
f*(f + 3)/5
Let f(p) = p**3 + 3*p**2 - 3*p - 5. Let w be f(-3). Factor -w*j**5 - 2*j**3 + 9*j - 13*j + 10*j**3.
-4*j*(j - 1)**2*(j + 1)**2
Let f(c) = c**3 + 5*c + 6. Let o(b) = 2*b**3 - b**2 + 10*b + 11. Let g(l) = -11*f(l) + 6*o(l). Factor g(h).
h*(h - 5)*(h - 1)
Let u(c) = -25*c**4 - 8*c**3 + 17*c**2 - 5*c + 5. Let i(k) = 38*k**4 + 12*k**3 - 26*k**2 + 8*k - 8. Let l(m) = 5*i(m) + 8*u(m). Factor l(w).
-2*w**2*(w + 1)*(5*w - 3)
Let u(v) = -2*v**4 + 8*v**3 - 72*v**2 + 148*v - 74. Let b(n) = 3*n**4 - 10*n**3 + 71*n**2 - 149*n + 75. Let x(h) = -4*b(h) - 5*u(h). Factor x(q).
-2*(q - 5)*(q - 1)**2*(q + 7)
Let k(r) be the first derivative of r**4/4 + 5*r**3/8 + 3*r**2/8 + 40*r + 2. Let g(p) be the first derivative of k(p). Factor g(f).
3*(f + 1)*(4*f + 1)/4
Let u(j) be the second derivative of 0*j**2 - 1/150*j**6 + 0*j**3 + 0*j**4 - 9*j + 0 + 1/100*j**5. Solve u(l) = 0 for l.
0, 1
Let b be ((-1)/(-3))/(-7 - (-129)/18). Let q(l) be the first derivative of 2/5*l**5 - l**b - 7/4*l**4 + 0*l + 7/3*l**3 + 7. Determine a so that q(a) = 0.
0, 1/2, 1, 2
Suppose -28*n**2 - 209*n + 72 - 214 - 218 - 2*n**3 - 13*n + 4*n**3 = 0. What is n?
-3, 20
Suppose 8 = -0*i + 4*i. Let s(m) be the second derivative of -3/5*m**5 + 0 - 3*m**2 - 5/2*m**3 + 11/4*m**4 + i*m. Factor s(v).
-3*(v - 2)*(v - 1)*(4*v + 1)
Let v = -1680 - -11762/7. Factor -4/7 + 2/7*k**2 + v*k**4 - 6/7*k + 6/7*k**3.
2*(k - 1)*(k + 1)**2*(k + 2)/7
Suppose 4 = 5*z - 3*z. Solve -7*l**z - 2*l**2 + 2*l + 11*l**2 = 0.
-1, 0
Let n(b) = 16*b + 1. Let z be n(-1). Let p = 19 + z. Determine v, given that 4*v**4 - 11 - 24*v**2 + 28*v + p*v - 1 = 0.
-3, 1
Let n = -951 + 2861/3. Factor 4/3*f - 10/3*f**2 - 2/3*f**4 + 0 + n*f**3.
-2*f*(f - 2)*(f - 1)**2/3
Let o(t) be the third derivative of t**8/2520 + t**7/252 - t**6/270 - 31*t**4/24 + 49*t**2. Let s(q) be the second derivative of o(q). Factor s(y).
2*y*(y + 4)*(4*y - 1)/3
Let o(i) = 2*i + 19. Let a be o(10). What is t in 26 - 14*t**3 - 26 + 21*t**4 - 31*t**3 - 3*t**5 + a*t**2 - 12*t = 0?
0, 1, 4
Suppose 0 = 18*d - 64*d + 184. Find r such that 4/7*r**3 + 0*r**d - 2/7*r**5 - 2/7*r + 0 + 0*r**2 = 0.
-1, 0, 1
Let r(d) be the second derivative of d**5/60 + d**4/8 + d**3/3 - 9*d**2/2 + 22*d. Let w(c) be the first derivative of r(c). Factor w(y).
(y + 1)*(y + 2)
Factor -5*r**3 + 0 + 5/2*r**4 - 15/2*r**2 + 0*r.
5*r**2*(r - 3)*(r + 1)/2
Let w(y) = 10*y**2 + 2*y - 2. Let p be w(1). Suppose p*i**2 - 38*i**2 + 2 + 6 + 8 - 48*i = 0. Calculate i.
-2, 2/7
Let y(c) = -12*c**3 - 116*c**2 + 372*c - 274. Let l(n) = -4*n**3 - 38*n**2 + 124*n - 91. Let g(r) = 10*l(r) - 3*y(r). Factor g(z).
-4*(z - 2)*(z - 1)*(z + 11)
Let z(n) be the first derivative of -n**5/5 - 27*n**4/4 - 63*n**3 - 13*n**2/2 + 1014*n - 532. Let z(p) = 0. Calculate p.
-13, -3, 2
Find x, given that -4283*x**3 - 60 + 4286*x**3 - 12 + 30*x**2 + 39*x = 0.
-8, -3, 1
Determine f, given that -52/17*f + 50/17 + 2/17*f**2 = 0.
1, 25
Let f(w) be the second derivative of 0*w**3 + 0 + 5/12*w**4 + 1/2*w**6 + 5/42*w**7 + 6*w + 3/4*w**5 + 0*w**2. Factor f(l).
5*l**2*(l + 1)**3
Let u(y) = -y**3 + 10*y**2 + 4*y + 4. Let v(f) = 10*f**2 + 5*f + 5. Let q(c) = 5*u(c) - 4*v(c). Factor q(h).
-5*h**2*(h - 2)
Let i be (-10)/(2/1) + -2. Let b = -5 - i. Find g, given that 2*g**3 - g + 0*g - 3*g**3 + b*g**3 = 0.
-1, 0, 1
Let d(u) = u - 1. Suppose -9*a + 5*a - 16 = 0. Let g(o) = o**3 + 4*o**2 + 2*o + 2. Let s(v) = a*d(v) - 2*g(v). Find b such that s(b) = 0.
-2, 0
Let z(t) be the first derivative of 1/20*t**5 + 1/2*t**2 + 0*t + 0*t**3 - 3/16*t**4 + 12. Suppose z(n) = 0. Calculate n.
-1, 0, 2
Let v(a) be the first derivative of 20*a**3/3 + 146*a**2 - 120*a - 45. Factor v(l).
4*(l + 15)*(5*l - 2)
Factor 20*t**2 + 3*t**3 + 2153*t - 2208*t - 64 - 86 + 2*t**3.
5*(t - 3)*(t + 2)*(t + 5)
Let l(m) be the first derivative of -m**3/3 - 5*m**2 - 4*m - 1. Let z(b) = 7*b - 4*b - 2*b - 2*b. Let w(k) = -l(k) + 6*z(k). Suppose w(y) = 0. Calculate y.
-2
Let h be 48/(-320)*(-3)/18. Let t(b) be the second derivative of -1/12*b**3 - 1/8*b**4 + 0 + 3/4*b**2 - 3*b + h*b**5. Factor t(q).
(q - 3)*(q - 1)*(q + 1)/2
Factor -28*f - 31*f + 2*f - 3*f + 64*f**3 + 96*f**2 + 8.
4*(f + 2)*(4*f - 1)**2
Factor 32/7*c + 1/7*c**3 + 0 + 12/7*c**2.
c*(c + 4)*(c + 8)/7
Let a(o) be the third derivative of -o**7/420 - o**6/360 + o**5/120 + 17*o**3/6 + 9*o**2. Let b(k) be the first derivative of a(k). What is n in b(n) = 0?
-1, 0, 1/2
Let u(m) be the second derivative of -1/12*m**4 - 1/3*m**3 + 0 + 27*m + 0*m**2. Find r, given that u(r) = 0.
-2, 0
Let i(g) be the third derivative of g**7/525 - g**6/300 - g**5/75 + 2*g**2 + 33*g. Suppose i(p) = 0. What is p?
-1, 0, 2
Let n(a) be the second derivative of -a**8/560 + 3*a**7/350 - 3*a**6/200 + a**5/100 - 4*a**2 - 6*a. Let y(f) be the first derivative of n(f). Factor y(l).
-3*l**2*(l - 1)**3/5
Let b(s) = -8*s - 28*s**4 - 42 + 0*s**3 - 4*s**3 + 34. Let a(h) = h**4 - h**3 + h**2 + h + 1. Let n(c) = 8*a(c) + b(c). Factor n(z).
-4*z**2*(z + 1)*(5*z - 2)
Factor -6*a**2 - 312*a**2 + 206*a - 27 + 18*a**3 + 3 - 10.
2*(a - 17)*(3*a - 1)**2
Let r(p) be the third derivative of -p**8/110880 - p**7/4620 - p**6/440 + 4*p**5/5 + p**3/3 - 3*p**2 - p. Let u(c) be the third derivative of r(c). Factor u(v).
-2*(v + 3)**2/11
Find q, given that -1/7*q**5 - 1/7*q**4 + 0*q + 0 + 0*q**2 + 2/7*q**3 = 0.
-2, 0, 1
Suppose -3*i - 2*j = -7 + 1, -4*j = -12. Suppose -3*w - 4*x + 1 = 0, 4*x = w - x - 13. Solve 4/9*c**2 + i + 0*c - 2/9*c**w = 0 for c.
0, 2
Let i(t) be the first derivative of -6*t**5/11 - 58*t**4/11 + 82*t**3/33 + 74*t**2/11 + 32*t/11 - 66. Suppose i(l) = 0. Calculate l.
-8, -2/5, -1/3, 1
Factor -81*b**2 + 84 - 51*b**2 + 135*b**2 - 33*b.
3*(b - 7)*(b - 4)
Let w be (-4 - -3)*8*-1. Factor w + 12 - 5*r**2 - 6*r - 9*r.
-5*(r - 1)*(r + 4)
Let b be 2/(8/21 - 4/(-14)). Let r(d) be the third derivative of -1/30*d**5 + 0*d - 1/6*d**4 + 0*d**b + 0 - 2*d**2. Factor r(k).
-2*k*(k + 2)
Let m be (4/190)/((-10)/(-50)). Find d such that -2/19*d**3 + m*d + 2/19*d**2 - 2/19*d**4 + 0 = 0.
-1, 0, 1
Let w(s) be the second derivative of 12*s + 1/135*s**6 + 0*s**4 + 0*s**3 + 5/189*s**7 + 0*s**2 + 0*s**5 + 0. Factor w(h).
2*h**4*(5*h + 1)/9
Let y(n) be the first derivative of n**6/540 - n**5/90 + 7*n**2/2 + 30. Let r(m) be the second derivative of y(m). Find x such that r(x) = 0.
0, 3
Let f be 8 + -6 - -12*1. Suppose -4*s = 2 - f. Determine n, given that 4*n**s - 5*n**2 - 4 - 2*n + 9*n**2 - 2*n**3 = 0.
-2, -1, 1
Let r(x) be the second derivative of -x**4/8 + 2*x**3 - 12*x**2 - 113*x. Solve r(o) = 0 for o.
4
Let l(a) be the third derivative of -a**7/840 + 23*a**6/480 - 27*a**5/80 + 97*a**4/96 - 19*a**3/12 - 22*a**2 + 2. Solve l(x) = 0 for x.
1, 2, 19
Factor 65 - 2*u**2 - 22 - 12*u - 29.
-2*(u - 1)*(u + 7)
Let u be ((-33)/231*-6)/((-25)/14 + 2). Solve 4/3*b**2 - u*b + 8/3 = 0.
1, 2
Let a(h) be the second derivative of -h**4/36 + 5*h**3/9 + 126*h. Suppose a(l) = 0. Calculate l.
0, 10
Let m be -7*(-4 + (-125)/(-35)) + 1. Let a(p) be the second derivative of 0*p**2 + 0*p**3 + 1/4*p**5 + 1/6*p**m + 0 + 5*p. Factor a(u).
u**2*(5*u + 2)
Let p be (6/(-4))/(-3 + -9 + 3). Let z(l) be the third derivative of -6*l**2 + p*l**3 + 1/240*l**5 + 0*l + 0 + 1/24*l**4. Factor z(n).
(n + 2)**2/4
Let w(k) = 7*k**4 - 31*k**3 + 44*k**2 - 17*k. Let h(q) = 8*q**4 - 32*q**3 + 44*q**2 - 16*q. Let n(x) = -3*h(x) + 4*w(x). What is j in n(j) = 0?
0, 1, 5
Let q(n) be the third derivative of n**8/168 - n**7/15 + n**6/4 - n**5/6 - 4*n**4/3 + 4*n**3 - 26*n**2. Let q(p) = 0. Calculate p.
-1, 1, 2, 3
Let c be 6*(9/189 - 0). Determine k, given that 4/7*k + 0 - c*k**2 = 0.
0, 2
Let v(i) = 7*i + 107. Let k = 171 + -186. Let b be v(k). Determine t so that 0 - 2/5*t**3 - 4/5*t - 6/5*t**b = 0.
-2, -1, 0
Suppose 5*q = -10*q - 90. Let a be (q/45)/((18/3)/(-30)). Factor a*c**2 + 2/3*c + 2/9*c**3 + 2/9.
2*(c + 1)**3/9
Suppose 0 = 4*i - 8*i. Let y be i - (8/(-4) - 0). Find l, given that -y*l**2 + 3*l**2 + 3*l + 9 - 9 = 0.
-3, 0
Let m be (-42)/(-24)*2/7. Let v(n) be the first derivative of 4 + 2*n**2 + 0*n + m*n**4 - 2*n**3. Factor v(i).
2*i*(i - 2)*(i - 1)
Let v(r) be the second derivative of r**5/70 - r**4/14 + r**3/7 - r**2/7 + r - 9. Factor v(u).
2*(u - 1)**3/7
Let g(l) be the third derivative of 27*l**2 + 0*l**4 - 4/9*l**3 +