hird derivative of -z**8/2352 + 2*z**7/735 - z**6/140 + z**5/105 - z**4/168 - 9*z**2. Solve p(a) = 0.
0, 1
Let r = -9362/11 - -852. Determine t so that r*t**2 + 4/11 - 14/11*t = 0.
2/5, 1
Let b(s) = -s**3 + 2*s - 1. Let g(f) = -2*f**3 + f**2 + 3*f - 3. Let i(c) = -7*b(c) + 3*g(c). Let d be i(-4). Factor -2/3 + y**3 + 1/3*y**4 - y + 1/3*y**d.
(y - 1)*(y + 1)**2*(y + 2)/3
Suppose 4*a - 3*g - g = 20, a = -4*g - 10. Let z = 57 + -169/3. Determine w so that -z + 11/3*w - 3*w**a = 0.
2/9, 1
Let i(a) = -6*a**2 - 103*a - 17. Let c be i(-17). Factor -1/4*u**2 + c + 0*u.
-u**2/4
Factor -232/3*r**2 - 28/3*r**3 - 128/3 - 512/3*r.
-4*(r + 4)**2*(7*r + 2)/3
Let h(a) be the third derivative of 1/28*a**4 + 0 + 1/21*a**3 + 0*a + a**2 + 1/420*a**6 + 1/70*a**5. Factor h(o).
2*(o + 1)**3/7
Let x(u) = u**3 - 9*u**2 - 23*u + 13. Let l be x(11). Factor -2/9*b**l + 4/9 - 2/9*b.
-2*(b - 1)*(b + 2)/9
Suppose -3*p + p + 8 = 0. Let b(h) be the third derivative of 0*h + 7/360*h**6 + 0*h**3 + 1/36*h**p + 2*h**2 + 0 + 1/20*h**5. Solve b(u) = 0 for u.
-1, -2/7, 0
Let b(t) = 5*t**2 - 5*t - 7. Let a be (2 + 2)*(-14)/(-4). Let g(w) = 14*w + 3*w - a*w**2 - 3*w + 20. Let o(l) = -8*b(l) - 3*g(l). Let o(m) = 0. Calculate m.
-1, 2
Let a = 1/55 + 97/715. Solve -4/13*d**3 + 4/13*d**2 - 2/13*d**4 + a*d**5 + 2/13*d - 2/13 = 0.
-1, 1
Let l(o) be the third derivative of -o**6/720 + o**5/80 - o**4/24 - o**3/3 - 5*o**2. Let v(h) be the first derivative of l(h). Factor v(w).
-(w - 2)*(w - 1)/2
Let i(y) = 25*y**2 - 2*y - 28*y**2 + 0 + 6*y + 3. Suppose c - 55 = 6*c. Let l(g) = 9*g**2 - 11*g - 9. Let n(w) = c*i(w) - 4*l(w). Factor n(a).
-3*(a - 1)*(a + 1)
Let 0 + 1/3*j**3 + 0*j + 1/3*j**2 = 0. Calculate j.
-1, 0
Let d(u) = -9*u**4 + 48*u**3 - 51*u**2 + 9*u - 3. Let n(j) = j**4 - j**3 - j**2 - 1. Let g(z) = -d(z) + 3*n(z). Solve g(p) = 0 for p.
0, 1/4, 1, 3
Let x = 1 + -1. Let k(p) be the second derivative of 0 + 1/36*p**4 + p - 1/6*p**2 + x*p**3. Factor k(l).
(l - 1)*(l + 1)/3
Let p be ((-1 - -5) + 0)*(8 - 7). Suppose 3/4*y**5 - 3/4*y**p + 0*y + 0 - 3/4*y**3 + 3/4*y**2 = 0. Calculate y.
-1, 0, 1
Let o(h) = -3*h - 9. Let k be o(-13). Let c be 108/k*(-20)/(-42). Let 4/7 - 8/7*q**2 - 6/7*q + 4/7*q**4 - 6/7*q**5 + c*q**3 = 0. Calculate q.
-1, 2/3, 1
Let c(p) be the third derivative of -p**9/30240 - p**8/5040 - p**5/30 + 2*p**2. Let s(n) be the third derivative of c(n). Solve s(j) = 0 for j.
-2, 0
Let i(k) be the third derivative of k**7/735 - k**6/420 - k**5/105 - 2*k**2. Determine m so that i(m) = 0.
-1, 0, 2
Let q be (-23)/(-30) - 3/18. Factor -q*s**3 + 0 - 3/5*s - 6/5*s**2.
-3*s*(s + 1)**2/5
What is v in -3*v**5 - 19*v**4 - 5*v**5 - 12*v**4 - 6*v**3 + 5*v**4 = 0?
-3, -1/4, 0
Suppose -i - 9 = -12. Factor -4/3*m**2 + 0 + 2/3*m**i + 0*m.
2*m**2*(m - 2)/3
Let f = -21 - -27. Suppose 3*l + 0 = f. Factor -4/3*t**l + 1/3 + t.
-(t - 1)*(4*t + 1)/3
Factor -4/3*v - 2 + 2/3*v**2.
2*(v - 3)*(v + 1)/3
Let j(g) = -g**3 + g**2 + 3. Let m be j(0). Factor 2*f + 8*f**4 - 1 - 8*f**m + 1 - 6*f**3 + 4*f**2.
2*f*(f - 1)**2*(4*f + 1)
Let m(d) = 13*d**5 - 11*d**4 + 18*d**3 + d**2. Let u(s) = -9*s**5 + 7*s**4 - 12*s**3 - s**2. Let t(a) = -5*m(a) - 7*u(a). Find r, given that t(r) = 0.
0, 1
Let l(b) = -10*b**2 - 14 + 70*b - 22 - 33*b**2 + 9*b**2. Let k(f) = -7*f**2 + 14*f - 7. Let y(w) = -16*k(w) + 3*l(w). Let y(m) = 0. What is m?
2/5, 1
Let f(d) be the second derivative of 3*d**4/4 + 3*d**3/2 - 3*d**2 + 2*d. Let h(y) = -y**2 - y. Let p(m) = f(m) + 6*h(m). Suppose p(j) = 0. Calculate j.
-2, 1
Let h = 201 + -6029/30. Let y(l) be the second derivative of 1/25*l**5 + h*l**4 + 0 - 2*l + 0*l**3 + 1/75*l**6 + 0*l**2. Factor y(a).
2*a**2*(a + 1)**2/5
Factor 32/11 + 0*u**3 - 16/11*u**2 + 2/11*u**4 + 0*u.
2*(u - 2)**2*(u + 2)**2/11
Let u(b) be the first derivative of 1/5*b**5 + 0*b - 2 + 0*b**2 + 1/3*b**3 + 1/36*b**6 + 1/3*b**4. Let v(k) be the third derivative of u(k). Factor v(z).
2*(z + 2)*(5*z + 2)
Let l(v) = v. Let n be l(5). Suppose 5 + 7 = 4*h, -i = 5*h - 15. Suppose -1/4*g**3 + 0*g**4 + 0*g**2 + i*g + 1/4*g**n + 0 = 0. What is g?
-1, 0, 1
Suppose 0*d - d + 3 = 0. Factor -2/3*o**4 + 0 + 0*o**d + 2/3*o**2 + 0*o.
-2*o**2*(o - 1)*(o + 1)/3
Suppose -4*b**2 + 120*b - 65*b - 63*b = 0. Calculate b.
-2, 0
Let t(z) = -12*z**5 + 17*z**4 + 25*z**3 + z**2 + 5*z - 9. Let c(n) = 3*n**5 - 4*n**4 - 6*n**3 - n + 2. Let v(m) = 9*c(m) + 2*t(m). Let v(r) = 0. What is r?
-1, -1/3, 0, 1
Let h(q) be the second derivative of -3*q**4/8 - 2*q**3 - 3*q**2 + 7*q. Factor h(k).
-3*(k + 2)*(3*k + 2)/2
Let l(a) = -a - 9. Let g be l(-9). Factor -1/2*i**3 + g*i**2 - 1/2*i**5 + 0 + 0*i + i**4.
-i**3*(i - 1)**2/2
Let x be (-3 + -10)*-1 + -3. Find t such that -24*t**4 - t - x*t + 48*t**3 - 2 - t - 2*t**2 - 8*t**4 = 0.
-1/4, 1
Let n(b) be the first derivative of 0*b**2 - 3 - 1/25*b**5 - 2*b - 1/30*b**4 + 0*b**3 - 1/75*b**6. Let o(t) be the first derivative of n(t). Factor o(f).
-2*f**2*(f + 1)**2/5
Let a = 3079/22 - 140. Let f = 13/44 + a. Factor 3/4*z**3 + 0 + f*z + 1/4*z**4 + 3/4*z**2.
z*(z + 1)**3/4
Let m = 54 - 53. Let n(s) be the first derivative of 0*s**3 + 1/20*s**5 + m + 0*s**2 - 1/8*s**4 + 0*s. Factor n(z).
z**3*(z - 2)/4
Let a(o) be the first derivative of -o**5/60 + o**4/36 + o**3/18 - o**2/6 + 3*o + 3. Let n(k) be the first derivative of a(k). Factor n(t).
-(t - 1)**2*(t + 1)/3
Factor 2/3*c - 1/3 - 2/3*c**3 + 1/3*c**4 + 0*c**2.
(c - 1)**3*(c + 1)/3
Let b(y) be the first derivative of 0*y + 1 - 9/2*y**2 + 3/5*y**5 - 15/4*y**4 + 7*y**3. Factor b(h).
3*h*(h - 3)*(h - 1)**2
What is u in 10*u - 5 - 6*u - 5*u**4 + 16*u + 20*u**3 - 30*u**2 = 0?
1
Let w(d) = -d**2 + d + 9. Let s be w(3). Let f(y) be the second derivative of -1/6*y**4 - 2/21*y**s + 3*y + 0 - 1/14*y**5 + 0*y**2. Factor f(k).
-2*k*(k + 1)*(5*k + 2)/7
Let o = -10561/21 + 503. Let v(b) be the first derivative of o*b**3 + 0*b**2 + 1 + 0*b. Factor v(j).
2*j**2/7
Let r = 2 + 0. Factor j**2 - j**4 + 0*j**r + 3*j**4 - 3*j**4.
-j**2*(j - 1)*(j + 1)
Let r(k) be the third derivative of k**7/350 - k**6/100 - 3*k**5/100 + k**4/5 - 2*k**3/5 + 4*k**2. Factor r(a).
3*(a - 2)*(a - 1)**2*(a + 2)/5
Let u(k) be the first derivative of -k**4/12 - 2*k**3/9 - k**2/6 - 32. Solve u(l) = 0 for l.
-1, 0
Let q(v) be the third derivative of v**6/24 - v**5 + 10*v**4 - 160*v**3/3 - 12*v**2. What is j in q(j) = 0?
4
Let k = 19981/37 + -540. Let u = k - -997/74. Suppose 0 + 9*i**4 - 2*i + u*i**5 - 21/2*i**3 - 10*i**2 = 0. Calculate i.
-2/3, -1/3, 0, 1
Let c(r) = -r**3 + r**2 + r - 7. Suppose -4*m + 9 = -7*m. Let i(b) = 2*b**3 - 2*b**2 - 2*b + 22. Let d(h) = m*i(h) - 10*c(h). What is v in d(v) = 0?
-1, 1
Let l(g) be the second derivative of -g**5/110 - g**4/22 - 2*g**3/33 - 3*g. Find n, given that l(n) = 0.
-2, -1, 0
Let c(r) = -5*r**3 + 9*r**2 - 3*r - 5. Let v(s) = 6*s**3 - 10*s**2 + 3*s + 4. Let m(t) = -5*c(t) - 4*v(t). Factor m(o).
(o - 3)**2*(o + 1)
Let x = 32/93 + 646/465. Let c(n) be the first derivative of 5/9*n**6 + 0*n - x*n**5 - 2/3*n**2 + 2 + 2/9*n**3 + 3/2*n**4. Factor c(a).
2*a*(a - 1)**3*(5*a + 2)/3
Let h(z) be the third derivative of z**7/350 + z**6/100 + z**5/100 - 14*z**2. Factor h(c).
3*c**2*(c + 1)**2/5
Let b(q) be the second derivative of q**5/40 + q**4/2 + 7*q**3/4 + 5*q**2/2 - 20*q. Determine j so that b(j) = 0.
-10, -1
Let y(k) be the third derivative of k**6/200 + k**5/100 - k**4/20 + 3*k**2. Factor y(u).
3*u*(u - 1)*(u + 2)/5
Let o(p) = -p**2 - 5*p + 6. Let z be o(-6). Suppose 7*y - 9*y = z. Factor 2/5*r**5 + y*r**3 - 4/5*r**4 - 2/5*r + 4/5*r**2 + 0.
2*r*(r - 1)**3*(r + 1)/5
Let x be (-5)/4 + (-84)/(-56). What is y in 1/2*y**3 - x + 1/4*y**4 - 1/2*y + 0*y**2 = 0?
-1, 1
Suppose -3*l - l = -92. Let h = 47/2 - l. Let h*q**2 + 0 + q = 0. What is q?
-2, 0
Let l(k) be the third derivative of -k**7/8820 + k**6/2520 - k**4/6 - 4*k**2. Let r(o) be the second derivative of l(o). Factor r(i).
-2*i*(i - 1)/7
Let t(j) = 4*j**2 + 3*j + 2. Let d be t(10). Let w be (1 - 7)*(-16)/d. Let 0 + 2/9*q**3 + w*q - 4/9*q**2 = 0. What is q?
0, 1
Factor 1/2*w**3 - 1/6*w**4 + 0 + 1/6*w - 1/2*w**2.
-w*(w - 1)**3/6
Let d(q) be the first derivative of 3*q**4/14 - 22*q**3/21 + 6*q**2/7 - 41. Suppose d(f) = 0. Calculate f.
0, 2/3, 3
Let j(x) be the first derivative of 1/5*x**5 + 0*x - 1/12*x**2 - 2/9*x**3 - 4 - 1/24*x**4. Find t,