1
Let f(n) be the second derivative of n**9/22680 + n**8/5040 + n**7/3780 + n**4/4 - 8*n. Let y(o) be the third derivative of f(o). Factor y(k).
2*k**2*(k + 1)**2/3
Let c(v) be the first derivative of -v**4/12 - v**3/2 - v**2 - 3*v + 3. Let f(l) be the first derivative of c(l). Let f(b) = 0. Calculate b.
-2, -1
Let g be 24/90*((-21)/18 - -2). Factor -2/9*a**3 + 4/9*a - g*a**2 + 0.
-2*a*(a - 1)*(a + 2)/9
Let n(d) = -5*d**4 + d**3 + d**2 - 5*d. Let h be (12/(-15))/(3/15). Let z(i) = 11*i**4 - 2*i**3 - 2*i**2 + 11*i. Let j(u) = h*z(u) - 9*n(u). Factor j(f).
f*(f - 1)**2*(f + 1)
Let u(k) = k - 4. Let v be u(0). Let b(t) = t - 2 + 6 - t**2 - 4. Let f(z) = -5*z**2 + 5*z. Let d(l) = v*b(l) + f(l). Find m such that d(m) = 0.
0, 1
Suppose 4*t = -3*z + 8, 10 = -0*t + 5*t. Factor -3*y**2 + z + 3/2*y**3 + 3/2*y.
3*y*(y - 1)**2/2
Let l be 2*(-6)/(-54)*12. Factor 2/3*n**5 + 8/3*n**4 + 4*n**3 + 2/3*n + l*n**2 + 0.
2*n*(n + 1)**4/3
Let q be (112/(-35))/(2/(-10)). Let r be ((-9)/(-6))/(108/q). Factor -2 - r*f**2 + 4/3*f.
-2*(f - 3)**2/9
Let a(u) be the first derivative of 2*u**5/15 - 2*u**3/9 - 3. What is j in a(j) = 0?
-1, 0, 1
Let t(w) be the second derivative of 1/20*w**4 - 3/100*w**5 - 1/30*w**3 + 1/150*w**6 + 0*w**2 + 0 + 4*w. What is a in t(a) = 0?
0, 1
Factor -21/2*p**3 - 3*p**2 + 3 + 21/2*p.
-3*(p - 1)*(p + 1)*(7*p + 2)/2
Factor 11/3*g**3 - 2/3 - 8*g**2 + 5*g.
(g - 1)**2*(11*g - 2)/3
Suppose 1 + 2 = 3*w. Let y be (-7)/(-21)*(1 - w). Factor -2*r**3 + y*r**3 + 3*r**3.
r**3
Let b(i) be the third derivative of -i**6/900 - i**5/150 + i**3/3 + 3*i**2. Let n(d) be the first derivative of b(d). Factor n(q).
-2*q*(q + 2)/5
Let k(f) be the first derivative of -f**6/24 - 7*f**5/20 - 15*f**4/16 - 3*f**3/4 + 28. Determine m so that k(m) = 0.
-3, -1, 0
Let l(v) be the second derivative of -v**7/168 - v**6/30 - 3*v**5/80 + v**4/12 + v**3/6 - 18*v. Suppose l(b) = 0. What is b?
-2, -1, 0, 1
Suppose 4*m - 32 = r, 2*m + 16 = 4*m + 5*r. Let a = m - 5. Let g**a - 2*g**3 - 5*g**4 + 4*g**4 = 0. Calculate g.
-1, 0
Let g(u) be the second derivative of -u**7/42 + u**5/20 + 10*u. Find x such that g(x) = 0.
-1, 0, 1
Let p = 30 + -30. Find q such that -1/2*q**2 + p*q + 0 = 0.
0
Let l(j) be the third derivative of j**8/1680 - j**6/120 - j**5/60 + j**3/6 + j**2. Let m(g) be the first derivative of l(g). Determine u so that m(u) = 0.
-1, 0, 2
Let h be 22/18 + 2/(-9). Let a = 3 - h. Find q, given that 2*q**2 + 1 + q + 1 + a*q + q = 0.
-1
Solve -9 + 9 - 9*b**3 + b**4 + 9*b**2 - 3*b + 2*b**4 = 0.
0, 1
Factor -x**2 - x**3 - 3*x**3 + 3*x**3 - x**2 - x.
-x*(x + 1)**2
Let h(g) = -10*g**2 - 4*g + 20. Let k(j) = j**3 - 29*j**2 - 11*j + 60. Let f(l) = -14*h(l) + 4*k(l). Factor f(m).
4*(m - 1)*(m + 2)*(m + 5)
Let d be -3 + 0 + 1152/378. Let f(t) be the second derivative of t + 1/42*t**4 + 0 - d*t**3 + 0*t**2. Find j, given that f(j) = 0.
0, 1
Let w = -24 + 14. Let g be (-9)/w + (-1)/2. What is k in -g*k**2 + 0*k + 2/5*k**3 + 0 = 0?
0, 1
Let i(p) = -7*p - 11. Let w be i(-2). Factor f**2 + 0 - 5/2*f**w + 3/2*f**4 + 0*f.
f**2*(f - 1)*(3*f - 2)/2
Let i(l) be the third derivative of -l**5/12 - 5*l**4/4 - 15*l**3/2 - 17*l**2. Factor i(g).
-5*(g + 3)**2
Suppose 28 = 2*z - 6*z. Let w = -3 - z. Factor -11*r**3 - r**5 + w*r + 3*r**5 - 4*r**2 + 7*r**5 + 6*r**4.
r*(r + 1)**2*(3*r - 2)**2
Factor 3/2*a**3 + 15/2*a - 6*a**2 - 3.
3*(a - 2)*(a - 1)**2/2
Let 1/6*l + 1/6*l**3 + 1/3*l**2 + 0 = 0. Calculate l.
-1, 0
Let u(p) = -p**3 - 3*p**2 - 4*p - 3. Let f be u(-2). Factor -2*m + f - 1/4*m**3 + 5/4*m**2.
-(m - 2)**2*(m - 1)/4
Let n be ((-2)/(-12))/(2/12). Factor 8*l**2 - 6*l**2 - n - 4*l - 5.
2*(l - 3)*(l + 1)
Suppose 5*n - 5*i - 4 - 31 = 0, 0 = -2*i - 10. Factor 3/2*g - 1/4 - 9/4*g**n.
-(3*g - 1)**2/4
Let o(h) = 22*h**2 + 148*h + 710. Let z(k) = -7*k**2 - 49*k - 237. Let a(r) = 5*o(r) + 16*z(r). Find c such that a(c) = 0.
-11
Let 10/13*h**4 - 36/13*h**3 + 0 + 14/13*h**2 + 12/13*h = 0. Calculate h.
-2/5, 0, 1, 3
Let u(v) be the third derivative of -v**8/6720 - v**7/7560 + v**4/8 - v**2. Let p(y) be the second derivative of u(y). Factor p(x).
-x**2*(3*x + 1)/3
Let b(x) be the third derivative of x**6/210 - 2*x**5/105 - 2*x**4/21 + 16*x**3/21 - 2*x**2. Let b(d) = 0. Calculate d.
-2, 2
Let u(f) be the second derivative of -3*f**6/40 + 3*f**5/80 + 5*f**4/16 - f**3/8 - 3*f**2/4 - 5*f - 1. Find p, given that u(p) = 0.
-1, -2/3, 1
Let u be (-6)/12 - 5/(-2). Suppose -u*i = -0*i - 4. Factor -2/3 - 2*o**i + 2*o + 2/3*o**3.
2*(o - 1)**3/3
Let t be (-9)/(-5) + (2 - (5 - 3)). Factor 0*a + 0 - 3/5*a**5 - 3/5*a**2 - t*a**4 - 9/5*a**3.
-3*a**2*(a + 1)**3/5
Let a(h) be the first derivative of -h**7/560 - h**6/240 + h**5/80 + h**4/16 - h**3 - 1. Let m(d) be the third derivative of a(d). Factor m(l).
-3*(l - 1)*(l + 1)**2/2
Let a = -32 - -24. Let m be a/70*(-45)/18. Factor 2/7*d**2 + m*d + 0.
2*d*(d + 1)/7
Let i(c) be the first derivative of 2*c + 2/3*c**3 - 2 + 2*c**2. Suppose i(f) = 0. What is f?
-1
Let p(w) = w**5 + w**4. Let l(q) = -12*q**5 + 22*q**4 - 18*q**3 + 4*q**2. Let u(s) = -l(s) - 2*p(s). Solve u(g) = 0 for g.
0, 2/5, 1
Let c(b) be the third derivative of 3/100*b**5 + 1/8*b**4 + 5*b**2 + 0*b - 1/5*b**3 + 0. What is h in c(h) = 0?
-2, 1/3
Let q(d) be the third derivative of d**6/40 - 3*d**5/20 + d**4/4 - 5*d**2. Find p, given that q(p) = 0.
0, 1, 2
Let o = 5 + -3. Factor -12*u**3 - 2*u + 32*u**3 - 4 + 26*u**o - 4*u**2.
2*(u + 1)*(2*u + 1)*(5*u - 2)
Let g = 127/39 + 1/13. Let a = g + -3. Factor 2/3*h + a*h**3 - h**2 + 0.
h*(h - 2)*(h - 1)/3
Let t(m) be the first derivative of -2*m**5/15 - 7*m**4/3 + 32*m**3/3 - 50*m**2/3 + 34*m/3 + 40. Let t(k) = 0. Calculate k.
-17, 1
Suppose 9*k**2 + 9*k**2 - 34*k**2 + 11*k**2 - 35*k = 0. What is k?
-7, 0
Find k such that 6/5*k + 0 - 9/5*k**2 = 0.
0, 2/3
Let h(y) = y**2 - 4*y - 3. Let d be h(5). Let -6*x**2 - 3*x**3 + d*x - 2*x = 0. What is x?
-2, 0
Let q(g) be the third derivative of -g**7/945 + 11*g**6/270 - 121*g**5/270 - 26*g**2. Suppose q(x) = 0. What is x?
0, 11
Let t be -1 + (0 - (-4 - -1)). Let o(i) be the first derivative of 1/10*i**4 + 8/15*i**3 + i**2 - t + 4/5*i. Factor o(v).
2*(v + 1)**2*(v + 2)/5
Let o = -4 + 6. Factor 2*t**3 - t**2 - 4*t - t**o + 4*t**2.
2*t*(t - 1)*(t + 2)
Let d(h) be the first derivative of -3*h**2/2 + 13*h + 8. Let j be d(4). Find o, given that -o + j + 1/4*o**2 = 0.
2
Let r(f) = -2*f**4 + 2*f**3 + 5*f**2 + 3*f + 1. Let u(s) = -s**5 + s**4 + s**3 - s - 1. Let q(i) = r(i) + u(i). Factor q(c).
-c*(c - 2)*(c + 1)**3
Factor -1/4*g**2 + 0*g + 0 + 1/2*g**3 - 1/4*g**4.
-g**2*(g - 1)**2/4
Let j(r) be the second derivative of r**7/21 - r**6/5 - r**5/10 + 7*r**4/6 - 4*r**2 - 10*r. What is f in j(f) = 0?
-1, 1, 2
Let o(c) be the second derivative of 2*c**7/105 + c**6/10 + c**5/5 + c**4/6 + c**2 - 8*c. Let u(t) be the first derivative of o(t). Factor u(g).
4*g*(g + 1)**3
Let p be 1/2 + (-161)/14. Let j = 34/3 + p. Let j*o**2 + 1/3*o - 2/3 = 0. Calculate o.
-2, 1
Let l(w) = -w**2 + 8*w - 2. Let y be l(7). Factor -4*q**y + 3*q**5 + q**4 + 2*q**5.
q**4*(q + 1)
Let o(y) = 8*y**3 - 4*y**2. Let x(c) = -15*c**3 + 8*c**2. Let a(q) = -11*o(q) - 6*x(q). Factor a(t).
2*t**2*(t - 2)
Let d(v) be the third derivative of -1/168*v**8 + 0*v**4 + 1/20*v**6 - 1/15*v**5 - 8*v**2 + 0*v**3 + 0*v**7 + 0*v + 0. Factor d(l).
-2*l**2*(l - 1)**2*(l + 2)
Factor 1/6*g - 1/6 + 1/6*g**2 - 1/6*g**3.
-(g - 1)**2*(g + 1)/6
Let d be -9 - -7 - (2 - 6). Find j such that 0 - 3/2*j + 9/4*j**d = 0.
0, 2/3
Let n be (-6)/(-18) + (-1 - (-4 - -3)). Factor n*w - 1/3*w**2 + 0.
-w*(w - 1)/3
Let m = 5/12 + -1/3. Let v(g) be the first derivative of 0*g - 1/20*g**5 - 2 + 1/16*g**4 + m*g**3 - 1/8*g**2. Factor v(o).
-o*(o - 1)**2*(o + 1)/4
Let d(b) be the third derivative of 0 - b**2 + 1/44*b**4 - 2/33*b**3 - 1/330*b**5 + 0*b. Factor d(h).
-2*(h - 2)*(h - 1)/11
Let b(h) be the third derivative of h**5/30 + h**4/6 + h**2. Factor b(u).
2*u*(u + 2)
Let s(x) be the first derivative of 2/35*x**5 + 0*x**2 - 2/21*x**3 + 1/14*x**4 + 0*x + 5 - 1/21*x**6. Factor s(m).
-2*m**2*(m - 1)**2*(m + 1)/7
Let a(s) be the second derivative of -s**7/14 + 3*s**6/10 + 9*s**5/20 - 7*s**4/4 - 3*s**3 - 27*s. Find m such that a(m) = 0.
-1, 0, 2, 3
Let q(j) be the second derivative of 0 + 4*j + 0*j**4 - 1/105*j**6 + 1/70*j**5 + 0*j**3 + 