5
Let q(k) = 1. Let g(d) = 4*d**2 - 12*d + 4. Let v(a) = -g(a) - 4*q(a). Factor v(i).
-4*(i - 2)*(i - 1)
Let q(f) be the third derivative of -f**8/60480 - f**7/15120 - f**5/60 - 5*f**2. Let c(h) be the third derivative of q(h). Factor c(i).
-i*(i + 1)/3
Let q(a) = 80*a**2 - 684*a + 216. Let p(b) = 9*b**2 - 76*b + 24. Let t(r) = 28*p(r) - 3*q(r). Suppose t(m) = 0. Calculate m.
1/3, 6
Suppose -4*p + 43 = -2*t + 277, 0 = -3*t + 15. Let u be ((-2)/4)/(7/p). Find k, given that -2*k**2 + 4*k**2 - 11*k**4 + 9*k**u = 0.
-1, 0, 1
Let x = 24 - 21. Let h(i) be the second derivative of 2*i + 0*i**x - 1/10*i**5 + 0*i**2 + 1/15*i**6 + 0 + 0*i**4. Factor h(c).
2*c**3*(c - 1)
Let d(l) be the third derivative of -l**6/180 + l**5/90 + l**4/36 - l**3/9 - 10*l**2. Let d(x) = 0. Calculate x.
-1, 1
Factor -2*i**2 + i**2 + 6*i - 2*i**2 + 3 - 6.
-3*(i - 1)**2
What is o in -5*o**3 - 69*o - 35*o**2 + 7*o - 13*o - 61 + 16 = 0?
-3, -1
Let q(v) be the third derivative of -1/8*v**4 + 0 + 1/12*v**6 - 1/3*v**3 + 0*v + 3/20*v**5 - 2*v**2. Let q(z) = 0. What is z?
-1, -2/5, 1/2
Let f(l) be the second derivative of 2/75*l**6 + 4/15*l**3 - 1/15*l**4 + 7*l + 0 - 2/25*l**5 + 0*l**2. What is d in f(d) = 0?
-1, 0, 1, 2
Let a(v) = -5*v**3 - 2*v**2 - 4. Let m(j) = -7*j**3 - j**2 - 5. Let u(c) = -5*a(c) + 4*m(c). Let u(k) = 0. Calculate k.
0, 2
Factor 13 - 16*g + 0*g**2 - 2*g**2 - 27.
-2*(g + 1)*(g + 7)
Let s(t) be the second derivative of t**5/20 + 5*t**4/48 + t**3/24 - 6*t + 2. Solve s(r) = 0 for r.
-1, -1/4, 0
Let x(h) be the second derivative of h**7/168 - h**6/120 - h**5/40 + h**4/24 + h**3/24 - h**2/8 + 15*h. Suppose x(i) = 0. Calculate i.
-1, 1
Let d(o) = -o**3 - 5*o**2 + 4*o. Suppose -20 = 3*w + 2*w. Let q(b) = -b**2 + b. Let h(v) = w*q(v) + d(v). What is x in h(x) = 0?
-1, 0
Let y(a) be the second derivative of -a**5/10 + a**3 - 2*a**2 + 8*a. Factor y(z).
-2*(z - 1)**2*(z + 2)
Let i be (8/(-2 - -6))/2. Let j be 2/i + 15/(-10). Let -a - j*a**2 - 1/2 = 0. Calculate a.
-1
Let d(h) be the third derivative of -h**7/1260 - h**6/72 - h**5/10 - 3*h**4/8 - 3*h**3/4 - 7*h**2. Let d(i) = 0. Calculate i.
-3, -1
Let r = -487 - -487. Let r*a + 2/7*a**3 + 0 - 2/7*a**2 = 0. Calculate a.
0, 1
Let a(s) be the first derivative of 0*s**3 - s**2 + 1/330*s**5 + 0*s - 1/66*s**4 + 2 + 1/660*s**6. Let r(o) be the second derivative of a(o). Factor r(h).
2*h*(h - 1)*(h + 2)/11
Suppose -2 = g + 5*z, 0 = -g + 5*z - z - 11. Let i = g - -9. Factor 2 - 2*u - i*u**2 + 0 + 6*u - 2*u - 2*u**3.
-2*(u - 1)*(u + 1)**2
Let t(f) be the second derivative of f**4/120 - 7*f**3/30 + 49*f**2/20 - f. Let t(q) = 0. Calculate q.
7
Determine t so that -2/13*t**3 - 6/13*t**2 - 2/13 - 6/13*t = 0.
-1
Let j(w) be the second derivative of w**4/78 - 4*w**3/39 - 12*w**2/13 - 21*w + 2. Factor j(h).
2*(h - 6)*(h + 2)/13
Suppose 26 = 17*z - 4*z. Let v(s) be the first derivative of 1/2*s**2 - 1/4*s**4 + 0*s**3 + z + 0*s. Factor v(j).
-j*(j - 1)*(j + 1)
Let g(n) be the third derivative of -n**5/30 - n**3/6 - 2*n**2. Let f(m) = -4*m**2 - 1. Let u(x) = -6*f(x) + 10*g(x). Factor u(d).
4*(d - 1)*(d + 1)
Let o(d) = d**3 - 6*d**2 - d + 8. Let q be o(6). Let i(a) be the second derivative of 0 + q*a**2 - 2*a + 7/3*a**3 + 4/3*a**4 + 3/10*a**5. Factor i(t).
2*(t + 1)**2*(3*t + 2)
Let q(z) = -2*z**2 - 12*z + 14. Let w(h) = -h + 1. Let g(k) = -q(k) + 6*w(k). Solve g(c) = 0 for c.
-4, 1
Let q(v) be the first derivative of -v**4/36 - 3*v + 1. Let j(y) be the first derivative of q(y). Factor j(a).
-a**2/3
Let p = 286 - 856/3. Suppose -2/3*y + 2/3*y**3 + p*y**2 - 2/3 = 0. What is y?
-1, 1
Factor 11 - 4*n**3 - 8*n**2 + 8431*n - 8427*n - 3.
-4*(n - 1)*(n + 1)*(n + 2)
Let z(m) be the first derivative of m**4/2 - 4*m**3 + 12*m**2 - 16*m - 11. Factor z(o).
2*(o - 2)**3
Let q be 4/(-32) + (-38)/(-48). Let s(g) = g**2 + 13*g + 15. Let j be s(-12). Let 2*a**4 - 4/3*a**j - q*a**5 - 4/3*a**2 + 2*a - 2/3 = 0. Calculate a.
-1, 1
Suppose b = 4*b - b. Let b + 0*o - 1/2*o**2 - 1/4*o**3 + 1/4*o**4 = 0. Calculate o.
-1, 0, 2
Let l(t) be the first derivative of -t**6/6 + t**4/4 - 5. Factor l(n).
-n**3*(n - 1)*(n + 1)
Let x(v) = 42*v + 297. Let k be x(-7). Factor 0 + k*j - 3/2*j**2.
-3*j*(j - 2)/2
Let l(y) be the first derivative of y**6/2 - 3*y**5/5 - 3*y**4/4 + y**3 - 6. Factor l(z).
3*z**2*(z - 1)**2*(z + 1)
Let z(p) be the third derivative of p**5/210 + p**4/42 + 17*p**2. Determine v, given that z(v) = 0.
-2, 0
Let q be 8*3*2/12. Suppose q*h**3 - 4*h**4 - 12*h**3 - 4*h**2 + 0*h**2 = 0. What is h?
-1, 0
Let y(t) be the first derivative of -3*t**5/80 - 3*t**4/16 - 8*t - 6. Let i(u) be the first derivative of y(u). Determine q, given that i(q) = 0.
-3, 0
Let n be (0/(20/4))/(-2). Let v(m) be the second derivative of -2/5*m**2 + 4*m - 1/15*m**3 + 1/30*m**4 + n. Factor v(g).
2*(g - 2)*(g + 1)/5
Let f(r) = -3*r**3 + 3*r**2 - 10*r - 11. Let g(p) = p**3 - p**2 + 5*p + 5. Let z(h) = -2*f(h) - 5*g(h). Factor z(j).
(j - 3)*(j + 1)**2
Let a = 3/40 - -9/8. Determine b so that 0*b - a*b**4 + 0 + 6/5*b**3 - 2/5*b**2 + 2/5*b**5 = 0.
0, 1
Let v(j) be the second derivative of 0*j**5 - 2/21*j**7 + 0*j**2 + 2/3*j**3 + 0 + 2/3*j**4 - 4/15*j**6 - j. Factor v(y).
-4*y*(y - 1)*(y + 1)**3
Factor 1/4*g**2 - 1/4*g + 0.
g*(g - 1)/4
Let c = 1327/9 + -147. Factor 0 + 0*d + 14/9*d**3 - c*d**2.
2*d**2*(7*d - 2)/9
Let u(a) be the second derivative of a**5/40 + 3*a**4/16 + a**3/2 + 3*a**2 + 7*a. Let n(r) be the first derivative of u(r). Factor n(i).
3*(i + 1)*(i + 2)/2
Let n(u) = -u**3 - 6*u**2 - 4*u - 19. Let h be n(-6). Factor -2/7*y**3 + 0 + 2/7*y**2 - 2/7*y**4 + 2/7*y**h + 0*y.
2*y**2*(y - 1)**2*(y + 1)/7
Determine x, given that 0*x**3 + 0 + 3/2*x**2 - 1/2*x**4 + x = 0.
-1, 0, 2
Let p(o) be the second derivative of -o**6/20 - o**5/45 + o**4/4 + 2*o**3/9 - 3*o**2/2 - 2*o. Let b(s) be the first derivative of p(s). Factor b(g).
-2*(g - 1)*(g + 1)*(9*g + 2)/3
Let y(l) = -l**2 + 6*l + 1. Let t be y(6). Let d be (0 + t)*24/8. Factor -7/4*u**d - 3/4*u**4 + 0 - 5/4*u**2 - 1/4*u.
-u*(u + 1)**2*(3*u + 1)/4
Let i = -313/7 + 45. Suppose -4/7 - i*d**3 - 8/7*d**2 - 10/7*d = 0. Calculate d.
-2, -1
Let f(g) = g**3 - 5*g**2 - 6*g. Suppose -20 = -2*a - 8. Let j be f(a). Factor j + 5*r**2 + 0 - 3*r**2.
2*r**2
Factor -4*x - 2*x**4 - 58*x**3 + 32*x**3 + 30*x**3 + 2*x**2.
-2*x*(x - 2)*(x - 1)*(x + 1)
Let i(s) = -13*s**4 - 7*s**3 + 35*s**2 - 33*s - 9. Let z(h) = 3*h**4 + 2*h**3 - 9*h**2 + 8*h + 2. Let g(l) = -2*i(l) - 9*z(l). Let g(m) = 0. Calculate m.
-6, 0, 1
What is m in -m**2 + 3/5*m**3 + 1/5*m + 1/5 = 0?
-1/3, 1
Suppose 0 = 5*c + 3*w - 20, 2*w - 4 = 3*c + 3. Let n be c*(0 - -3)/1. Find k such that -2*k + k**n + 3*k - 2*k = 0.
-1, 0, 1
Let u(q) = -3*q - 46. Let s be u(-16). Let 5/4*g**3 + 0 + 1/2*g + 7/4*g**s = 0. Calculate g.
-1, -2/5, 0
Let c(s) = 10*s**4 - 9*s**3 + 3*s**2 + 2*s + 3. Let p(m) = -19*m**4 + 19*m**3 - 6*m**2 - 4*m - 5. Let k(g) = -5*c(g) - 3*p(g). Factor k(a).
a*(a - 1)**2*(7*a + 2)
Let t = -2/21 - -25/42. Let m(r) be the second derivative of -t*r**2 + 0 - 5/48*r**4 - 2/3*r**3 + 7/80*r**5 - r. Factor m(p).
(p - 2)*(p + 1)*(7*p + 2)/4
Let 0*j**2 + 0*j**3 - 1/4*j**5 + 0 - 1/4*j**4 + 0*j = 0. Calculate j.
-1, 0
Let y(s) be the second derivative of 1/21*s**3 - 4*s + 0 + 0*s**4 + 0*s**2 - 1/70*s**5. Factor y(u).
-2*u*(u - 1)*(u + 1)/7
Suppose 0 = 4*a + 4*n + 16, 0 = a - 2*n - 3*n - 14. Let d = 4 + a. Factor 0*s**2 + 2*s**2 - d*s - s.
2*s*(s - 2)
Let c be (287/328)/((-2)/(-16)). Factor 76/7*d + 49*d**4 - 30*d**2 + c*d**3 - 8/7.
(d + 1)*(7*d - 2)**3/7
Let r = -166 + 166. Let r - 8/5*b**3 - 6/5*b**4 + 2/5*b**2 + 4/5*b = 0. Calculate b.
-1, 0, 2/3
Suppose -u + 4 - 3 = 0. Factor -u - 2*x**2 + 1/2*x**3 + 5/2*x.
(x - 2)*(x - 1)**2/2
Solve 25*i**4 - 40*i**4 - 2*i**3 + 17*i**4 - 4*i**2 = 0 for i.
-1, 0, 2
Let z be (3/(-9))/1*2. Let o = 7/6 + z. Factor 1/2 - q**2 + o*q**4 + 0*q + 0*q**3.
(q - 1)**2*(q + 1)**2/2
Let w = 2 + 0. Let h(m) = -m**w + 16*m - 7*m - 6 - m**2 - 2*m**2. Let k(d) = 11*d**2 - 26*d + 19. Let z(u) = 8*h(u) + 3*k(u). Let z(i) = 0. What is i?
3
Let u be (3/2)/((-15)/(-10)). Let b = 40 + -77/2. Factor -b*z**2 + u - 5/2*z.
-(z + 2)*(3*z - 1)/2
Factor -u**2 - 4*u - 8 + u**2 + 4*u**2.
4*(u - 2)*(u + 1)
Factor m**3 + m**2 + 0 + 1/3*m + 1/3*m**4.
m*(m + 1)**3/3
Let y(f) be the first derivative of -