, 1
Let l(k) = k**3 - k**2 - k + 1. Let x(r) = 8*r**3 - 16*r**2 + 8*r. Let a(t) = -4*l(t) + x(t). Factor a(s).
4*(s - 1)**3
Let n(w) be the second derivative of 0*w**4 - 1/360*w**6 + 1/120*w**5 - 1/2*w**3 + 0 - 6*w + 0*w**2. Let d(s) be the second derivative of n(s). Factor d(h).
-h*(h - 1)
Let f(u) = u**2 + u - 2. Let o be f(-3). Let t(q) = -q**3 + 7*q**2 - 11*q - 12. Let p(y) = -y**3 + 4*y**2 - 5*y - 6. Let l(j) = o*t(j) - 7*p(j). Factor l(x).
3*(x - 2)*(x + 1)**2
Let o(j) be the second derivative of 0 - 1/4*j**4 - 54*j**2 + 6*j**3 - 18*j. Determine y so that o(y) = 0.
6
What is x in -4/3*x**2 + 4/3*x**3 + 0 + 0*x = 0?
0, 1
Let b(i) = i**3 + 16*i**2 + 13*i - 21. Suppose 0*v + 2*v - 5*y + 35 = 0, -y = 5*v + 74. Let k be b(v). Factor -8*x**4 + 3*x**3 + x**2 - x**3 + k*x**4.
x**2*(x + 1)**2
Suppose -3*d + 4*x + 8 = 0, 2*d - 12 = -0*x + 4*x. Let c be (-10)/(-6) - d/((-28)/7). Factor -c*i**2 + 0 + 2/3*i.
-2*i*(i - 1)/3
Let l(w) be the second derivative of -w**7/525 + w**6/60 - 7*w**5/150 + w**4/20 + 7*w**2 + 7*w. Let k(t) be the first derivative of l(t). Factor k(z).
-2*z*(z - 3)*(z - 1)**2/5
Let n be (39/6)/((-2)/4). Let b(o) = -6*o**2 - 12*o + 13. Let k(x) = -13 + 6*x + 2*x**2 + 27 + x**2 - 20. Let m(h) = n*k(h) - 6*b(h). Factor m(v).
-3*v*(v + 2)
Let m = -154 + 156. Factor 2/15*i**4 - 8/15*i**3 + 0 + 2/3*i**m - 4/15*i.
2*i*(i - 2)*(i - 1)**2/15
Let x(a) = a - 24. Let l(w) = -w**3 + 5*w**2 + 3*w + 9. Let t be l(5). Let z be x(t). Determine b so that -1/4*b**5 + 1/4*b**3 + 0*b**2 + 0 + z*b**4 + 0*b = 0.
-1, 0, 1
Suppose -3*x - 12 = 0, 2*s + 7*x - 3*x = -16. Let t(h) = -h + 13. Let y be t(s). Factor 32*n**3 + 56*n**2 + y*n + 7*n + 4 + 9*n - n.
4*(n + 1)*(2*n + 1)*(4*n + 1)
Let n be -1 - 0 - (9/3 + -24). Let 27*q**4 - 16*q**3 - 23*q**4 - q - 7*q + n*q**2 = 0. Calculate q.
0, 1, 2
Suppose 3*h = -3*k + 24, 4*h = 5*k - k. Let f be (-14)/h - -3 - -1. Factor 0 - 9/2*t**3 + 2*t**4 - f*t + 3*t**2.
t*(t - 1)**2*(4*t - 1)/2
Suppose -3*a = k - 295 + 28, 0 = a + 3*k - 81. Factor 5*m**2 + 44*m + 20 - a*m + 66*m.
5*(m + 2)**2
Let v(m) be the third derivative of -m**5/12 - 5*m**4/12 - 5*m**3/6 + 117*m**2. Factor v(b).
-5*(b + 1)**2
Let w(f) be the first derivative of -f**3/9 + 3*f**2/2 - 8*f/3 - 260. Factor w(j).
-(j - 8)*(j - 1)/3
Factor 67*f**4 - 33*f + 13*f - 19*f**2 - 2*f**5 - 21*f**4 + f**5 - 27*f**4 + 21*f**3.
-f*(f - 20)*(f - 1)*(f + 1)**2
Suppose -d = -2*w + 9, -5*w - 4*d = 5 + 5. Factor -w*u**3 - 73*u**5 - u**3 + 38*u**5 + 38*u**5.
3*u**3*(u - 1)*(u + 1)
Let j = 6/11 + 31/44. Let t(a) be the first derivative of 13 + 5*a**3 + 0*a + 5*a**2 + j*a**4. Factor t(y).
5*y*(y + 1)*(y + 2)
Let u(h) be the third derivative of 3*h**8/28 + 4*h**7/105 - 27*h**6/5 - 12*h**5/5 + 243*h**4/2 + 108*h**3 - 110*h**2. Suppose u(l) = 0. Calculate l.
-3, -2/9, 3
Let c(r) be the second derivative of -r**4/6 + 4*r**3 - 65*r. Let c(q) = 0. Calculate q.
0, 12
Let s(j) be the first derivative of 0*j**3 + 0*j**2 + 1/2*j**4 + 8 + 0*j. Solve s(y) = 0 for y.
0
Let h(c) = c**2 + 5*c + 4. Let d be h(-4). Suppose d*q = 2*q - 3*q. Factor 0 + 1/2*n**2 + 1/2*n**3 - 1/2*n**4 - 1/2*n**5 + q*n.
-n**2*(n - 1)*(n + 1)**2/2
Let h(x) = 7*x**2 + 75*x - 124. Let n(c) = -12*c**2 - 150*c + 249. Let y(u) = -11*h(u) - 6*n(u). Solve y(k) = 0 for k.
2, 13
Suppose 2 = -5*o + 22. Factor -o + g**5 + 2*g**2 + 5*g**2 + 30*g**4 - 18*g**4 - 15*g**4 - g**3.
(g - 2)**2*(g - 1)*(g + 1)**2
Let z(w) = -w**3 - 17*w**2 - 28*w + 32. Let r(p) = p - 33. Let t be r(18). Let q be z(t). Suppose 2/3 + 2/9*u**q + 8/9*u = 0. Calculate u.
-3, -1
Let r(b) = -b**3 + 10*b**2 - 6*b - 77. Let l be r(7). Determine c so that l*c**3 + 16/5*c + 10*c**4 + 88/5*c**2 + 0 = 0.
-2, -2/5, 0
Let l(h) be the first derivative of 18 - 6/13*h**3 + 8/13*h + 16/13*h**2. Find i such that l(i) = 0.
-2/9, 2
Let 72*r**3 + 3/2 + 7*r - 101/2*r**4 + 13*r**5 - 43*r**2 = 0. What is r?
-3/26, 1
Factor -5/4*t + 1/4*t**2 + 0.
t*(t - 5)/4
Let c(s) = -s**5 - s**4 + 2*s**2 - s - 1. Let b(m) = 135*m**5 + 324*m**4 + 234*m**3 + 72*m**2 - 9*m - 12. Let l(p) = b(p) - 12*c(p). What is d in l(d) = 0?
-1, -1/7, 0
Let q(b) be the third derivative of 0*b**4 + 0*b**3 + 0 + 0*b - 1/360*b**5 - 14*b**2 + 1/720*b**6. Solve q(v) = 0.
0, 1
Let z be 45/(-4860)*(-2 + -1). Let i(u) be the second derivative of -1/18*u**3 + z*u**4 + 0 + 6*u + 0*u**2. Factor i(r).
r*(r - 1)/3
Suppose -98*r + 71*r = -54. Solve -2*v**3 + 0*v**4 + 1/2*v**5 + 1 + 3/2*v - v**r = 0.
-1, 1, 2
Factor 0 - 24/5*t**2 + 3/5*t**3 + 48/5*t.
3*t*(t - 4)**2/5
Let n(f) = -57*f**3 + 879*f**2 + 1830*f + 927. Let c(m) = 7*m**3 - 110*m**2 - 229*m - 116. Let o(b) = -33*c(b) - 4*n(b). Let o(y) = 0. Calculate y.
-1, 40
Let t be (-6)/33 - (2 + (-370)/99). Let n = -5 + 7. Factor 4/9 - 28/9*v**n - t*v - 10/9*v**3.
-2*(v + 1)*(v + 2)*(5*v - 1)/9
Let v be 9 + 72/(-16) - 1/(-2). Let q(k) be the third derivative of -3/32*k**4 - 1/80*k**v - 1/4*k**3 - k**2 + 0 + 0*k. Factor q(b).
-3*(b + 1)*(b + 2)/4
Let f(m) be the second derivative of -m**6/30 - 11*m**5/20 - 7*m**4/2 - 32*m**3/3 - 16*m**2 + 19*m. Factor f(y).
-(y + 1)*(y + 2)*(y + 4)**2
Let a(j) be the third derivative of -j**5/100 + 3*j**4/40 + 42*j**2. Let a(n) = 0. What is n?
0, 3
Let l(z) be the second derivative of -5*z**7/14 + 2*z**6/3 + z**5/2 - 5*z**4/3 + 5*z**3/6 + 389*z. Find p, given that l(p) = 0.
-1, 0, 1/3, 1
Let b(y) = 15*y**2 - 222*y + 170. Let c be b(14). Factor 1/3*x**c - 8/3*x - 3.
(x - 9)*(x + 1)/3
Let o(r) be the first derivative of r**4/2 + 8*r**3 - 512*r - 283. Let o(i) = 0. Calculate i.
-8, 4
Suppose -111 + 137 = 13*f. Factor -4/3*r**f + 4/3*r**4 + 2/3*r - 2/3*r**5 + 0*r**3 + 0.
-2*r*(r - 1)**3*(r + 1)/3
Let o(x) be the second derivative of 2/57*x**3 - 11*x - 1/190*x**5 + 1/114*x**4 + 0*x**2 + 0. Suppose o(v) = 0. What is v?
-1, 0, 2
Let r(c) be the second derivative of -c**4/90 - c**3/5 + 36*c - 1. Determine z, given that r(z) = 0.
-9, 0
Let t be (-1)/(7/(-353)) - (-288)/(-96). Let g = t - 46. Factor g*k**2 - 8/7*k**3 + 0 - 4/7*k + 2/7*k**4.
2*k*(k - 2)*(k - 1)**2/7
Let n(w) = -6*w**4 + 36*w**2 + 15*w - 45. Let r(x) = 13*x**4 + x**3 - 72*x**2 - 31*x + 89. Let v(m) = 7*n(m) + 3*r(m). Suppose v(s) = 0. Calculate s.
-2, 1, 4
Let j(y) = -y - 5. Let h be j(-5). Suppose -49*s = 4*a - 52*s - 16, 0 = 4*s. Suppose -2/7*o**2 + h*o - 2/7*o**a + 0 + 4/7*o**3 = 0. Calculate o.
0, 1
Let u(g) be the third derivative of -g**8/181440 - g**7/15120 + g**6/1620 - g**5/6 - g**3/3 + g**2 + 1. Let q(b) be the third derivative of u(b). Factor q(w).
-(w - 1)*(w + 4)/9
Let t(c) be the third derivative of 0*c - 35*c**2 - 1/5*c**4 + 7/100*c**5 + 0 - 1/200*c**6 - 8/5*c**3. Suppose t(g) = 0. What is g?
-1, 4
Let d be -3*4/(-54) + (-34)/(-9). Let u(s) = -3*s - 2. Let l be u(-2). Solve -l + 5*a**2 + 4 + 5*a + 0*a**2 - 5*a**d - 5*a**3 = 0.
-1, 0, 1
Suppose 32*t = 27*t + 30. Let k(n) be the third derivative of 1/120*n**t + 0*n**5 + 0 + 2*n**2 + 1/3*n**3 - 1/8*n**4 + 0*n. Suppose k(b) = 0. What is b?
-2, 1
Let k(p) = -14*p**3 + 1278*p**2 + 181510*p + 8589864. Let f(c) = 5*c**3 - 426*c**2 - 60504*c - 2863288. Let o(m) = 17*f(m) + 6*k(m). Factor o(g).
(g + 142)**3
Let t(c) be the first derivative of -c**4/66 - c**3/33 + 11*c - 1. Let m(z) be the first derivative of t(z). What is q in m(q) = 0?
-1, 0
Let y be (340 - 358) + (0 - -21). Determine x so that 3/5*x**y + 3*x**2 + 6/5*x - 24/5 = 0.
-4, -2, 1
Let o(h) be the third derivative of -1/6*h**5 + 0 + 125/144*h**4 - 5/6*h**3 - 7/144*h**6 + 0*h - 19*h**2. Factor o(q).
-5*(q - 1)*(q + 3)*(7*q - 2)/6
Suppose 3/5*u**2 - 1728/5*u + 248832/5 = 0. What is u?
288
Solve 12/5*s - 28/5*s**2 + 16/5 = 0.
-4/7, 1
Solve 18/5*u**4 - 21/5*u**3 + 0 - 3/5*u**5 + 24/5*u - 18/5*u**2 = 0 for u.
-1, 0, 1, 2, 4
Suppose 72*q - 54*q = 72. Let s(g) be the second derivative of -9*g**2 + 1/45*g**6 + 7*g + 4/15*g**5 + 0*g**3 + g**q + 0. Factor s(c).
2*(c - 1)*(c + 3)**3/3
Let z(y) be the first derivative of -y**4 - 4*y**3/3 + 48*y**2 - 144*y + 415. Factor z(l).
-4*(l - 3)*(l - 2)*(l + 6)
Suppose 469*g = 473*g - 8. Let x(y) be the first derivative of 4 - 3/2*y**2 + 0*y - 3/4*y**4 + g*y**3. Factor x(c).
-3*c*(c - 1)**2
Let l = 122 - 122. Suppose l = -3*v - 19*v. Factor 0 + v*m**3 + 0*m + 3/5*m**4 - 3/5*m**2.
3*m**2*(m - 1)*(m + 1)/5
Let z(i) be the first derivative of i**8