 + 0*j**2 - 16/5*j**r + 0*j = 0. Calculate j.
-4, 0
Let h(j) be the second derivative of j**4/54 + 7*j**3/27 + 10*j**2/9 - j + 32. Let h(k) = 0. Calculate k.
-5, -2
Let w(s) be the second derivative of -s**3/2 - s**2 + 13*s. Let u(n) = n**2 - n - 1. Let a(p) = -4*u(p) + 4*w(p). Find k such that a(k) = 0.
-1
Let r be 5/2 + 646/76 + -9. Factor -288/11 + 48/11*f - 2/11*f**r.
-2*(f - 12)**2/11
Let n(i) be the first derivative of 1/6*i**4 - 1/50*i**5 - 8/15*i**3 + 2 + 4/5*i**2 + i. Let y(c) be the first derivative of n(c). Let y(u) = 0. Calculate u.
1, 2
Suppose -4*l + 3*d = -14 + 2, 0 = 5*l - 2*d - 15. Suppose -3 - l = -a. Find n, given that -4*n**2 - a*n**3 + 4*n + 2*n**3 + 0*n**2 + 4*n**4 = 0.
-1, 0, 1
Let b be 63/6*(-9)/(-63). Suppose 0 = -2*w - 4*v + 8, 4*w - 8 = w - 4*v. Factor -1/2*h**4 + 1/2*h + w + b*h**3 - 3/2*h**2.
-h*(h - 1)**3/2
Let f(w) be the second derivative of -w**8/1120 + w**7/630 + w**6/30 - 2*w**5/15 + w**4/6 - 8*w. Let u(g) be the third derivative of f(g). Factor u(d).
-2*(d - 2)*(d + 2)*(3*d - 2)
Let j(i) be the third derivative of i**6/420 + 3*i**5/70 - 5*i**4/42 - 12*i**2 + 1. Let j(n) = 0. What is n?
-10, 0, 1
Let u(m) = -2*m**2 - 72*m + 504. Let r be u(-42). Factor 1/3 + r*x**2 + 1/2*x - 1/6*x**3.
-(x - 2)*(x + 1)**2/6
Let u(r) = -r**3 - 14*r**2 + 17*r + 2. Let k(c) = c**3 - c**2 + c + 1. Let y(d) = 2*k(d) - u(d). Factor y(i).
3*i*(i - 1)*(i + 5)
Let b = -757/6 + 761/6. Suppose 2/3*h - 4/3 + 4/3*h**2 - b*h**3 = 0. What is h?
-1, 1, 2
Let w = 30509/61010 - 2/30505. Factor 2*g + w*g**2 + 2.
(g + 2)**2/2
Let t(z) be the first derivative of 2*z**5/15 - 7*z**4/2 + 104*z**3/3 - 496*z**2/3 + 384*z - 246. Solve t(a) = 0.
4, 9
Let h be 3*-2 - (-8 - 5 - -4). Factor -1272/7*j**h - 96/7 - 240/7*j**2 - 21*j**5 - 114*j**4 + 528/7*j.
-3*(j + 2)**3*(7*j - 2)**2/7
Let i(d) be the second derivative of 0 + 0*d**3 + 1/10*d**6 + 0*d**2 + 0*d**4 + 3*d + 1/10*d**5. Factor i(m).
m**3*(3*m + 2)
Suppose 0 = -q + 4*q - 12. Suppose -u = q*m - 4, -m - 2*u = m + 4. Factor 0*k**2 + 6 - 4*k**m - 8*k - 6.
-4*k*(k + 2)
Suppose -3*x + 8 = x. Let a = 475/61 + -3739/488. Factor 1/4*z + a*z**x - 3/8.
(z - 1)*(z + 3)/8
Let s(f) = f + 20. Let o be s(-19). Let p(r) = r**2 - 2*r + 1. Let k be p(o). Suppose 1/2*d - 1/2*d**3 + k + 0*d**2 = 0. What is d?
-1, 0, 1
Let h be ((-485)/84)/((-115)/69) - 1/(-4). Factor 12/7 + h*l + 16/7*l**2 + 2/7*l**3.
2*(l + 1)**2*(l + 6)/7
Let y(h) = h**2 - 9*h - 8. Let n be y(10). Let g(w) = -4*w + 5*w**n + 1 + 2*w + 10 - 9*w. Let z(s) = s**2 - 2*s + 2. Let f(v) = -2*g(v) + 11*z(v). Factor f(l).
l**2
Find w such that -1/3*w**3 + 1/3*w + 0*w**2 - 1/6*w**4 + 1/6 = 0.
-1, 1
Let l = 3312 + -3309. Factor 0*u + 1/5*u**l - 2/5*u**2 + 0.
u**2*(u - 2)/5
Let v(r) = r**2 - 8*r + 3. Let t be v(7). Let p be -2 - 1 - (3 + -5 + t). Factor 2/5*y**p + 0*y - 2/5*y**2 + 0.
2*y**2*(y - 1)/5
Let k = -18 - -14. Let z be (-14)/k - (1 - -2). Factor 1/2*m**3 - m + z*m**2 + 0.
m*(m - 1)*(m + 2)/2
Let x(w) = -4*w**2 + 3*w**2 - 126*w + 127*w. Let i(y) = -150*y**3 + 77*y**2 + 9*y - 8. Let d(q) = -2*i(q) - 14*x(q). Solve d(b) = 0 for b.
-1/3, 2/5
Let t(j) be the second derivative of 0 + 6*j**3 + 1/15*j**5 + 6*j**2 - 6*j - j**4. Let n(q) be the first derivative of t(q). Factor n(h).
4*(h - 3)**2
Let x be 15/1*10/10. Suppose -2*k - 6*k**5 + 20 - 55*k**2 + 7*k - 4*k**5 + x*k + 35*k**4 - 10*k**3 = 0. What is k?
-1, -1/2, 1, 2
Let k(w) be the first derivative of 2*w**4/9 + 10*w**3/27 - 7*w**2/9 - 4*w/9 + 37. Factor k(p).
2*(p - 1)*(p + 2)*(4*p + 1)/9
Let f(g) be the first derivative of -3/13*g**6 - 54/65*g**5 + 11 + 8/13*g**3 + 0*g - 7/13*g**4 + 8/13*g**2. Let f(x) = 0. Calculate x.
-2, -1, -2/3, 0, 2/3
Let m(c) = -c**2 + 0*c**2 + 2 + 0 - 3 + c. Let d(q) = -4*q**3 + 36*q**2 - 44*q + 18. Let k(s) = -2*d(s) - 12*m(s). Factor k(w).
4*(w - 6)*(w - 1)*(2*w - 1)
Determine m, given that -2*m - 1/2*m**2 + 5/4*m**3 + 0 - 1/4*m**4 = 0.
-1, 0, 2, 4
What is x in -22/3*x - 20/3*x**2 + 0 + 2/3*x**3 = 0?
-1, 0, 11
Let i be 0*((-6)/(-28) - 22/(-77)). Suppose 10 + 3 = 5*f + 3*a, -f - 5*a + 7 = i. Factor 2/3*y**4 + 2/3*y**3 - 2/3*y**f - 2/3*y**5 + 0*y + 0.
-2*y**2*(y - 1)**2*(y + 1)/3
Let b(f) be the third derivative of f**5/12 - 65*f**4/24 - 25*f**2 + 2*f. Let b(l) = 0. What is l?
0, 13
Factor 11*i**3 + 41*i**3 + 2*i**4 + 0*i**4 + 0*i**3 - 12*i**3.
2*i**3*(i + 20)
Let f(x) = 4*x**2 - x - 3. Suppose s - 2*s + 3 = 0. Let w(g) = -11*g**2 + s*g**2 + 4*g + 8 - 4*g**2. Let h(i) = -14*f(i) - 5*w(i). Let h(y) = 0. What is y?
1/2, 1
Let h be -2 - 51/(-15) - (-3)/5. Factor -2*m**3 + 10*m**h + 10*m**2 + 8*m + 0*m**4 - 2*m**5 - 8*m**4 - 16.
-2*(m - 1)**2*(m + 2)**3
Find q, given that 1/2*q**2 + 0 - 19/2*q = 0.
0, 19
Factor 2/3*s**4 + 0 - 8/3*s + 2*s**3 + 0*s**2.
2*s*(s - 1)*(s + 2)**2/3
Let v(n) be the first derivative of -n**4/34 + 3*n**2/17 + 4*n/17 + 44. Factor v(p).
-2*(p - 2)*(p + 1)**2/17
Suppose 49*u = -148*u + 394. Factor 2/5*s**u + 2/5*s - 4/5.
2*(s - 1)*(s + 2)/5
Let a = 28 + -25. Factor -80*v**4 + 14*v**3 + 36*v**5 + 33*v**a - 19*v**3 + 24*v**3 - 8*v**2.
4*v**2*(v - 1)**2*(9*v - 2)
Let w(l) be the second derivative of -3*l**4/2 - 4*l**3 - 4*l**2 + 5*l + 13. Factor w(u).
-2*(3*u + 2)**2
Suppose -28 + 4 + 46*v**2 - 47*v**2 + 10*v = 0. Calculate v.
4, 6
Let s(x) be the third derivative of 0*x**4 - 10*x**2 + 0*x + 0*x**3 - 1/480*x**6 - 1/120*x**5 + 0. Solve s(t) = 0 for t.
-2, 0
Let m(t) be the third derivative of t**5/270 - t**4/18 + 5*t**3/27 + t**2 - 22. Find c, given that m(c) = 0.
1, 5
Let h(x) = -4*x**3 + 4*x**2 + 4*x + 3. Let n(t) = -t**3 + t**2 + t + 1. Let f(o) = 2*h(o) - 7*n(o). Solve f(a) = 0 for a.
-1, 1
Factor -4*c - 6*c**4 - 3*c**3 + 4*c**4 + 6*c**3 + 63*c**2 - 59*c**2 - c**5.
-c*(c - 1)**2*(c + 2)**2
Suppose 0 = -11*n + 44. Determine r so that -6*r**3 + 12 + 6 - 9 + r**n + r**2 + 24*r + 7 = 0.
-1, 4
Let i(d) = -2*d - 6. Let j be i(-4). Let h be (-37)/(37/5) + 150/26. Find s, given that -8/13*s**4 + 16/13*s**3 - h*s - 4/13 - 6/13*s**5 + 12/13*s**j = 0.
-2, -1, -1/3, 1
Factor -2*v**2 + 37/3*v - 10 - 1/3*v**3.
-(v - 3)*(v - 1)*(v + 10)/3
Let g(k) = -2*k**4 + 2*k**3 - 2*k - 2. Let v(p) = -p**3 - p**2 + p - 1. Let l be 0 + -4 - (-15 + 12). Let n(u) = l*g(u) + 2*v(u). Suppose n(i) = 0. What is i?
-1, 0, 1, 2
Let t = 1 - -4. Suppose -4*w = h - 22, -24 = -2*h - t*w + w. Find y such that -4*y + y**3 + 2*y**h + 4*y = 0.
-2, 0
Let y = -448 - -451. Let m(d) be the first derivative of 0*d**y + 0*d**4 + 0*d + 12 + 0*d**2 + 1/5*d**5 + 1/6*d**6. Factor m(q).
q**4*(q + 1)
Let d be -8 + 226 - (-4)/18. Let c = d + -218. Factor 16/9*m - 32/9 - c*m**2.
-2*(m - 4)**2/9
Let d(g) be the first derivative of -10/3*g**3 + 5*g**4 - 25/2*g**2 + 5/6*g**6 + 4*g**5 - 39 - 10*g. Find v such that d(v) = 0.
-2, -1, 1
Let u(y) = y + 7. Let d(v) = -v**2 - 16*v - 20. Let i be d(-15). Let s be u(i). Factor 6*x**3 + 3*x - 8*x**3 - 2*x**s - 3*x.
-2*x**2*(x + 1)
Let b = 12 + -8. Factor -2*s**b - s**4 + 4*s - 5*s**3 + 2 + s**3 + s**4.
-2*(s - 1)*(s + 1)**3
Suppose -80193*q + 80164*q = 0. Find p, given that 2/5 - 2/5*p**4 - 4/15*p**5 + 4/3*p**3 - 16/15*p + q*p**2 = 0.
-3, -1, 1/2, 1
Let b(l) be the third derivative of -l**9/15120 + l**8/2520 + 3*l**5/10 + 4*l**2. Let s(w) be the third derivative of b(w). Factor s(o).
-4*o**2*(o - 2)
Let p = 1019 - 1017. Let x(z) be the first derivative of 4 + 0*z + 0*z**4 + 1/42*z**6 + 0*z**p + 0*z**3 + 0*z**5. Find j such that x(j) = 0.
0
Let q(u) = 39*u**3 + 10*u**2 + 4. Let v(z) = 430*z**3 + 110*z**2 + 45. Suppose 0 = -4*o + 3*r - 4, -4*r + 3*r - 4 = 0. Let b(m) = o*v(m) + 45*q(m). Factor b(k).
5*k**2*(7*k + 2)
Let a = -16 + 26. Suppose 4*h - a = -h. Let -c**4 + 7*c**3 - 5*c**4 + 2*c + 3*c**3 - 8*c**h + 2*c**4 = 0. What is c?
0, 1/2, 1
Let w(h) be the third derivative of 0 + 1/30*h**5 - 7/6*h**3 + 1/6*h**4 + 1/360*h**6 + 9*h**2 + 0*h. Let y(x) be the first derivative of w(x). Factor y(j).
(j + 2)**2
Let h(i) be the first derivative of i**6/39 - 12*i**5/65 + i**4/2 - 8*i**3/13 + 4*i**2/13 - 31. Factor h(q).
2*q*(q - 2)**2*(q - 1)**2/13
Let w = -21/709 - -3067/7799. Determine t, given that 2/11*t**2 + w + 6/11*t = 0.
-2, -1
Let b be ((-2)/8)/(11/(-176)). Let q(s) be the first derivative of -3/2*s**2 + s - b + s**3 - 1/4*s**4. Factor q(f).
-(f - 1)**3
Let v = -30/551 - -611/1102. L