*3.
-2*g**3*(g - 1)
Let x(w) be the third derivative of w**9/5040 + w**8/1120 + w**7/840 + w**4/12 + 5*w**2. Let v(f) be the second derivative of x(f). Factor v(k).
3*k**2*(k + 1)**2
Let g be (1 + 0)/(3/(-252)). Let j be (-66)/g + 1/(-2). Factor j*u + 2/7*u**2 + 0.
2*u*(u + 1)/7
Let r(f) = -f**3 - f. Let w(q) = -4*q**5 - 4*q**4 + 16*q**3 + 8*q**2 + 4*q - 4. Let j(g) = 8*r(g) + w(g). Factor j(l).
-4*(l - 1)**2*(l + 1)**3
Let q(m) be the first derivative of m**4/14 - 3*m**2/7 + 4*m/7 - 4. Find p such that q(p) = 0.
-2, 1
Suppose 3*g + y = 0, -4*g - 20*y = -23*y. Determine a, given that -3*a - 3/2*a**2 + 3/2*a**3 + g = 0.
-1, 0, 2
What is u in 3/2*u**2 - 33/2*u + 15 = 0?
1, 10
Let b(v) = 4*v**2 - 4*v - 4. Let k(w) = -4*w**2 + 7. Let s(q) = -3*q**2 + 5. Let a(n) = 5*k(n) - 7*s(n). Let j(m) = -10*a(m) + 2*b(m). Factor j(z).
-2*(z + 2)**2
Let c be 460/483 - -4*(-3)/18. Solve -1/7*t**4 + 1/7 + 2/7*t + 0*t**2 - c*t**3 = 0.
-1, 1
Let k be 1 + 2*3/(-2). Let a be (k/(-3))/((-1)/(-3)). Let -2*j**a - 4 - 4*j + 5*j - 7*j = 0. What is j?
-2, -1
Factor -4*o**5 - 12*o**2 - 13*o**3 + 645*o - 20*o**4 - 645*o - 15*o**3.
-4*o**2*(o + 1)**2*(o + 3)
Let t(l) be the third derivative of 3*l**2 + 1/12*l**4 + 0 - 1/15*l**5 + 1/60*l**6 + 0*l + 0*l**3. Factor t(z).
2*z*(z - 1)**2
Let d(r) = 5*r**2 - 10*r - 19. Let m(w) = 9*w**2 - 20*w - 39. Let n(f) = -11*d(f) + 6*m(f). Factor n(l).
-(l + 5)**2
Suppose j + 10 = 3*j, -4*s + 27 = 3*j. Let p be s/1 + (1 - 1). Factor 2*m**4 + m**2 - 2*m - 3*m**2 + 3*m**p - m**3.
2*m*(m - 1)*(m + 1)**2
Let o(n) = -12*n**2 - 30*n - 20. Let y(i) = -i**3 + 11*i**2 + 30*i + 21. Let g(q) = 3*o(q) + 2*y(q). Factor g(k).
-2*(k + 1)*(k + 3)**2
Suppose -2 - 3*z - 7*z + 8*z - 2*z**3 + 2*z**2 + 4*z = 0. What is z?
-1, 1
Determine l so that 1/3*l**3 + 0 + 1/6*l**2 - 1/3*l - 1/6*l**4 = 0.
-1, 0, 1, 2
Suppose 4*p = 9 + 7. Let o(g) be the third derivative of 0*g + 1/840*g**8 + 0*g**3 + 0*g**5 + 0*g**7 - g**2 + 1/60*g**p + 0 - 1/150*g**6. Factor o(r).
2*r*(r - 1)**2*(r + 1)**2/5
Let o(f) be the third derivative of f**5/60 + f**4/24 - 7*f**2. Let o(d) = 0. What is d?
-1, 0
Let z be (-18)/(-4) - 5/10. Suppose -f = z - 7. Factor 2/3*d**4 + 4/3*d**f + 0*d + 0 + 2/3*d**2.
2*d**2*(d + 1)**2/3
Let d be (-224)/35 + -1 + 8. Solve -36/5*n + 18/5*n**2 + 24/5 - d*n**3 = 0.
2
Let 9*i**4 + 34*i**3 + 5*i**5 - 40*i**3 + 10*i**5 = 0. What is i?
-1, 0, 2/5
Let x(k) be the third derivative of -k**5/240 + k**3/6 + k**2. Solve x(n) = 0.
-2, 2
Let m(h) be the second derivative of -3*h - 19/12*h**4 - 4/3*h**3 - 3/5*h**5 - 1/2*h**2 + 0. Solve m(u) = 0.
-1, -1/3, -1/4
Let k(v) be the second derivative of -v**4/42 + 8*v**3/21 - 12*v**2/7 - v + 5. Factor k(i).
-2*(i - 6)*(i - 2)/7
Factor 8/23*f + 0 + 10/23*f**3 + 16/23*f**2 + 2/23*f**4.
2*f*(f + 1)*(f + 2)**2/23
Let o = 3/7 - 1/35. Solve o*z**2 + 0 - 2/5*z = 0 for z.
0, 1
Let p(m) be the second derivative of 0*m**2 + 6*m + 0 + 1/36*m**4 + 0*m**3. Suppose p(f) = 0. Calculate f.
0
Suppose 16/7 - 64*h**3 - 88/7*h**5 + 388/7*h**4 - 44/7*h**2 + 176/7*h = 0. Calculate h.
-1/2, -1/11, 1, 2
Let s(g) be the second derivative of g**8/6720 - g**6/720 + 5*g**4/12 - 5*g. Let f(i) be the third derivative of s(i). Determine u so that f(u) = 0.
-1, 0, 1
Let m be 4/1 + 1 + -5. Let k(j) be the second derivative of -1/2*j**2 - 1/2*j**3 - 1/20*j**5 - 1/4*j**4 + m - 3*j. Factor k(p).
-(p + 1)**3
Factor -1317*s**5 - 416*s - 7468*s**3 + 3268*s**2 + 511*s**4 - 799*s**5 + 6205*s**4 + 16.
-4*(s - 1)**3*(23*s - 2)**2
Factor -2/9*c**2 + 0 + 0*c - 2/9*c**3.
-2*c**2*(c + 1)/9
Let l(m) = 5*m**3 + 10*m**2 + 10*m - 2. Let n(c) = -c**3 + c**2 + c + 1. Let d(u) = -l(u) - 2*n(u). Suppose d(g) = 0. What is g?
-2, 0
Suppose -15 = -2*v + 15. Suppose 2*f - 20 = 5*w - 2*f, -v = 5*w - 3*f. Factor 0*l + w + 2/3*l**3 + 2/3*l**4 + 0*l**2.
2*l**3*(l + 1)/3
Let k(d) be the second derivative of d**6/60 + 3*d**5/40 + d**4/24 - d**3/4 - d**2/2 + 33*d + 1. Factor k(v).
(v - 1)*(v + 1)**2*(v + 2)/2
Let r(j) be the third derivative of -1/20*j**5 + 0 + 1/8*j**4 + 0*j + 0*j**3 - j**2. Factor r(o).
-3*o*(o - 1)
Let n(c) be the third derivative of c**2 - 1/21*c**3 + 1/735*c**7 - 1/210*c**6 + 0*c**5 + 0 + 0*c + 1/42*c**4. Factor n(u).
2*(u - 1)**3*(u + 1)/7
Let n(y) be the second derivative of 3*y**5/20 - 3*y**4/8 - y**3/2 + 9*y**2/4 + 12*y. Determine x so that n(x) = 0.
-1, 1, 3/2
Let g(o) = o**5 + o**3 - o**2 + 1. Let p(m) = 2*m**5 - m**4 - m**3 - m**2 + 1. Let s(w) = -g(w) + p(w). Factor s(j).
j**3*(j - 2)*(j + 1)
Let z be (1 - -1) + -1 - 2. Let l = z - -4. Suppose -3*f**4 + 3*f**4 + l*f**3 + 5*f**4 - 2*f**2 = 0. What is f?
-1, 0, 2/5
Let m(f) be the first derivative of -1/30*f**5 + 2 + 1/3*f**3 + f**2 + 0*f**4 + 0*f. Let b(d) be the second derivative of m(d). Factor b(j).
-2*(j - 1)*(j + 1)
Let d(u) be the first derivative of 5 - 1/4*u**4 + 0*u**2 + 0*u**3 + 0*u**5 + 1/6*u**6 + 0*u. Factor d(f).
f**3*(f - 1)*(f + 1)
Let x(r) be the second derivative of r**5/50 - r**4/5 + 3*r**3/5 - 4*r**2/5 - 7*r. Factor x(z).
2*(z - 4)*(z - 1)**2/5
Suppose -4*b = -5*x + 2*x - 12, 3*b - 4 = x. Let o be 0*1/2 + b. What is g in -3*g + o*g - 3*g**2 + g**3 - 1 + g + 5*g = 0?
1
Suppose -4*x = -8*x - 2*x. Let p(d) be the second derivative of 1/40*d**5 + 0*d**2 + 0 - 2*d - 1/12*d**3 + x*d**4. Factor p(s).
s*(s - 1)*(s + 1)/2
Let u(b) be the third derivative of b**8/588 - 2*b**7/147 + b**6/21 - 2*b**5/21 + 5*b**4/42 - 2*b**3/21 + 4*b**2 - 2*b. Factor u(k).
4*(k - 1)**5/7
Let m(l) = -3*l + 48. Let a be m(15). Let x(t) be the second derivative of 0 + 0*t**2 - 1/10*t**5 + 0*t**a + 0*t**4 + 3*t. Determine c so that x(c) = 0.
0
Let y(b) be the first derivative of -b**3/6 + b**2/4 + b + 22. Factor y(u).
-(u - 2)*(u + 1)/2
Let h(g) be the first derivative of 1/5*g**5 + 3/16*g**4 + 3 + 0*g**2 - 1/12*g**3 + 0*g. Determine y so that h(y) = 0.
-1, 0, 1/4
Let u(m) be the second derivative of m**4 - 4*m**3 + 0 + 8*m**2 - 1/10*m**5 - 3*m. Suppose u(g) = 0. What is g?
2
Let u(s) = -s**5 + s**4 + s**3 + s**2 - 1. Let g(i) = 6*i**5 - 9*i**4 - 6*i**3 - 5*i**2 + 7. Let h(m) = -3*g(m) - 21*u(m). Determine w so that h(w) = 0.
-2, -1, 0, 1
Let u(v) be the third derivative of 1/20*v**5 + 2*v**2 + 0*v + 1/6*v**3 + 0 - 1/6*v**4. Find r, given that u(r) = 0.
1/3, 1
Factor -12/5*y + 3/5*y**2 + 12/5.
3*(y - 2)**2/5
Let y(x) = -x**3. Let f = -19 + 18. Let u(s) = 8*s**3 - 12*s**2 + 12*s. Let a(z) = f*u(z) - 5*y(z). Find j, given that a(j) = 0.
0, 2
Let f(a) = a**2 - 31*a + 2. Let h be f(0). Find q such that 16/19*q**h - 2/19 - 14/19*q = 0.
-1/8, 1
Factor 1/4*f + 1/4*f**5 + 1/2*f**2 - 1/2*f**3 - 1/4*f**4 - 1/4.
(f - 1)**3*(f + 1)**2/4
Let l(q) be the second derivative of q**5 + 4*q**4 + 6*q**3 + 4*q**2 - 6*q. Solve l(d) = 0.
-1, -2/5
Let q(s) be the third derivative of 1/36*s**4 - 1/45*s**6 + 0*s**3 + 3*s**2 - 1/30*s**5 + 0*s + 0. Factor q(b).
-2*b*(b + 1)*(4*b - 1)/3
Let d = 10 + -7. Let 0*x**2 + 3*x**4 + 2*x**d - 2*x**4 - x - 2*x**2 - 3 - x**5 + 4 = 0. Calculate x.
-1, 1
Let -40*q**2 + 14*q - 15*q**3 + 7*q + 10*q**5 - q - 15*q**3 + 15 + 25*q**4 = 0. What is q?
-3, -1, -1/2, 1
Let o(t) be the second derivative of -1/6*t**3 + 0 + 1/12*t**4 - 4*t + 1/6*t**2 - 1/60*t**5. Find f such that o(f) = 0.
1
Let p(h) = -h**2 + 13*h + 5. Suppose 7*n = 4 - 18. Let o be (-5)/(-1)*(-1)/(-1). Let q(w) = 6*w + 2. Let z(r) = n*p(r) + o*q(r). Factor z(g).
2*g*(g + 2)
Let c(z) be the second derivative of z**6/50 + 3*z**5/100 - z**4/10 - 10*z. Factor c(y).
3*y**2*(y - 1)*(y + 2)/5
Let i(p) be the third derivative of p**7/1050 - p**5/100 - p**4/60 + 11*p**2. Solve i(m) = 0.
-1, 0, 2
Let f(y) be the second derivative of -y**7/840 + y**5/240 + y**2/2 - 3*y. Let c(t) be the first derivative of f(t). Let c(p) = 0. What is p?
-1, 0, 1
Let c = 15 - 18. Let j be 2/c - -1 - 0. Factor -2/3 - j*s - 5/3*s**3 + 8/3*s**2.
-(s - 1)**2*(5*s + 2)/3
Let n(i) = -2*i**3 + 14*i**2 + 14*i + 8. Let f(j) = -j - 5. Let x be f(-6). Let w(h) = -h**3 + h**2 + h + 1. Let d(o) = x*n(o) - 5*w(o). Factor d(b).
3*(b + 1)**3
Suppose 0 + 2 - 1444*o + 1439*o + 3*o**2 = 0. What is o?
2/3, 1
Let o(x) = x**3 + 5*x**2 - x. Let y be o(-5). Let z = y - 1. Factor 1/5*g**3 - 1/5*g**z + 1/5*g**2 - 1/5*g + 0.
-g*(g - 1)**2*(g + 1)/5
Let q(y) be the first derivative of -y**4/20 - 2*y**3/5 - 9*y**2/10 + 15