ind c, given that 11*c**2 - 13*c**3 - w*c + 11*c**3 + 7*c**2 + 54 = 0.
3
Let k(a) be the third derivative of -a**8/672 - 3*a**7/140 + a**6/120 + 3*a**5/20 - a**4/48 - 3*a**3/4 + 344*a**2. What is h in k(h) = 0?
-9, -1, 1
Let x(k) = -12*k**4 + 12*k**2 + 9. Let g(c) = -c**4 + c**2 + 1. Let q be (-6 - (1 - 4)) + 2. Let h(f) = q*x(f) + 9*g(f). Factor h(v).
3*v**2*(v - 1)*(v + 1)
Solve 4/3*m**2 - 368/3 + 176/3*m = 0 for m.
-46, 2
Let d(m) be the first derivative of m**6/420 - 3*m**5/140 + m**4/14 + m**3/3 - 13. Let k(g) be the third derivative of d(g). Factor k(a).
6*(a - 2)*(a - 1)/7
Let t(h) be the third derivative of 1/21*h**3 + 1/42*h**5 + 1/14*h**4 + 0*h + 0 + 10*h**2. Factor t(f).
2*(f + 1)*(5*f + 1)/7
Suppose -w - 3*w = 5*k + 102, -5*k - 84 = -2*w. Let u be k/(-12)*(-60)/(-18). Factor -16/7*o**2 + 64/7*o**u + 0*o - 32*o**4 - 124/7*o**3 + 0.
4*o**2*(o - 4)*(4*o + 1)**2/7
Let l(k) be the second derivative of k**6/72 - k**5/12 - 5*k**4/8 - 5*k**3/2 - 5*k. Let g(j) be the second derivative of l(j). Find i such that g(i) = 0.
-1, 3
Let q(x) be the second derivative of x**5/20 + x**4/12 - 35*x. Let b(m) = 4*m**3 + 14*m**2 - 20*m. Let z(f) = -b(f) - q(f). Determine r, given that z(r) = 0.
-4, 0, 1
Let k(z) = 19*z**3 + 2. Let l be k(0). What is t in 8/3 - 2/3*t**5 - 16/3*t - 2/3*t**4 + 2/3*t**l + 10/3*t**3 = 0?
-2, 1
Factor -6*a**2 - 27/2 + 18*a.
-3*(2*a - 3)**2/2
Let h(n) be the first derivative of -5*n**3/3 + 350*n**2 - 24500*n + 190. Factor h(u).
-5*(u - 70)**2
Let a(g) be the first derivative of 1/2*g**3 - 1/2*g**2 - 32 + 0*g - 1/8*g**4. Suppose a(s) = 0. What is s?
0, 1, 2
Let k(r) be the second derivative of r**5/60 - 7*r**4/72 + 7*r**3/36 - r**2/6 - 191*r. Factor k(w).
(w - 2)*(w - 1)*(2*w - 1)/6
Let g be (-6)/(-10)*(3 - -2). Let q(l) = l**3 + 4*l**2 - 3*l. Let u be q(-4). Factor 10*x**2 + g*x**2 - u*x**2 + 2*x**2.
3*x**2
Suppose 20*g**2 + 5*g**3 + 2041*g**4 - 2046*g**4 - 9*g + 3*g - 14*g = 0. What is g?
-2, 0, 1, 2
Let o be 63/(-45) + 4/10. Let x be (o/2)/(7/(-28)). Factor -4*f + 0 + 4*f**2 - 2 - 6*f**x.
-2*(f + 1)**2
Let r(d) be the first derivative of 2/9*d**2 + 1/2*d**4 + 0*d + 1/27*d**6 + 2/9*d**5 + 10 + 14/27*d**3. Factor r(p).
2*p*(p + 1)**3*(p + 2)/9
Let x(f) be the second derivative of 0*f**2 + 5/3*f**3 + 0 - 2/15*f**6 - 11/10*f**5 - 22*f - 2/3*f**4. Suppose x(z) = 0. What is z?
-5, -1, 0, 1/2
Suppose -119*k - 24 = -123*k. Let o be 3 + (-1 - (-9)/k)*-6. Suppose 1/6 - 1/6*j**2 + o*j = 0. Calculate j.
-1, 1
Suppose 1/3*h**4 + h**2 + 0 - h**3 - 1/3*h = 0. What is h?
0, 1
Let s(j) be the second derivative of 4*j**7/147 + 2*j**6/21 - j**5/35 - j**4/3 - 2*j**3/21 + 4*j**2/7 + j - 12. Determine r, given that s(r) = 0.
-2, -1, 1/2, 1
Let f = 4197 - 146908/35. Let q = 17/35 - f. Solve -6*z**3 + q*z - 40/7*z**2 + 4/7 = 0 for z.
-1, -2/7, 1/3
Suppose 0*z + 0 - 1/6*z**5 - 211/6*z**3 - 107/6*z**4 - 35/2*z**2 = 0. Calculate z.
-105, -1, 0
Let j(g) be the first derivative of -3/16*g**4 - 5/12*g**3 - 1/4*g**2 + 1/24*g**6 + 1/20*g**5 + 0*g - 6. Factor j(s).
s*(s - 2)*(s + 1)**3/4
Let h(v) = 14*v**3 + 4*v**2 - 58*v + 144. Let l(d) = -12*d**3 - d**2 + 57*d - 144. Let o(f) = -5*h(f) - 6*l(f). Factor o(k).
2*(k - 9)*(k - 2)*(k + 4)
Let l(s) = -s**2 - 24*s - 87. Let m(i) = -2*i + 4. Let n(h) = 3*h - 5. Let x(k) = -4*m(k) - 3*n(k). Let u(b) = l(b) - 6*x(b). Factor u(c).
-(c + 9)**2
Let h(k) be the third derivative of k**8/13440 - k**6/480 - k**5/4 + 6*k**2. Let a(s) be the third derivative of h(s). Factor a(j).
3*(j - 1)*(j + 1)/2
Let z = 3377 + -3377. Find g, given that -g**2 - 3/2*g + z = 0.
-3/2, 0
Let w(x) be the third derivative of -x**6/24 - 5*x**5/12 + 5*x**4/4 + 17*x**2 + 12. Determine d, given that w(d) = 0.
-6, 0, 1
Let a(m) be the third derivative of -m**10/1360800 + m**8/60480 + m**7/22680 - m**5/60 - 4*m**2. Let i(j) be the third derivative of a(j). Factor i(o).
-o*(o - 2)*(o + 1)**2/9
Let r(v) = 4*v + 51. Let u be r(-12). Suppose 8/11*h + 6/11*h**4 - 10/11*h**u - 6/11*h**2 + 2/11*h**5 + 0 = 0. What is h?
-4, -1, 0, 1
Let p(q) be the first derivative of -q**6/1620 - q**5/540 + q**4/54 + 14*q**3/3 - 8. Let d(b) be the third derivative of p(b). Solve d(t) = 0 for t.
-2, 1
Factor 9*m**3 + 28 + 182*m**2 - 35*m**3 - 144*m + m**3 + 13*m**2.
-(m - 7)*(5*m - 2)**2
Let 17/4*n**3 - 5*n + 11/4*n**4 - 1/2*n**2 - 2 + 1/2*n**5 = 0. Calculate n.
-2, -1/2, 1
Let m(s) be the first derivative of -s**4/28 + 2*s**3/21 + 5*s**2/14 - 6*s/7 + 93. Let m(v) = 0. Calculate v.
-2, 1, 3
Determine r so that 0*r**3 + 0*r + 0*r**2 - 1/4*r**4 + 0 + 1/4*r**5 = 0.
0, 1
Let c(d) be the second derivative of 0*d**3 - 9/98*d**7 + 0 - 8/35*d**6 - 3/28*d**5 + 19*d + 1/14*d**4 + 0*d**2. Solve c(v) = 0.
-1, 0, 2/9
Suppose -5*y - 2*h + 6 = -0*h, -3*y = 2*h - 2. Determine m, given that -9 - 103*m**y + 104*m**2 + 7 - m = 0.
-1, 2
Let i = -1561 - -1563. Let -2/13*h**i - 4/13*h + 0 = 0. What is h?
-2, 0
Let t be (-10 - 111/(-12))*16/(-18). Let 2/3*m**4 + 2/3*m**3 - 2/3*m**2 - t*m + 0 = 0. What is m?
-1, 0, 1
Let l be 2/(9 - 136/16). Let h(o) be the second derivative of -1/165*o**6 + 0*o**l + 4/33*o**3 + 0 + 4*o - 3/110*o**5 + 0*o**2. Factor h(t).
-2*t*(t - 1)*(t + 2)**2/11
Suppose 8 = -60*t + 64*t. Let f = -6 - -8. Determine l so that 2*l + l**f - 2*l**2 + t*l**2 = 0.
-2, 0
Let q(x) = 3*x**2 + 29*x - 4*x**2 + 2 - 26*x. Let d be q(3). Find g, given that 9*g**4 + 3*g**3 - 8*g**d + 2*g**2 + 0*g**4 = 0.
-1, 0, 2/3
Let s(y) be the third derivative of 0 - 1/280*y**7 - 5*y**2 + 1/32*y**4 + 0*y**3 + 3/160*y**6 + y - 3/80*y**5. Factor s(k).
-3*k*(k - 1)**3/4
Let z(k) be the second derivative of k**7/14 - 3*k**6/10 - 3*k**5/5 + 3*k**4 - 16*k - 13. Find l such that z(l) = 0.
-2, 0, 2, 3
Factor 14*u**2 - 18*u**2 + 392 + 6*u**2 + 56*u.
2*(u + 14)**2
Let i(h) be the second derivative of -h**6/2 - 9*h**5/10 + 13*h**4/4 + 3*h**3 - 12*h**2 - 590*h. Find v such that i(v) = 0.
-2, -1, 4/5, 1
Find y such that 4/5*y + 6/5*y**2 - 6/5*y**4 - 2/5*y**3 + 0 - 2/5*y**5 = 0.
-2, -1, 0, 1
Suppose -3*m + 9 = 9. Let w(s) be the first derivative of 12 + m*s**2 + 0*s**3 + 0*s + 3/5*s**5 + 0*s**4. Factor w(k).
3*k**4
Let g(v) be the third derivative of 0 - 1/36*v**4 + v**2 - 1/18*v**3 + 0*v - 1/180*v**5. What is z in g(z) = 0?
-1
Suppose -29223 = 14*r - 29251. Factor -3/4*p - 1/2 - 1/4*p**r.
-(p + 1)*(p + 2)/4
Let g(u) be the third derivative of 0*u**3 + 0 - 40*u**2 + 1/30*u**6 - 1/3*u**4 + 1/15*u**5 + 0*u. Factor g(y).
4*y*(y - 1)*(y + 2)
Suppose 3*m = -17*m + 80. Suppose -12*x = -m*x - 16. Suppose -2/3*t**x - 2/3*t + 4/3 = 0. What is t?
-2, 1
Let v be 207/115*(-20)/(-3). Let i be (-16)/(-12)*54/v. Suppose -4*m**3 + 0*m - 2/3*m**4 - i*m**2 + 0 = 0. Calculate m.
-3, 0
Let b(f) be the third derivative of 18*f**2 + 27/16*f**8 - 49/30*f**5 + 11/6*f**4 + 4/3*f**3 + 0 + 3/7*f**7 - 611/120*f**6 + 0*f. Solve b(a) = 0.
-1, -2/9, 2/7, 1
Suppose -5*f + 2*t + 63 = 67, 0 = 2*f + 5*t - 39. Factor -24/7 + 54/7*m + 51/7*m**f + 9/7*m**3.
3*(m + 2)*(m + 4)*(3*m - 1)/7
Factor -32/5 + 0*v - 1/5*v**3 + 6/5*v**2.
-(v - 4)**2*(v + 2)/5
Let g(a) be the first derivative of -a**3 - 96*a**2 - 3072*a + 94. Factor g(d).
-3*(d + 32)**2
Let p(h) be the second derivative of h**4/12 + h**3/6 + 5*h**2 - h. Let m(l) = 5 + 0 + 2 + 2. Let f(w) = 4*m(w) - 3*p(w). Solve f(v) = 0 for v.
-2, 1
Let w(i) be the second derivative of -961*i**5/4 + 1705*i**4/4 - 105*i**3/2 + 5*i**2/2 - 65*i. Solve w(k) = 0.
1/31, 1
Suppose 0 = 4*z + 8*z - 396. Suppose -z = -34*l + 35. Solve -16/3*i + 8/3*i**3 + 4*i**l - 4/3*i**4 - 16/3 = 0 for i.
-1, 2
Let h(l) be the first derivative of l**6/600 + l**5/40 + 3*l**4/20 + 6*l**3 + 4. Let g(a) be the third derivative of h(a). Factor g(q).
3*(q + 2)*(q + 3)/5
Let n(s) = -s**2 - 2. Let i(r) = -5*r**3 - 56*r**2 - 45*r - 12. Let q(a) = i(a) - 6*n(a). Factor q(o).
-5*o*(o + 1)*(o + 9)
Let k be (3/(-18))/1 + 2387/30. Let y = -79 + k. Suppose 4/5 - 2/5*h**3 + 2/5*h**4 - 6/5*h**2 + y*h = 0. What is h?
-1, 1, 2
Let n(b) = -6*b**4 - b**3 - 6*b**2. Let s(j) = j**4 + j**2. Let x be (-4)/(-6) + ((-240)/9 - -4). Let f(p) = x*s(p) - 4*n(p). Factor f(w).
2*w**2*(w + 1)**2
Suppose -k - 3*r - 13 = -8*r, 0 = -2*k + 5*r - 11. Let i be (-55)/(-45) - (k - 21/9). Let 8/9*m**3 + i*m**2 + 0 - 4/9*m = 0. Calculate m.
-2, 0, 1/4
Let c(i) be the third derivat