d**4 - 3/2*d**5 + 21*d**3 + 0*d = 0.
-7, 0, 2
Let w be 5/25 + 196/20. Let q(x) = -x**2 - x + 4. Let j be q(0). Find h, given that -16*h**2 + w*h - 36*h**3 + 13*h + 36*h**j - 7*h = 0.
-2/3, 0, 2/3, 1
Let a(w) be the third derivative of -2/3*w**3 + 0*w + 15*w**2 + 1/20*w**5 + 0 + 0*w**4 + 1/120*w**6. Factor a(f).
(f - 1)*(f + 2)**2
Let l(k) be the third derivative of -2*k**7/105 + 4*k**6/15 - 2*k**5/5 - 4*k**4/3 + 14*k**3/3 + 250*k**2. Factor l(j).
-4*(j - 7)*(j - 1)**2*(j + 1)
Suppose 2*u - x = -2*x + 13, -4*x + 4 = 2*u. Factor -u*o + o**3 - 20*o**2 - 9*o**3 - 8*o**3 - 4*o**4.
-4*o*(o + 1)**2*(o + 2)
Let y(t) = -t. Let j(w) = -14*w**3 - 102*w**2 - 24*w. Let g(m) = j(m) + 4*y(m). Find c such that g(c) = 0.
-7, -2/7, 0
Let a(v) be the first derivative of -4/3*v - 1 - 2/9*v**3 - 3/2*v**2. Factor a(k).
-(k + 4)*(2*k + 1)/3
Suppose -5*t + 57 = 7. Suppose -3*y + t = -y. Factor 1/4*a**4 + 0*a**2 + 0*a + 0*a**3 + 0 - 1/4*a**y.
-a**4*(a - 1)/4
Let i be (5 + -4)/(5/100). Suppose 0 = i*j - 22*j + 8. Let -1/5*n + 1/5 - 1/5*n**5 + 2/5*n**3 - 2/5*n**2 + 1/5*n**j = 0. Calculate n.
-1, 1
Let x be (102/(-3519))/((-28)/(-6)). Let l = 93/161 + x. Determine p, given that 0 + 2/7*p + 2/7*p**3 + l*p**2 = 0.
-1, 0
Let g(r) be the third derivative of 5*r**8/336 - r**7/42 - 5*r**6/4 - 37*r**5/6 - 335*r**4/24 - 35*r**3/2 + 3*r**2 + 70*r. Factor g(x).
5*(x - 7)*(x + 1)**3*(x + 3)
Let -3*p + 1/2*p**4 + 0 + 3*p**3 - 1/2*p**2 = 0. What is p?
-6, -1, 0, 1
Let p be 1/(-1) - (9 + -13). Factor 3*m**2 + m**3 - 2*m**p - 3 - 2*m**3 + 3*m.
-3*(m - 1)**2*(m + 1)
Let v(y) be the third derivative of 8*y**6/9 + 76*y**5/9 - 395*y**4/72 + 25*y**3/18 - 2*y**2 - 30. Suppose v(w) = 0. What is w?
-5, 1/8
Let l = 36 - 36. Factor l*f**2 + 5*f**2 - 6 - 3*f - 6*f**2 - 2*f.
-(f + 2)*(f + 3)
Factor -4*h - 32*h**4 - 4*h + 0*h + 18*h**4 + 38*h**3 - 16*h**2.
-2*h*(h - 2)*(h - 1)*(7*h + 2)
Let s = -35 - -37. Factor -5*b - 3*b**4 - 8*b**3 - 15*b**s - 4*b**3 - b.
-3*b*(b + 1)**2*(b + 2)
Let m(j) be the first derivative of -j**9/30240 - j**8/8400 + j**6/1800 + j**5/1200 + 6*j**3 - 8. Let n(g) be the third derivative of m(g). Factor n(i).
-i*(i - 1)*(i + 1)**3/10
Factor 144/11 - 2/11*v**3 - 24/11*v - 20/11*v**2.
-2*(v - 2)*(v + 6)**2/11
Let i(h) = 6*h**4 - 8*h**3 + 10*h**2 + 12*h - 8. Let r(v) = 13*v**4 - 16*v**3 + 21*v**2 + 25*v - 16. Let y = 28 - 24. Let w(u) = y*r(u) - 9*i(u). Factor w(c).
-2*(c - 2)**2*(c - 1)*(c + 1)
Suppose 41*q - 80 = o, 1 = o - 3*q + 5. Factor 6/7*p**5 + 4/7*p**2 + 0*p + o*p**3 + 16/7*p**4 + 0.
2*p**2*(p + 1)**2*(3*p + 2)/7
Factor 60/7 - 60/7*i**2 + 2/7*i**3 - 2/7*i.
2*(i - 30)*(i - 1)*(i + 1)/7
Suppose 3 = 6*j - 9*j. Let i be -2 - ((-15)/9 + j). Factor 0 + 4/9*r + 2/9*r**3 + i*r**2.
2*r*(r + 1)*(r + 2)/9
Let d(u) be the second derivative of -u**8/2240 + u**7/840 + u**6/48 + 3*u**5/40 - 11*u**4/12 + 16*u. Let a(v) be the third derivative of d(v). Factor a(x).
-3*(x - 3)*(x + 1)**2
Let p(y) = -y**2 - 8. Let f(j) = -4*j**3 - 116*j**2 - 960*j - 2336. Let t(r) = f(r) - 4*p(r). Factor t(b).
-4*(b + 4)*(b + 12)**2
Let d(l) be the second derivative of 5*l**4/12 + 115*l**3/2 + 170*l**2 + 225*l. Factor d(a).
5*(a + 1)*(a + 68)
Determine m so that 2*m**3 - 7*m + 2 + 21*m**3 + 27*m**2 + 7*m**4 + 5*m + 21*m - 6*m = 0.
-1, -2/7
Let h(f) be the third derivative of f**5/20 + 17*f**4/8 + 30*f**3 + 921*f**2. Solve h(m) = 0.
-12, -5
Suppose 15336 = -18*u + 15354. Suppose -3/2*k + 1/2*k**3 + 0*k**2 + u = 0. What is k?
-2, 1
Let u(j) = j**3 - 81*j**2 + 3*j + 81. Let x(r) = -r**3 + 82*r**2 - 5*r - 82. Let g(n) = -3*u(n) - 2*x(n). Factor g(b).
-(b - 79)*(b - 1)*(b + 1)
Let s(j) be the second derivative of 2*j**6/15 - 2*j**5/5 - j**4 - 85*j + 1. Let s(t) = 0. What is t?
-1, 0, 3
Let v(a) be the second derivative of 3/8*a**4 + 0 + 22*a + 1/80*a**5 + 27*a**2 + 9/2*a**3. Find h such that v(h) = 0.
-6
Let j(r) be the second derivative of r**4/4 - 21*r**3/2 - 69*r**2 + 479*r. Suppose j(a) = 0. Calculate a.
-2, 23
Suppose 0*d - 26/7*d**4 + 8/7*d**2 + 0 - 10/7*d**5 - 8/7*d**3 = 0. What is d?
-2, -1, 0, 2/5
Factor -2/11*l - 6/11 + 2/11*l**3 + 6/11*l**2.
2*(l - 1)*(l + 1)*(l + 3)/11
Let n be ((-13)/((-494)/19))/(6/27). Factor 0 + 0*g - 3/2*g**3 - 3/4*g**5 + 0*g**2 + n*g**4.
-3*g**3*(g - 2)*(g - 1)/4
Let n(m) = 2*m + 15. Let c be n(-3). Let r be 10/4 - (c/6 + -2). Factor 2/5*a**r + 0 + 4/5*a**2 + 2/5*a.
2*a*(a + 1)**2/5
Let o(b) be the second derivative of b**5/10 - b**4/8 - b**3/12 - b + 7. Determine y so that o(y) = 0.
-1/4, 0, 1
Factor 12/7*v + 0 - 3/7*v**2.
-3*v*(v - 4)/7
Let z(c) be the third derivative of -c**5/20 - 7*c**4/4 + 15*c**3/2 - c**2 - 8. Factor z(a).
-3*(a - 1)*(a + 15)
Suppose 114 + 118 + 116 - 352 + p**2 = 0. Calculate p.
-2, 2
Let v(i) be the first derivative of -i**6/1800 + i**5/150 - i**4/40 + 7*i**3/3 - 12. Let z(l) be the third derivative of v(l). Factor z(w).
-(w - 3)*(w - 1)/5
Suppose 4/11*s**3 - 4/11*s + 10/11*s**2 + 0 - 10/11*s**4 = 0. What is s?
-1, 0, 2/5, 1
Factor -219700*w + 3570125 - 52*w**3 + 5070*w**2 + 1/5*w**4.
(w - 65)**4/5
Let q(g) = -g**3 + 6*g**2 + 9*g - 12. Let v be q(7). What is p in 202*p**2 + 3*p**3 - 99*p**2 - 100*p**v = 0?
-1, 0
Let o(n) = -n**2 + n + 1. Let x(g) = 6*g**2 + 16*g - 77. Let r(d) = -20*o(d) - 4*x(d). Solve r(v) = 0.
-24, 3
Find r such that 0 - 24/5*r + 4*r**2 + 4/5*r**3 = 0.
-6, 0, 1
Let x(v) be the third derivative of 1/18*v**4 + 1/90*v**5 + 0*v + 0*v**3 - 2*v**2 + 0. Suppose x(u) = 0. Calculate u.
-2, 0
Let n(a) be the third derivative of -a**6/30 + 2*a**5/15 + a**4/6 - 4*a**3/3 + 89*a**2. Solve n(u) = 0 for u.
-1, 1, 2
Let f(a) be the first derivative of 5*a**6/27 - 4*a**5/5 - 4*a**4/9 + 99. Factor f(l).
2*l**3*(l - 4)*(5*l + 2)/9
Suppose 8*a - 779 + 779 = 0. Let c(i) be the second derivative of 0 + 0*i**6 - 1/70*i**7 + 11*i + a*i**2 + 0*i**4 + 3/50*i**5 - 1/10*i**3. Factor c(m).
-3*m*(m - 1)**2*(m + 1)**2/5
Let u(y) be the third derivative of -y**9/393120 + y**8/131040 + y**5/12 - 7*y**2. Let v(h) be the third derivative of u(h). Factor v(x).
-2*x**2*(x - 1)/13
Let m(p) be the third derivative of -p**8/4032 - p**7/1008 + p**6/72 - 3*p**5/20 - 3*p**2. Let z(a) be the third derivative of m(a). What is w in z(w) = 0?
-2, 1
Let h be 10/120 - (-5)/12. Let b(x) be the first derivative of -1/10*x**5 + 6 - x**3 - h*x**4 - 1/2*x - x**2. Find z such that b(z) = 0.
-1
Let y(h) = -3*h**3 + 6*h**2. Let l(f) = -f**3. Let g(d) = -d**3 + 10*d**2 - 8*d - 11. Let n be g(9). Let j(b) = n*l(b) + 2*y(b). Factor j(q).
-4*q**2*(q - 3)
Let i(s) = -6*s**2 - 6*s + 16. Let p be i(-2). Let m be 1/5 + (-45)/(-25). Factor -2/11*v**p - 6/11*v**3 - 2/11*v + 0 - 6/11*v**m.
-2*v*(v + 1)**3/11
Determine b so that -2/3*b + 2/3*b**3 - 22*b**2 + 22 = 0.
-1, 1, 33
Factor s - s**3 - 1/4*s**2 + 1/4*s**4 + 0.
s*(s - 4)*(s - 1)*(s + 1)/4
Determine y so that -1/4*y**5 + 0*y**2 - 25*y**3 - 5*y**4 + 0 + 0*y = 0.
-10, 0
What is z in -219/4*z + 3/2*z**2 + 27 = 0?
1/2, 36
Let s(d) be the second derivative of 8/3*d**3 - 1/2*d**5 + 0 + 15*d + 1/21*d**7 + 1/15*d**6 - 4*d**2 - 1/6*d**4. Find k such that s(k) = 0.
-2, 1
Solve -3/2*i**2 + 1/6*i**3 + 0*i + 0 = 0.
0, 9
Suppose 350*p - 258 = 264*p. Factor 0*o**2 - 3/5*o**p + 0 + 3/5*o.
-3*o*(o - 1)*(o + 1)/5
Let t(p) be the third derivative of -p**5/60 - p**4/4 + 2*p**3/3 + 7*p**2. Let z be t(-6). Let -12*h + 7 + 3*h**2 - z + 9 = 0. Calculate h.
2
Let s(y) = -y**3 + 11*y**2 - 10*y - 1. Let l be s(10). Let q = 6 + l. Factor q*n**2 - 1 + 6*n - 2*n**2 + 4.
3*(n + 1)**2
Let j = -23322 - -23324. Factor -1/2*p**4 - 3*p**j - 2*p**3 - 2*p - 1/2.
-(p + 1)**4/2
Let l = -104 + 70. Let k(q) = 4*q**2 + 4*q + 3. Let w(j) = 23*j**2 + 23*j + 17. Let i(x) = l*k(x) + 6*w(x). Suppose i(n) = 0. Calculate n.
-1, 0
Let z be (-150)/(-39) - 162/(-1053). Factor 3/2*j**3 - 13/4*j**2 - 1 - 1/4*j**z + 3*j.
-(j - 2)**2*(j - 1)**2/4
Suppose -l + 2*z = 6, -1 = -3*l - 4*z + 11. Suppose -26*r + 31*r = l. Find f such that r*f - 4/3*f**4 + 8/3*f**2 + 0*f**3 - 4/3 = 0.
-1, 1
Factor 109*v**2 + 125*v + 105*v**2 - 22 - 224*v**2 + 34 + 53.
-5*(v - 13)*(2*v + 1)
Let c = -152 + 155. Suppose 4*a - 2*v = 9*a + 4, -4 = 4*a + 2*v. Factor 0*r**2 - 4/11*r**5 - 2/11*r**4 + a*r + 0 + 0*r**c.
-2*r**4*(2*r + 1)/11
Factor 2/7*n**4 + 32/7*n**2 - 16/7*n**3 + 0 + 0*n.
2*n**2*(n - 4)**2/7
Let o(b) = -b**2 +