let f = 87/40 + -181/120. Factor -10/3*x + 8/3*x**2 + f.
2*(x - 1)*(4*x - 1)/3
Let v(f) be the first derivative of -f**3/3 + 11*f**2/2 + 42*f + 155. Factor v(m).
-(m - 14)*(m + 3)
Let b(x) be the third derivative of -5/3*x**3 + 1/12*x**5 + 30*x**2 - 5/24*x**4 + 0*x + 0. Factor b(g).
5*(g - 2)*(g + 1)
What is t in -144/13 - 1540/13*t**2 - 1002/13*t + 726/13*t**3 = 0?
-3/11, 8/3
Solve 2*c**3 + 0*c + 4/3*c**2 + 1/6*c**5 + c**4 + 0 = 0 for c.
-2, 0
Let i(q) be the first derivative of q**5/30 + q**4/12 - 5*q**2 - 19. Let h(v) be the second derivative of i(v). Factor h(c).
2*c*(c + 1)
Suppose 2*o + 16 = 2*m, 0 = -2*m + o + 6 + 6. Factor 5*l - 9 + 0 - m*l**2 - 13*l - 4*l.
-(2*l + 3)**2
Suppose -18*k = 6*k. Factor 0*f**3 + k*f + 0 - 2/9*f**4 + 2/9*f**2.
-2*f**2*(f - 1)*(f + 1)/9
Let h(g) = -4*g**3 + 24*g**2 - 51*g + 32. Let v be 12/10*(-55)/22. Let q(o) = 8*o**3 - 48*o**2 + 103*o - 64. Let p(n) = v*q(n) - 7*h(n). Factor p(k).
4*(k - 2)**3
Factor -201*o**2 + 296*o**4 - 78*o**2 - 135*o**3 - 293*o**4 - 141*o.
3*o*(o - 47)*(o + 1)**2
Suppose 5*o + 2*v - 28 = 0, o = 5*v - 4*v. Suppose 0 = -3*r - a - 1 - 1, -o*a - 8 = 2*r. Factor 0 + 1/3*c + r*c**2 - 1/3*c**3.
-c*(c - 1)*(c + 1)/3
Let y(r) = -2*r**4 + 22*r**3 + 186*r**2 + 240*r - 1461. Let u(d) = d**4 + d**3 + d**2 + d + 1. Let c(f) = -12*u(f) - 4*y(f). Find p such that c(p) = 0.
-9, 2
Let b(i) be the first derivative of -i**6/15 + 7*i**5/20 - 5*i**4/12 - 11*i + 12. Let l(n) be the first derivative of b(n). Factor l(q).
-q**2*(q - 1)*(2*q - 5)
Let v(h) be the first derivative of h**4/2 - 20*h**3/3 + 21*h**2 + 285. Factor v(s).
2*s*(s - 7)*(s - 3)
Determine n so that -1/9*n**2 + 0 - 2/9*n**3 - 1/9*n**4 + 0*n = 0.
-1, 0
Let l = -1614 + 158197/98. Let o(m) be the second derivative of 0*m**3 - l*m**7 + 0 + 0*m**2 + 1/2*m**6 - 33/140*m**5 + 1/28*m**4 - 8*m. What is i in o(i) = 0?
0, 1/5, 1
Let y(h) = h**2 + 14*h - 15. Let a be y(-15). Suppose -31*o + 33*o - 6 = a. Factor -2/7*i**4 + 4/7*i**2 + 0*i**o - 2/7 + 0*i.
-2*(i - 1)**2*(i + 1)**2/7
Let p(f) be the third derivative of 1/10*f**7 + 7/8*f**4 - 1/4*f**5 - f**3 + 22*f**2 - 1/56*f**8 - 1/8*f**6 + 0 + 0*f. Determine l, given that p(l) = 0.
-1, 1/2, 1, 2
Factor -10*v**4 + 10*v**3 + 88*v**2 - v**5 - 32 + 32 + 48*v + 21*v**3.
-v*(v - 4)*(v + 1)**2*(v + 12)
Let g(b) = 7*b + 408. Let k be g(-58). Let f be (-5)/(-12) + 2/6. Factor -f*a - 5/4*a**k + 0.
-a*(5*a + 3)/4
Let x(f) be the second derivative of -15*f**7/14 + f**6/3 + 18*f**5 - 20*f**4/3 - 120*f**3 + 80*f**2 - 41*f + 2. Solve x(j) = 0.
-2, 2/9, 2
Let g(b) be the second derivative of -b**7/70 - 3*b**6/40 - b**5/10 - 8*b**2 + 5*b. Let t(z) be the first derivative of g(z). Factor t(m).
-3*m**2*(m + 1)*(m + 2)
Let c(p) be the first derivative of -p**4/114 + 2*p**3/57 - p**2/19 + 16*p + 15. Let u(k) be the first derivative of c(k). Let u(q) = 0. Calculate q.
1
Let t(w) be the first derivative of -w**5 - 57*w**4/4 - 197*w**3/3 - 195*w**2/2 - 50*w - 49. Find f such that t(f) = 0.
-5, -1, -2/5
Let o(y) = y**4 - y**3 + 3*y + 1. Let l(z) = -6*z**4 + 72*z**3 + 1088*z**2 + 1003*z - 7. Let w(b) = -5*l(b) - 35*o(b). Let w(p) = 0. Calculate p.
-32, -1, 0
Let y(a) be the first derivative of -2*a**5/15 + a**4/3 + 16*a**3/9 - 6*a**2 + 6*a + 89. Find z, given that y(z) = 0.
-3, 1, 3
Let a(t) be the first derivative of t**3/6 - t**2 - 21*t/2 - 24. Factor a(g).
(g - 7)*(g + 3)/2
Suppose 90 = 64*m + 90. Let b(g) be the third derivative of 1/108*g**4 + 5*g**2 + 2/27*g**3 + 0*g - 1/90*g**5 + m. Solve b(y) = 0.
-2/3, 1
Let u be 0 + 6/(-3) - -28. Suppose 246 = 2*w + 2*j, 5*w - 2*j + u = 620. Factor 59*q**5 - 3 - 15*q - 11*q**5 - w*q**4 + 75*q**3 + 15*q**2 + 0.
3*(q - 1)**3*(4*q + 1)**2
Let j = 7688/3 - 2562. Let w(h) be the first derivative of -4/15*h**5 + 0*h - j*h**3 + 0*h**2 + 7/6*h**4 - 11. Factor w(f).
-2*f**2*(f - 3)*(2*f - 1)/3
Let s(q) = q**3 - 103*q**2 - 967*q - 2921. Let b(n) = 2*n**3 - 154*n**2 - 1450*n - 4382. Let u = -21 - -16. Let m(v) = u*b(v) + 8*s(v). Factor m(a).
-2*(a + 9)**3
Let l(o) = 20*o**2 - 1065*o + 2865. Let k(y) = -3*y**2 + 152*y - 409. Let f(s) = 15*k(s) + 2*l(s). Let f(t) = 0. What is t?
3, 27
Let z be (3/(-5) + 138/30)/1. Factor 108*i**2 - 100*i**2 + 2 + 4*i**3 - 2*i**4 - 7*i - 6*i**3 - 3*i**5 + z*i**5.
(i - 1)**4*(i + 2)
Let m be 14/(-24)*-26 - 4. Let o = m - 11. Determine l so that 1/6 - o*l**2 + 0*l = 0.
-1, 1
Suppose 126 = 3*c - 5*s, -5*s - 200 = -6*c + c. Solve -10*m**3 - 3*m**4 + 28*m**2 - c*m**2 + 27*m - 5*m**3 = 0.
-3, 0, 1
Let y be (-698)/(-70) - (-16)/(-28). Let x = y - 9. Factor 0 + 0*v**2 + 2/5*v**3 - x*v.
2*v*(v - 1)*(v + 1)/5
Let i(v) = 7*v - 31. Let l be i(5). Factor -16*c + 3*c + l*c + 3*c**2.
3*c*(c - 3)
Suppose 0 = 11*b - 850 + 762. Let t(p) be the first derivative of 0*p + 2*p**2 - b + 10/3*p**3. Suppose t(d) = 0. What is d?
-2/5, 0
Let i be 6/7281*(4 + -1). Let g = 3222/5663 + i. Let -g*u + 4/7 + 1/7*u**2 = 0. Calculate u.
2
Let j be (0 + -1)*-2 - (-7 + 6). Suppose -5*k + o + 43 = 0, j*k - 2*o = 26 + 4. Solve 10/7*a**3 + 36/7 + 66/7*a - k*a**2 = 0.
-2/5, 3
Let x be ((12/(-42))/1)/((-30)/35). Factor -1/3 + x*k**2 + 1/3*k - 1/3*k**3.
-(k - 1)**2*(k + 1)/3
Suppose -3*a + 28 - 10 = -2*g, -34 = -2*a + 5*g. Factor -64*p - 512/3 - 8*p**a - 1/3*p**3.
-(p + 8)**3/3
Let w(j) = -9*j**3 - 43*j**2 + 62*j - 1. Let x(u) = 64*u**3 + 302*u**2 - 434*u + 2. Let z(q) = 44*w(q) + 6*x(q). Factor z(a).
-4*(a - 1)*(a + 8)*(3*a - 1)
Let i(z) be the second derivative of 2*z**6/15 - 2*z**5/5 - z**4/3 + 4*z**3/3 - 49*z + 1. Factor i(q).
4*q*(q - 2)*(q - 1)*(q + 1)
Let j(k) = -k + k**3 - 42*k**2 + 2*k + 42*k**2. Let x(g) = 6*g**3 - g**2 + g. Let c(f) = 12*j(f) - 4*x(f). Solve c(m) = 0 for m.
-2/3, 0, 1
Suppose a = 3*c + 12, 0 = -2*a - 2*a + 5*c + 34. Suppose -a*v + 12 = -3*v. Solve -7 - 4*n + 16*n**2 - 8 + 2 - 4*n**5 - 8*n**v + 5 + 8*n**3 = 0.
-2, -1, 1
Let i(u) be the first derivative of -11 - 4/11*u - 2/33*u**3 + 3/11*u**2. Factor i(y).
-2*(y - 2)*(y - 1)/11
Let n(x) be the second derivative of -5*x**4/12 - 20*x**3/3 - 35*x**2/2 - 96*x. Factor n(p).
-5*(p + 1)*(p + 7)
Let f(d) be the first derivative of d**4/12 - d**3/6 + 17*d + 13. Let s(x) be the first derivative of f(x). Factor s(t).
t*(t - 1)
Let q be (10/8)/((-5)/4 - -1). Let x(g) = 15*g**3 - 25*g**2 + 15*g. Let n(p) = -22*p**3 + 37*p**2 - 22*p. Let o(l) = q*n(l) - 7*x(l). Factor o(j).
5*j*(j - 1)**2
Factor -15*t**3 + 12*t**3 + 53*t - 1 - 2 - 50*t + 3*t**2.
-3*(t - 1)**2*(t + 1)
Suppose -3*k + 4*k = -3*u + 15, -k - 3 = 0. Factor -1 - 11 - 3*s**2 + 15*s + 3*s - u*s.
-3*(s - 2)**2
Let l = -563/9 - -578/9. Factor l*i - 5/3*i**3 - 5/3*i**2 + 5/3.
-5*(i - 1)*(i + 1)**2/3
Let i be (-68)/(-18) + (-4)/(-18). Let q = -2 + i. Factor 12*f - 4*f**3 - 2*f + 8 - 8*f**q - 6*f.
-4*(f - 1)*(f + 1)*(f + 2)
Suppose 0 = -5*k + 37 - 7. Suppose -8 = 2*y - k*y. Factor -x - y*x**2 + 3*x + 11*x**2.
x*(9*x + 2)
Let c = -105 - -127. Suppose 3*a + 1 = -3*k + 22, 4*a = -k + c. Factor 3/4*n**3 + 0 - 3/4*n + 0*n**k.
3*n*(n - 1)*(n + 1)/4
Suppose 0*k + 2*k - 4 = 0. Let h = k + 2. Factor 14*v**3 - 10*v**4 + 2*v**4 - h*v**4 + 3*v**5 - 6*v**2 + v**3.
3*v**2*(v - 2)*(v - 1)**2
Let z(p) be the second derivative of -1/30*p**6 + 0 + 5/24*p**3 + 1/4*p**2 - 1/20*p**5 - 1/168*p**7 + 1/24*p**4 + 5*p. Factor z(m).
-(m - 1)*(m + 1)**3*(m + 2)/4
Let u(z) be the first derivative of -3/7*z**2 + 3/14*z**4 + 3/35*z**5 + 0*z - 1/7*z**3 - 29. What is c in u(c) = 0?
-2, -1, 0, 1
Let q be -2 + (-34)/(-8) - (-3)/(-12). Factor 28*l - 8*l**2 - 12 - 3*l**3 - 12*l**q + 6*l**3 + l**3.
4*(l - 3)*(l - 1)**2
Let w = 25 - 22. Find y such that -4*y - 14*y**2 - 3*y**2 + 58*y**w + 5*y**2 + 12 - 54*y**3 = 0.
-1, 1, 3
Let j(d) be the third derivative of d**7/210 + d**6/12 - d**5/60 - 5*d**4/12 + 2*d**2 + 417*d. Factor j(z).
z*(z - 1)*(z + 1)*(z + 10)
Let g be (-2