.
-2*(g + 4)*(3*g - 1)/3
Let u(o) be the first derivative of -o**5/60 + 7*o**4/36 - 11*o**3/18 + 5*o**2/6 - 2*o + 19. Let p(b) be the first derivative of u(b). Factor p(s).
-(s - 5)*(s - 1)**2/3
Suppose -3*d - 10 = -4. Let c(s) = 4*s**2 + 10*s - 12. Let j(k) = k**2 + k - 1. Let h(i) = d*j(i) + c(i). Factor h(b).
2*(b - 1)*(b + 5)
Let l(c) = -65*c**2 + 35*c + 85. Let d(z) = z - 1. Let u(h) = -11*h**2 + 11*h + 9. Let n(m) = -5*d(m) + u(m). Let q(b) = -6*l(b) + 35*n(b). Factor q(t).
5*(t - 2)*(t + 2)
Suppose 5*t = 6*t - 136. Let i = t + -134. Factor -2/3 + 11/3*l + 7/3*l**3 - 16/3*l**i.
(l - 1)**2*(7*l - 2)/3
Find u, given that 1/3*u**3 - u**5 - 7/3*u**2 + 2/3*u + 7/3*u**4 + 0 = 0.
-1, 0, 1/3, 1, 2
Let f(b) = -b**3 + b**2 + b - 1. Let h(k) = 0*k + 2*k**2 - 6 + 0*k - 5*k**3 + k**3. Let n(m) = -6*f(m) + h(m). Factor n(p).
2*p*(p - 3)*(p + 1)
Let l(b) be the third derivative of b**10/75600 - b**8/3360 - b**7/1260 + 19*b**5/60 - 27*b**2. Let o(c) be the third derivative of l(c). Factor o(z).
2*z*(z - 2)*(z + 1)**2
Let z(g) be the second derivative of -3*g - 1/3*g**4 + 0*g**3 + 0*g**2 + 0. Let z(m) = 0. Calculate m.
0
Suppose -61*f + 58 = -32*f. Factor 8/11*u + 8/11 + 2/11*u**f.
2*(u + 2)**2/11
What is m in 3*m**2 + 2*m**2 - 5*m + 14*m**4 + 3*m + 8*m**2 + 2*m**3 - 27*m**2 = 0?
-1, -1/7, 0, 1
Let r be 0/9 - 0/3. Suppose r*y = -4*y - y. Factor y*o + 6/7*o**4 + 4/7*o**3 + 0 - 2/7*o**2.
2*o**2*(o + 1)*(3*o - 1)/7
Let g(r) = -2*r**4 - r**3 + 5*r**2 + 13*r. Let f(q) = -q**4 - 4*q**3 + 3*q**2 + 12*q. Let y(z) = 3*f(z) - 2*g(z). Factor y(h).
h*(h - 10)*(h - 1)*(h + 1)
Factor 12 + 3/2*m**3 + 15*m**2 + 51/2*m.
3*(m + 1)**2*(m + 8)/2
Let c(d) be the third derivative of 8*d**2 - 1/390*d**5 + 0*d**4 + 0*d**3 + 0 + 0*d. Find h such that c(h) = 0.
0
Factor -4*q**2 + 7*q - q**2 + 4*q**2 + 14*q - 38.
-(q - 19)*(q - 2)
Let p = 29 + -27. Let 9*i - 10*i**2 - 15*i + 0*i**4 + i**p + 3*i**4 = 0. Calculate i.
-1, 0, 2
Suppose -20 = 5*l - 5, f = -3*l + 77. Suppose -f*r - 8 = -90*r. Let 0 + 1/2*m - 1/4*m**r = 0. Calculate m.
0, 2
Let a(n) be the third derivative of 2*n**2 + 0*n + 1/4*n**5 - 2*n**3 + 27 + 19/8*n**4. Suppose a(u) = 0. Calculate u.
-4, 1/5
Let k(m) be the third derivative of 1/12*m**5 + 0*m - 13*m**2 + 0*m**4 + 0 - 5/6*m**3. What is a in k(a) = 0?
-1, 1
Suppose 2*f - 3*c - 149 = 0, c - 4*c = 5*f - 362. Let u = -71 + f. Let -2/3*v**u + 0 + 0*v = 0. What is v?
0
Let k(w) = 402*w**3 + 987*w**2 + 383*w + 37. Let r(g) = -2815*g**3 - 6910*g**2 - 2680*g - 260. Let b(a) = 20*k(a) + 3*r(a). Factor b(c).
-5*(c + 2)*(9*c + 2)**2
Determine a, given that -96 - 6*a**3 - 8/3*a**2 + 2/3*a**4 + 104*a = 0.
-4, 1, 6
Let h(i) be the third derivative of i**6/60 - 3*i**5/10 + 5*i**4/4 - 7*i**3/3 + 351*i**2 + 1. Factor h(q).
2*(q - 7)*(q - 1)**2
Let c(z) = z - 10*z**2 - 3*z**2 + 12*z**2 + 1. Let t(m) = -m**3 + 6*m**2 - 5*m - 2. Let s(w) = -6*c(w) - 3*t(w). Suppose s(n) = 0. What is n?
0, 1, 3
Let z(h) = 15*h**3 - 536*h**2 + 4500*h + 3242. Let q(a) = -75*a**3 + 2683*a**2 - 22500*a - 16211. Let t(y) = 2*q(y) + 11*z(y). Factor t(c).
5*(c - 18)**2*(3*c + 2)
Let n(r) be the second derivative of 27/5*r**5 + 24*r**3 - 2/3*r**6 + 0 - 3*r - 50/3*r**4 - 16*r**2. Suppose n(j) = 0. Calculate j.
2/5, 1, 2
Let l(g) be the first derivative of -g**3/3 - 31*g**2 - 961*g + 27. Factor l(q).
-(q + 31)**2
Let x(u) be the second derivative of -34*u + 0 + 1/30*u**5 + 1/2*u**4 + 9*u**2 + 3*u**3. Determine h, given that x(h) = 0.
-3
Solve 11/2*s**4 - 5*s + 2*s**5 + 0*s**3 + 0 - 17/2*s**2 = 0 for s.
-2, -1, 0, 5/4
Let y(u) = -2*u**4 + 14*u**2 + 32*u + 16. Let a(i) = -i**4 + 4*i**3 + 15*i**2 + 32*i + 16. Let m(j) = 2*a(j) - 3*y(j). Factor m(p).
4*(p - 2)*(p + 1)**2*(p + 2)
Let a(h) = -2*h + 21. Let l be a(9). Factor -3 - 2*f**2 - 5*f - 10*f**l + 11*f**3 + f**2.
(f - 3)*(f + 1)**2
Let b be 21 - 4 - (2 + -1). Let 2320*n**2 - b*n**4 + 3*n**3 - 2308*n**2 + 4 - 20*n + 17*n**3 = 0. What is n?
-1, 1/4, 1
Let r = -8719 - -8721. Factor -8/7 - 4/7*n**r - 12/7*n.
-4*(n + 1)*(n + 2)/7
Let l be ((-237)/(-35) - (-3 + 10))*(-63)/18. Factor 1/5*b + 1/5*b**5 + 6/5*b**3 + 4/5*b**4 + 0 + l*b**2.
b*(b + 1)**4/5
Factor 0 + 0*l - 3/2*l**4 + 0*l**2 + 9/4*l**3 - 3/4*l**5.
-3*l**3*(l - 1)*(l + 3)/4
Suppose 3*t + 7 = -4*g + 30, 5*g = 5*t - 15. Let z be -2*(-1)/3*3*g. Factor -1/2*v**z + 0*v + 27/2 + 4*v**3 - 9*v**2.
-(v - 3)**3*(v + 1)/2
Let f(n) be the second derivative of 1/28*n**4 + 0 - 11*n + 0*n**5 + 0*n**3 - 1/70*n**6 + 0*n**2. Solve f(d) = 0.
-1, 0, 1
Factor 0 - 100/17*v + 190/17*v**2 + 6/17*v**4 - 64/17*v**3.
2*v*(v - 5)**2*(3*v - 2)/17
Suppose -5*i = -s - 2*i + 17, -4*i - 22 = -s. Let m(q) be the third derivative of 0*q + 0 + 1/36*q**4 + 1/18*q**3 + 1/180*q**5 - 6*q**s. Factor m(d).
(d + 1)**2/3
Determine p, given that 0 + 2/3*p**2 - 1/6*p**4 + 0*p**3 + 0*p = 0.
-2, 0, 2
Let d(i) be the third derivative of 7*i**5/40 - 23*i**4/48 + i**3/6 + 468*i**2. Factor d(l).
(l - 1)*(21*l - 2)/2
Determine v so that -71*v**3 - 17 + 70*v**3 - 35*v + 10*v**2 - 29*v**2 = 0.
-17, -1
Let o(d) = 2*d**2 - 7*d - 5. Let c be o(-4). Let y = 57 - c. Let 18/11*k**5 - 16/11*k**3 - 2/11*k + 12/11*k**y + 0 - 12/11*k**4 = 0. What is k?
-1, 0, 1/3, 1
Suppose 1 = 4*j - 23. Factor -3*c**5 + j*c**2 + 6*c**3 - 3 + 4*c**4 - 8*c**4 - 2*c**4 - 3*c + 3*c**4.
-3*(c - 1)**2*(c + 1)**3
Let p(c) be the first derivative of c**2 + 0*c**4 - 3/4*c - 13 - 1/2*c**3 + 1/20*c**5. Find v, given that p(v) = 0.
-3, 1
Let w(s) = -11*s**2 - 326*s + 302. Let y(a) = -5*a**2 - 162*a + 152. Let k(p) = -3*w(p) + 7*y(p). Suppose k(z) = 0. Calculate z.
-79, 1
Let t(o) be the first derivative of 5*o + 1/15*o**3 - o**2 - 2. Factor t(n).
(n - 5)**2/5
Let o(l) = 2*l**3 + 3*l**2 + 3*l. Suppose -7 = -9*a + 20. Let n(p) = p**3 - 1. Let g(s) = a*n(s) - 3*o(s). Find j such that g(j) = 0.
-1
Let y(d) = -174*d**2 - 3*d + 2. Let r be y(1). Let c be (4/6)/(r/42)*-5. Let -2/5*n**2 - 6/5*n - c = 0. What is n?
-2, -1
Let l be 12 + (-12)/(-2 + 5). Let d = 11 - l. What is c in -8*c**4 - d*c**4 + 2*c**2 + 12*c**5 - 14*c**4 + c**3 = 0?
-1/4, 0, 1/3, 2
Factor 3/4*y**5 + 5/2*y**4 - 3/2 - 1/4*y - 21/2*y**3 + 9*y**2.
(y - 1)**3*(y + 6)*(3*y + 1)/4
Let t = -93/10 + 19/2. Suppose 12 = -3*k - 4*h, -11 - 4 = -10*k + 5*h. Find q such that 2/5*q**2 + 1/5*q + t*q**3 + k = 0.
-1, 0
Let c(p) be the first derivative of p**4/16 + 5*p**3/2 + 63*p**2/2 + 98*p - 114. Determine z so that c(z) = 0.
-14, -2
Let l(s) be the first derivative of -2*s**3/3 - s**2 + 12*s + 57. Suppose l(w) = 0. Calculate w.
-3, 2
Let g(v) = 4*v**3 - 19 + 19 + v**2 - 3*v**3. Let r(j) = 6*j**3 - 2*j**2. Let o(i) = -4*g(i) + r(i). Factor o(d).
2*d**2*(d - 3)
Let o(i) = 11*i**2 + 34*i + 41. Let n(l) = 31*l**2 + 102*l + 122. Let d(h) = 6*n(h) - 17*o(h). Factor d(x).
-(x - 35)*(x + 1)
Suppose b = -4, -3*d + 6*b - 8*b - 8 = 0. Factor -1/5*n**2 + d - 3/5*n.
-n*(n + 3)/5
Let j be 106/371 - 2146/7560. Let y(d) be the third derivative of 0*d + 0 + d**2 + 1/108*d**4 + j*d**6 + 0*d**3 + 1/135*d**5. Factor y(o).
2*o*(o + 1)**2/9
Let k(s) be the second derivative of -s**7/357 - 8*s**6/255 - 5*s**5/34 - 19*s**4/51 - 28*s**3/51 - 8*s**2/17 - 118*s. Factor k(m).
-2*(m + 1)**2*(m + 2)**3/17
Let j(p) = 15*p - 45. Let t be j(12). Let c be 1/5 + t/75. Factor -6/5*k**c + 2/5 - 4/5*k.
-2*(k + 1)*(3*k - 1)/5
Suppose 0 = -5*i + 4*g + 55, -36 = -3*i - 0*i + 3*g. Factor -5*u**2 - 13*u - 30 + 15 - i*u.
-5*(u + 1)*(u + 3)
Determine m, given that 0 + 4/5*m**3 + 0*m - 24/5*m**4 + 0*m**2 + 11/5*m**5 = 0.
0, 2/11, 2
Let r = 935 + -931. Let j(n) be the first derivative of -1/3*n**3 - 8 + 0*n + 0*n**2 + 1/8*n**r. Factor j(o).
o**2*(o - 2)/2
Let i(y) = y**4 - y**2 + y - 1. Let t(z) = 4*z**4 - 12*z**2 + 2*z + 6. Let l(o) = -2*i(o) + t(o). Solve l(s) = 0.
-2, -1, 1, 2
Let r be 4/7*((-25)/(-10) + 1). Solve 0*k + 1/2*k**4 + 0*k**r + 0 - 1/2*k**5 + k**3 = 0.
-1, 0, 2
Let n(z) be the third derivative of z**6/120 + 7*z**5/60 + z**4/2 - 281*z**2. Find u, given that n(u) = 0.
-4, -3, 0
Let i be ((-2)/5 - (-96)/140)/((-5)/(-35)). Factor 26/5*k**i + 14/5*k**4 + 0 + 2/5*k**5 + 8/5*k + 6*k**3.
2*k*(k + 1)**3*(k + 4)/5
Let s(v) = -v**2 - 7*v - 8. Let y(g) = 2*g**2 + 8*g + 10. Let j(z) = 5*s(z) + 4*y(z). Find d, given that j(d) = 0.
0, 1
Let z be 54/15 - (-22)/55. Let i be ((-18)/4 + z)*(-4 - 6). So