u - 3)**2
Suppose -2*p - 8 = -4*p. Suppose x + x + p*n = 12, -9 = -4*x - 3*n. Determine z, given that 2/3*z**3 - 2*z**2 + x + 0*z = 0.
0, 3
Let x(v) = 53*v**2 - 142*v + 37. Let z(p) = 18*p**2 - 47*p + 12. Let t(n) = -2*x(n) + 7*z(n). Factor t(q).
5*(q - 2)*(4*q - 1)
Let z(k) be the second derivative of -3*k**5/140 + 3*k**4/14 + 48*k**3/7 + 48*k**2 - 623*k + 1. Find p such that z(p) = 0.
-4, 14
Let o(u) be the third derivative of -1/720*u**5 + 2*u**2 + 0 + 0*u + 1/144*u**4 + 0*u**3. Factor o(l).
-l*(l - 2)/12
Suppose 5*i - i - 156 = 0. Let u be 1 - -4 - 189/i. Suppose -2/13*d**4 + u + 4/13*d + 0*d**2 - 4/13*d**3 = 0. Calculate d.
-1, 1
Let b(m) be the first derivative of -3*m**7/1400 - m**6/75 - 13*m**5/600 - m**4/60 - 26*m**3/3 - 1. Let t(y) be the third derivative of b(y). Factor t(h).
-(h + 2)*(3*h + 1)**2/5
Let h(b) be the third derivative of b**5/12 + 115*b**4/3 + 21160*b**3/3 + 17*b**2. What is w in h(w) = 0?
-92
Let y(q) be the second derivative of 5*q**4/6 + 13*q**3/6 - 19*q**2 + 8*q. Let n(l) = 3*l**2 + 4*l - 12. Let g(x) = 7*n(x) - 2*y(x). Factor g(o).
(o - 2)*(o + 4)
Let w(q) be the first derivative of 10 + 2/3*q**3 + 5*q**2 - 5/2*q**4 + 0*q - 2/5*q**5. Solve w(l) = 0.
-5, -1, 0, 1
Let y(l) be the third derivative of 0*l**4 + 0*l**3 + 1/525*l**7 - 7*l**2 + 0*l + 1/840*l**8 + 0 - 1/300*l**6 - 1/150*l**5. What is b in y(b) = 0?
-1, 0, 1
Let w(s) = -s**2 - 2*s + 5. Let o(k) = -k**2 - k + 4. Suppose -7*i + 3*i - 36 = 0. Let y be (21/(-14))/(i/(-12)). Let r(b) = y*w(b) + 3*o(b). Factor r(x).
-(x - 2)*(x + 1)
Let m = -103 - -98. Let g be (-5)/(-2) - (2 + m + 5). Solve 1/4*z**3 + 0*z**2 + g - 3/4*z = 0.
-2, 1
Let i(y) be the second derivative of -9*y + 0 + 0*y**5 - 1/273*y**7 - 1/39*y**4 + 1/39*y**3 + 2/195*y**6 + 0*y**2. Suppose i(r) = 0. What is r?
-1, 0, 1
Let k(f) be the third derivative of 0 + 0*f**3 - 1/6*f**4 + 2*f**2 + 0*f + 1/10*f**5 + 1/3*f**6. Factor k(q).
2*q*(4*q - 1)*(5*q + 2)
Factor 21*r**3 + r**4 - 10*r**3 + 35*r**4 + 25*r**3 - 3*r**4 - 3*r**5.
-3*r**3*(r - 12)*(r + 1)
Let g(v) = 4*v**4 + 24*v**3 + 39*v**2 - 3*v - 3. Let a(x) = -12*x**4 - 72*x**3 - 118*x**2 + 10*x + 10. Let t(q) = 3*a(q) + 10*g(q). Factor t(z).
4*z**2*(z + 3)**2
Let b(w) be the second derivative of -w**6/180 - 2*w**5/45 - w**4/12 + w**2/2 + 15*w. Let x(s) be the first derivative of b(s). Factor x(t).
-2*t*(t + 1)*(t + 3)/3
Suppose -o + 2*o = -3*l + 21, 0 = 4*o. Suppose -5*k - l*f - 15 = -2*f, 3*k - 3*f = 21. Factor 8 - 2*j**k + 0*j**2 - 8 + 4*j.
-2*j*(j - 2)
Let p(t) be the third derivative of -t**6/90 + 7*t**5/30 - t**4 - 3*t**3 - 44*t**2. Let f(r) be the first derivative of p(r). Find g such that f(g) = 0.
1, 6
Let z = 16379 - 16377. Let 4/5*o + z*o**2 - 2/5*o**5 + 6/5*o**3 - 2/5*o**4 + 0 = 0. Calculate o.
-1, 0, 2
Let c(p) = p**4 - 3*p**3 - 3*p**2 + 3*p - 2. Let z(o) = o**3 + o**3 + 8 + 12*o**2 - 4*o**4 - 11*o + 11*o**3. Let l(s) = -9*c(s) - 2*z(s). Factor l(i).
-(i - 1)**3*(i + 2)
Let r(v) = -3*v**2 - 196*v + 4807. Let f(q) = -2*q**2 - 196*q + 4806. Let u(k) = -5*f(k) + 4*r(k). Find h, given that u(h) = 0.
49
Let d(x) be the first derivative of -x**4/6 + 328*x**3/3 - 26896*x**2 + 8821888*x/3 + 906. Factor d(t).
-2*(t - 164)**3/3
Let x(s) = s**2 - 2. Let l(v) = 5*v**3 + 5*v**2 - 20*v - 50. Let a(t) = l(t) + 15*x(t). Determine w, given that a(w) = 0.
-4, -2, 2
Suppose 103*z = 36*z + 134. Suppose 6/13*a**3 - 14/13*a + 6/13*a**z + 6/13 - 4/13*a**4 = 0. Calculate a.
-3/2, 1
Let s(d) be the first derivative of 7/9*d**3 + 1/3*d**2 + 0*d - 54 - 1/5*d**5 + 1/6*d**4. Factor s(m).
-m*(m - 2)*(m + 1)*(3*m + 1)/3
Let o(q) = 7*q**2 - 9*q - 1. Suppose -5*c + z + 35 = 0, -4*z + 0*z = -20. Let y(l) = 11*l**2 - 14*l - 1. Let h(x) = c*o(x) - 5*y(x). Factor h(g).
(g - 3)*(g + 1)
Let r(g) be the second derivative of g**6/15 + g**5/10 - g**4/6 - g**3/3 + 115*g. Factor r(n).
2*n*(n - 1)*(n + 1)**2
Let f be 8/(-48) - 11/(-22). Let g(y) be the first derivative of 2*y**2 - 1/4*y**4 - f*y**3 + 4*y + 1. Factor g(z).
-(z - 2)*(z + 1)*(z + 2)
Let l(k) be the first derivative of 0*k + 1/3*k**6 + k**2 - 8/3*k**3 - 8/5*k**5 + 3*k**4 - 1. Factor l(i).
2*i*(i - 1)**4
Let z(b) be the third derivative of 0 - 2/525*b**7 + 0*b**5 + 1/15*b**4 + 27*b**2 - 1/75*b**6 + 0*b + 2/15*b**3. Determine v, given that z(v) = 0.
-1, 1
Let w(i) be the third derivative of -i**6/420 + i**5/105 + 11*i**4/84 - 4*i**3/7 + 348*i**2. Solve w(l) = 0 for l.
-3, 1, 4
Let a(i) be the second derivative of -i**6/45 - i**5/30 + i**4/18 + i**3/9 - 110*i. Factor a(s).
-2*s*(s - 1)*(s + 1)**2/3
Suppose 0 = -5*h - 2*t - 229, 3*h - 5*t + 156 = -0*h. Let n = -327/7 - h. Solve 0 + 2/7*o**2 + n*o = 0.
-1, 0
Suppose -2*s - 2 + 6 = 0. Suppose -10*y - 7*y**s + 0*y**2 - 4 + 4*y**2 - 2*y**3 - 5*y**2 = 0. What is y?
-2, -1
Let p(b) be the first derivative of b**3/3 - 106*b**2 + 11236*b - 460. Factor p(s).
(s - 106)**2
Suppose 3*s - 11*y = -14*y - 3, -5*y - 17 = 2*s. Factor -400*x**3 - 1625/4*x**s - 44*x - 625/4*x**5 - 190*x**2 - 4.
-(x + 1)*(5*x + 2)**4/4
Let r(g) be the third derivative of g**5/15 - 7*g**4/3 - 64*g**3/3 + 3*g**2 - 3*g. Factor r(u).
4*(u - 16)*(u + 2)
Let v be (258/(-27) + 9)/(25/(-15)). Let m be 6/(-4)*(-6)/27. Factor 2/3*s - 2/3*s**3 + 0*s**2 - m*s**4 + v.
-(s - 1)*(s + 1)**3/3
Let r(d) = d + 24. Suppose -5*k - 2*g = 126, -58 = 4*k + 4*g + 50. Let h be r(k). Factor 8/13 + h*o - 2/13*o**2.
-2*(o - 2)*(o + 2)/13
Determine q so that -8 + 40/3*q - 6*q**2 + 2/3*q**3 = 0.
1, 2, 6
Let l(z) be the third derivative of -z**6/1080 + z**5/360 - z**3 + z**2. Let k(g) be the first derivative of l(g). Solve k(u) = 0.
0, 1
Let x = -2372 - -2372. Let n(f) be the second derivative of 1/13*f**2 + 1/13*f**3 - 3/130*f**5 + x - 6*f + 1/78*f**4 - 2/195*f**6. Find k, given that n(k) = 0.
-1, -1/2, 1
Let k(u) be the first derivative of u**6/45 + 11*u**5/90 + 5*u**4/36 - 2*u**3/9 + 7*u**2/2 - 22. Let b(o) be the second derivative of k(o). Factor b(q).
2*(q + 1)*(q + 2)*(4*q - 1)/3
Factor q**2 + 6*q + 7*q + q + 4*q - 16*q.
q*(q + 2)
Let c(m) be the first derivative of 41*m**3/6 + 23*m**2/5 + 2*m/5 - 12. Find s, given that c(s) = 0.
-2/5, -2/41
Let f(w) be the third derivative of w**6/60 - w**5/15 - w**4/4 + 4*w**2. Let m(z) = -z**2 + 1. Let i(n) = f(n) - 4*m(n). Factor i(v).
2*(v - 2)*(v + 1)**2
Let f(x) = x**2 - x - 1. Let v(u) = -10*u**3 + u**2 + 9*u + 4. Let j = 33 + -34. Let r(d) = j*v(d) - 4*f(d). Factor r(o).
5*o*(o - 1)*(2*o + 1)
Let z(b) be the third derivative of 0*b + 1/1080*b**6 - 31*b**2 + 0 - 1/216*b**4 + 0*b**5 + 0*b**3. Solve z(f) = 0.
-1, 0, 1
Let h(a) be the second derivative of -25/2*a**4 - 250*a**3 - 2500*a**2 - 1/4*a**5 + 0 + 24*a. Suppose h(b) = 0. What is b?
-10
Let h(w) be the second derivative of -4/3*w**3 + 2*w + 0 + 1/60*w**6 + 0*w**4 + w**2 + 1/10*w**5. Let c(z) be the first derivative of h(z). Factor c(j).
2*(j - 1)*(j + 2)**2
Let m(k) be the second derivative of 5*k**7/42 - k**6/6 - k**5/4 + 5*k**4/12 - k + 271. Find v, given that m(v) = 0.
-1, 0, 1
Let n(o) be the third derivative of o**8/168 + 31*o**7/210 + 11*o**6/12 - 19*o**5/12 - 14*o**4/3 + 32*o**3/3 + 107*o**2. Determine y, given that n(y) = 0.
-8, -1, 1/2, 1
Let i(p) = p**3 - 4*p**2 + p + 7. Let l be i(4). Factor -4*v + v**2 + 25 + 4*v - v + l*v.
(v + 5)**2
Suppose 187 = -g + 55. Let q be 11/(g/(-40)) - 3. Determine m so that -q*m - 1/3*m**3 + 0 + 2/3*m**2 = 0.
0, 1
Let b(z) be the first derivative of 3*z**5/5 - 3*z**4/4 - 16*z**3 - 30*z**2 - 23. Factor b(o).
3*o*(o - 5)*(o + 2)**2
Let z(w) be the second derivative of -w**4/3 + 26*w**3/3 - 24*w**2 + 2*w + 10. Suppose z(l) = 0. Calculate l.
1, 12
Let q(f) = -f**4 - 7*f**3 - f**2 - 3*f - 3. Let j(l) = 5*l**4 + 31*l**3 + 3*l**2 + 13*l + 13. Let r(k) = -6*j(k) - 26*q(k). Suppose r(g) = 0. What is g?
-2, 0, 1
Let y be (-54)/351*13/(-15). Solve -y*d**3 - 6/5*d + 8/15 + 4/5*d**2 = 0.
1, 4
Let i = -2132208199/471 - -4526984. Let h = i + -3/157. Factor 2/3*o**2 + 0*o - h.
2*(o - 2)*(o + 2)/3
Let s(x) = x**3 - 3*x**2 - 2*x. Let n(j) = 25*j**5 + 70*j**4 + 35*j**3 + 15*j**2 + 10*j. Let b(i) = -n(i) - 5*s(i). Factor b(d).
-5*d**3*(d + 2)*(5*d + 4)
Let f(u) be the second derivative of -u**6/30 - 3*u**5/2 - 75*u**4/4 + 413*u. Factor f(x).
-x**2*(x + 15)**2
Suppose -8*p**3 + 15*p**2 - 57*p**2 - 18 - 22 - 3*p**3 - 68*