4*c + 15. Let n(k) = -8*k**3 + 832*k**2 + 1672*k - 2. Let i(j) = -15*n(j) - 2*s(j). Factor i(v).
4*v*(v - 209)*(v + 2)
Let p(k) be the first derivative of k**6/90 + k**5/30 + 8*k**3 - 41. Let n(g) be the third derivative of p(g). Determine r, given that n(r) = 0.
-1, 0
Let x(s) be the third derivative of s**5/180 + 113*s**4/72 + 15*s**2 - 5. Factor x(c).
c*(c + 113)/3
Let w = 24631 + -24629. Factor -2/7*m**5 + 32/7*m + 0*m**3 + 0 + 8/7*m**4 - 32/7*m**w.
-2*m*(m - 2)**3*(m + 2)/7
Let g(y) = -15*y**3 + 186*y**2 - 376*y + 226. Let s(u) = 13*u**3 - 186*u**2 + 375*u - 220. Let p(q) = -6*g(q) - 7*s(q). Let p(l) = 0. What is l?
1, 184
What is s in 498*s**2 + 326/3*s**3 + 0 - 1404*s - 2/3*s**5 - 2*s**4 = 0?
-9, 0, 2, 13
Let y(m) be the third derivative of 0*m + 9/4*m**4 - 1 - 81*m**3 + 17*m**2 - 1/40*m**5. Determine o so that y(o) = 0.
18
Let j = 26 - 22. Solve -4*y**4 - 3*y**2 + 7*y**2 - 4*y**3 + 0*y**4 + j*y**2 = 0 for y.
-2, 0, 1
Let -59*t**2 + 35*t**2 - 652*t + 26*t**2 + 53138 = 0. Calculate t.
163
Let f(h) = -h**3 + h**2 + 11*h - 10. Let r be f(-4). Factor -8*u - 15*u - 86*u**2 - 42*u**3 + r*u**4 - 6*u**3 + 11*u.
2*u*(u - 3)*(u + 1)*(13*u + 2)
Let d(l) = l**3 + 16*l**2 - 17*l + 14. Let s be d(-17). Let -s*v**3 + 6*v**4 + 8*v**5 - 19*v**4 + 8*v**4 - 4*v**2 + 15*v**4 = 0. What is v?
-2, -1/4, 0, 1
Let c(g) be the first derivative of 65/6*g**3 + 5/8*g**4 - 30*g - 5/4*g**2 - 1/2*g**5 + 100. Suppose c(v) = 0. What is v?
-3, -1, 1, 4
Factor -7*n**2 + 16/5 + 62/5*n.
-(n - 2)*(35*n + 8)/5
Factor -22/5*t + 12 + 2/5*t**2.
2*(t - 6)*(t - 5)/5
Let w(l) be the first derivative of -l**4 - 28*l**3/3 + 36*l**2 + 10566. Factor w(f).
-4*f*(f - 2)*(f + 9)
Let s(j) be the third derivative of -j**5/60 - j**4/24 - 13*j**2 - j. Let r(z) = 4*z**2 - 53*z - 841. Let p(o) = 2*r(o) + 10*s(o). Solve p(f) = 0.
-29
Let l(n) be the first derivative of n**9/1512 - n**7/210 + n**5/60 + 2*n**3 - 3*n - 179. Let v(r) be the third derivative of l(r). Find c such that v(c) = 0.
-1, 0, 1
Let v(d) = 95*d**2 - 161*d + 4. Let o(i) = -119*i**2 + 162*i - 5. Let l(q) = -4*o(q) - 5*v(q). Determine x, given that l(x) = 0.
-157, 0
Let c = 30 - 28. Find n, given that -16*n**c - 18 + 3*n**3 + 20*n**2 + 3*n + 8*n**2 + 0*n**3 = 0.
-3, -2, 1
Let m be ((-4 - -8) + 3 + 248/(-32))/((-105)/70). Factor -m*u**3 + 7*u**2 + 0 - 49/2*u.
-u*(u - 7)**2/2
Let w(z) = 12*z**2 + 40*z - 26. Let c = 12 - 6. Let s(f) = 12*f**2 + 40*f - 27. Let u(o) = c*s(o) - 5*w(o). Factor u(t).
4*(t + 4)*(3*t - 2)
Let p(v) be the second derivative of v**4/48 + 183*v**3/8 + 137*v**2/2 + v + 1394. Factor p(y).
(y + 1)*(y + 548)/4
Let w be 374/561 + -82*1/150. Let q(r) be the second derivative of 14/5*r**2 - 7/15*r**4 + 25*r + 0 + 2/5*r**3 - w*r**5. Let q(y) = 0. What is y?
-7/3, -1, 1
Let z(b) be the third derivative of 5*b**8/336 + b**7/42 - 11*b**6/12 + 11*b**5/3 - 5*b**4 - 12*b**2 + 9. Factor z(w).
5*w*(w - 2)**2*(w - 1)*(w + 6)
Let d be 3/((-9)/(-300)) - (8 + -8). Factor 387*j + j**3 - 2*j - d*j**2 + 1210 + j**3 + 3*j**3.
5*(j - 11)**2*(j + 2)
Let a = -55 + 35. Let k be ((-9)/5)/(6/a). Find q such that 0*q**2 + 3*q**4 + 4*q**2 - k*q**4 - q**4 = 0.
-1, 0, 1
Suppose -2702/5*v + 1352/5 + 1348/5*v**2 + 2/5*v**3 = 0. What is v?
-676, 1
Let n(s) be the second derivative of -5*s**7/112 + 33*s**6/80 - 33*s**5/32 - 21*s**4/32 + 9*s**3/2 - 113*s - 4. Let n(c) = 0. Calculate c.
-1, 0, 8/5, 3
Let z(l) = 6*l**2 - 233*l - 56. Let x(m) = -m**2 + 6*m + 2. Let u(t) = -57*x(t) - 3*z(t). Factor u(b).
3*(b + 9)*(13*b + 2)
Let t(q) be the second derivative of 1/50*q**5 - 60*q - 1/75*q**6 + 0 + 2/5*q**2 + 1/10*q**4 - 1/3*q**3. Find y such that t(y) = 0.
-2, 1
Let h(b) = -2*b**2 + 732*b + 82085. Let i be h(-90). Factor 6/5*k**i + 6*k**4 + 0 + 0*k + 0*k**2 - 36/5*k**3.
6*k**3*(k - 1)*(k + 6)/5
Suppose -2224 = -458*p - 334*p + 236*p. Let n = 1/10 - -7/5. Find u, given that 0*u + n*u**2 + 1/4*u**3 + 1/4*u**5 - u**p + 0 = 0.
-1, 0, 2, 3
Let l(q) = q**3 + 14*q**2 - 2*q - 10. Let n be l(-14). Factor -10 - 4*u**2 - 41*u - 5*u + n*u + 42.
-4*(u - 1)*(u + 8)
Let a(j) be the second derivative of -j**5/4 - 385*j**4 - 354195*j**3/2 + 1071845*j**2 - 204*j - 3. Factor a(p).
-5*(p - 2)*(p + 463)**2
Let c be ((-26)/897)/(4/6). Let n = c - -95/69. Factor -n - 1/3*g**2 + 4/3*g.
-(g - 2)**2/3
Let w = -72 - -73. Let z(j) = j**3 - j**2 - j + 1. Let o(n) = 16*n**4 + 91*n**3 + 134*n**2 + 50*n + 9. Let l(y) = w*o(y) - 3*z(y). Solve l(x) = 0.
-3, -2, -1/4
Factor 3240/7*u - 2/7*u**4 - 5832/7 - 60/7*u**3 - 234/7*u**2.
-2*(u - 3)**2*(u + 18)**2/7
Suppose -u - 2483 = -8587. Factor -15*k**2 + 6104*k + 95*k**3 - 30*k**3 - u*k.
5*k**2*(13*k - 3)
Let y = -10528 + 105283/10. Let v(q) be the second derivative of 2/3*q**3 - 3/4*q**4 - 1/30*q**6 + 0 + 9*q + 0*q**2 + y*q**5. Factor v(m).
-m*(m - 4)*(m - 1)**2
Let x(g) be the first derivative of -1/27*g**3 + 1/18*g**2 + 61 + 2/9*g. Factor x(z).
-(z - 2)*(z + 1)/9
Let x(y) be the third derivative of 32 + 0*y + 1/120*y**6 - 2/3*y**3 + 2*y**2 + 1/60*y**5 - 1/6*y**4. Factor x(a).
(a - 2)*(a + 1)*(a + 2)
Let r(g) be the third derivative of 1/48*g**4 + 26*g**2 + 1/1680*g**7 + 0 + 0*g + 1/160*g**5 - 1/240*g**6 - 1/12*g**3. Suppose r(f) = 0. What is f?
-1, 1, 2
Let y(q) be the third derivative of -q**8/1680 + 61*q**7/1680 - q**6/16 + 47*q**5/60 - 20*q**2. Let s(p) be the third derivative of y(p). Solve s(v) = 0 for v.
1/4, 15
Let k = -28 - -839/30. Let w = 27/10 + k. Factor 1/3*t**2 + 4/3 - t**3 + w*t.
-(t - 2)*(t + 1)*(3*t + 2)/3
Let v(x) = -x**3 + 14*x**2 - 11*x - 23. Let r(l) = -l. Let h be r(-13). Let g be v(h). Solve 5*t**g - 3*t**3 - 8*t**2 + 3*t + 3*t = 0 for t.
0, 1, 3
Let z = -254 - -259. Let -8*q**3 - 15*q**2 + 13*q**2 + 4*q**z + 2*q**2 + 4*q**4 = 0. What is q?
-2, 0, 1
Factor 200*b - 536*b + 161*b + b**2 + 0*b**2 + 4*b**2.
5*b*(b - 35)
Let s(h) = -64*h**3 - 5*h**2 - 5*h - 1. Let x be s(-1). Let y be (2/6)/(x/27). Let y*w**2 + 0*w - 1/7 = 0. Calculate w.
-1, 1
Suppose -i - 3*i + 8 = 0. Suppose -10 = -h + 4*r, i*h - 4*r - 2 = -5*r. Factor 32 - 132 + 7*f**h - 11*f**2 + 40*f.
-4*(f - 5)**2
Solve 14/3*f - 44/9 + 2/9*f**2 = 0 for f.
-22, 1
Let f = -5648 + 5653. Factor 10/9*i**4 - 20/9*i**3 - 2/9*i**f + 2/9 - 10/9*i + 20/9*i**2.
-2*(i - 1)**5/9
Suppose -89*w - 26 = -91*w. Determine m so that -97*m**3 + 20*m + w*m**4 + 27*m**2 - m**3 - 4 + 13*m**4 + 29*m**4 = 0.
-2/5, 2/11, 1
Let m(c) be the third derivative of -c**6/300 + 13*c**5/6 - 647*c**4/60 + 323*c**3/15 + 636*c**2 + c. Find r, given that m(r) = 0.
1, 323
Let d(o) be the third derivative of 0 + 23/120*o**6 + 35/8*o**4 - 1/140*o**7 - 49/12*o**3 + 0*o - 17/10*o**5 - 86*o**2. Suppose d(p) = 0. What is p?
1/3, 1, 7
Factor 264/7*n - 3/7*n**2 - 5808/7.
-3*(n - 44)**2/7
Let f(n) be the second derivative of -n**5/75 + n**4/10 + 8*n**3/15 - 4*n**2 + 62*n. Let i(o) be the first derivative of f(o). Factor i(h).
-4*(h - 4)*(h + 1)/5
Suppose -1 - 8 = 9*a. Let v be -4 + a + 8 + 3. Factor 3*h**2 + 10 - 15*h + v*h**2 - 4*h**2.
5*(h - 2)*(h - 1)
Let m = 477483 + -477481. Solve -8/3*a**3 + 28/3*a**2 - m*a**4 - 8/3*a - 2 = 0.
-3, -1/3, 1
Let p(n) be the first derivative of -2*n**5/75 - n**4/3 - 14*n**3/9 - 10*n**2/3 - 16*n/5 - 5307. Find y, given that p(y) = 0.
-4, -3, -2, -1
Factor 0*i + 2/3*i**4 - 1/12*i**5 + 0*i**2 + 0 + 0*i**3.
-i**4*(i - 8)/12
Let o(v) be the first derivative of -v**7/30 - 19*v**6/90 + v**5/5 + 178*v**3/3 - 147. Let m(s) be the third derivative of o(s). Suppose m(j) = 0. Calculate j.
-3, 0, 2/7
Let o(a) be the first derivative of -4*a**3/3 - 104*a**2 - 2688*a - 8970. Factor o(v).
-4*(v + 24)*(v + 28)
Let f = 9234 + -9232. Let a(i) be the second derivative of 28*i + 1/2*i**4 - 27/20*i**5 + 0 + 0*i**f + 0*i**3 + 7/10*i**6. Factor a(t).
3*t**2*(t - 1)*(7*t - 2)
Let t(j) = j**3 + 13*j**2 + 63*j + 455. Let a be t(-11). Let m(u) be the second derivative of -26/33*u**3 + 7/66*u**a + 0 - 8/11*u**2 - 9*u. Factor m(h).
2*(h - 4)*(7*h + 2)/11
Let n = -53 + 55. Let u be 0 + (-9)/(-24) + (-1)/(-40). Suppose 2/5 + u*c**n + 4/5*c = 0. Calculate c.
-1
Let l(g) be the first derivative of -2*g**3/11 - 6027*g**2/11 + 12060*g/11 - 5094. Determine x so that l(x) = 0.
-2010, 1
Suppose 0 = 45*c - 9*c - 2628. Factor 55*n**2 + 21 + c*n - 58*n - 61*n**2.
-3*(n + 1)*(2*n - 7)
Let d(j) be the second derivativ