 m(k).
-5*(k + 17)*(5*k - 2)
Let y(x) be the second derivative of 15*x**2 + 15/4*x**4 - 27/2*x**3 - 3/10*x**5 - 5 - 10*x. Suppose y(d) = 0. What is d?
1/2, 2, 5
Let w(x) = 10*x**2 + 94*x - 38. Let d be w(-11). Suppose -119*j + 73*j + d = 0. Factor 0 + 0*o**j - 2*o**4 + 2/3*o**5 + 8/3*o**2 + 0*o.
2*o**2*(o - 2)**2*(o + 1)/3
Let o(w) = 51*w + 818. Let g be o(-16). Let m(x) be the first derivative of 8 - 5/3*x**g - 4/3*x + 2/3*x**3. Suppose m(t) = 0. Calculate t.
-1/3, 2
Let y = -2176 - -2180. Let o(s) be the third derivative of 1/20*s**5 - 1/40*s**6 + 5*s**2 + 0*s - 1/2*s**3 + 1/8*s**y + 0. Factor o(j).
-3*(j - 1)**2*(j + 1)
Factor 271441 - 521*d + 1/4*d**2.
(d - 1042)**2/4
Suppose 0 = -n - c - 15, -15 = n - 0*n + 3*c. Let a = 15 + n. Factor 2*q**5 + 0*q**3 + 0*q**5 + a*q**3 - 2*q**3.
2*q**3*(q - 1)*(q + 1)
Factor 2/13*d**3 - 8/13*d - 4/13*d**2 + 16/13.
2*(d - 2)**2*(d + 2)/13
Let o(r) = r**4 - 104*r**3 - 299*r**2 - 189*r. Let l(w) = 2*w**4 - 260*w**3 - 746*w**2 - 472*w. Let a(k) = 5*l(k) - 12*o(k). Factor a(t).
-2*t*(t + 1)*(t + 2)*(t + 23)
Let a(d) be the second derivative of d**6/960 + d**5/160 - d**4/32 - d**3/6 - 27*d**2 - 154*d. Let r(o) be the first derivative of a(o). Solve r(j) = 0.
-4, -1, 2
Let w = -33 - -37. Suppose 35 = -29*n + 122. Factor 0 - 1/5*r**2 + 1/5*r**w + 2/5*r - 2/5*r**n.
r*(r - 2)*(r - 1)*(r + 1)/5
Let v be 0/(-4 - -8) - -2. Suppose 10 + 27*h**v + 16*h**3 + 6 - 4 - 72*h + 17*h**3 = 0. What is h?
-2, 2/11, 1
Suppose j = b - 12, j = -6*b + 11*b - 48. Determine m, given that b*m**2 + 68*m + 31*m**2 - 8 + 23*m**3 - 59*m**3 = 0.
-1, 1/9, 2
Let s = -71 + 75. Solve -q**5 + 3421*q**4 + s*q**3 + 8*q**2 - 3*q**3 - 10 - 3419*q**4 + 13*q**3 - 13*q = 0 for q.
-2, -1, 1, 5
Factor 21/4*c**3 + 81096*c + 23064 + 2607/2*c**2.
3*(c + 124)**2*(7*c + 2)/4
Suppose -5*b + 23 = -2*q, -3*b + 29 = -3*q + 8. Factor -16*d + 0*d**b - 16*d**2 + 4*d**5 + 14*d**3 - 2*d**3 + 18*d**4 - 2*d**4.
4*d*(d - 1)*(d + 1)*(d + 2)**2
Factor 76/3*g**2 - 80/3*g + 0 + 8/3*g**3 - 4/3*g**4.
-4*g*(g - 5)*(g - 1)*(g + 4)/3
Suppose 0 = 76*x - 161 - 143. Suppose -5*c = -5*r + 25, 9 + 6 = 3*c + 3*r. What is i in -85*i**4 + 89*i**4 + 0 + c - x*i**2 = 0?
-1, 0, 1
Let x(z) = -6*z. Let l(o) = -o**2 - 7*o - 1. Suppose 11 - 5 = -2*m. Let a(g) = m*x(g) + 4*l(g). Factor a(h).
-2*(h + 2)*(2*h + 1)
Factor -269*a - 1/2*a**2 - 72361/2.
-(a + 269)**2/2
Let z(p) be the second derivative of -25*p**7/84 - 13*p**6/4 + 7*p**5/5 + 11*p**4/2 + 8*p**3/3 - 6174*p. Suppose z(l) = 0. What is l?
-8, -2/5, 0, 1
Let r(w) be the third derivative of w**6/40 + 123*w**5/10 - 3591*w**4/8 + 6370*w**3 - 54*w**2 + 132*w. Factor r(o).
3*(o - 7)**2*(o + 260)
Let o(p) be the first derivative of 2*p**6/3 + 12*p**5/5 - 4*p**4 - 611. Let o(q) = 0. What is q?
-4, 0, 1
Let c(y) be the second derivative of 5*y**4/4 + 87*y**3/16 + 81*y**2/16 + 1036*y. Find s such that c(s) = 0.
-9/5, -3/8
Let v(p) be the second derivative of p**7/630 - p**6/18 + 3*p**5/10 - 7*p**4/12 - 2*p**2 + 7*p - 3. Let b(j) be the third derivative of v(j). Factor b(c).
4*(c - 9)*(c - 1)
Let v(i) = -3*i**5 + 7*i**4 - 14*i**3 + 17*i**2 - 10*i + 3. Let o(u) = u**2 + 358*u**5 + 1 - 360*u**5 + 2*u**4 - u**4 - u. Let h(a) = o(a) - v(a). Factor h(c).
(c - 2)*(c - 1)**4
Let i(b) be the second derivative of 0*b**6 - 4 - 1/147*b**7 - 4/21*b**3 - b + 0*b**2 + 0*b**4 + 1/14*b**5. Find a such that i(a) = 0.
-2, -1, 0, 1, 2
Factor -1048/3*l - 2/3*l**2 + 5290/3.
-2*(l - 5)*(l + 529)/3
Suppose -27*b = 4*b - 2356. Find f, given that 579*f**3 - 290*f**3 - 722*f + b*f**2 - 291*f**3 = 0.
0, 19
Let s(p) = -2*p**2 - 4*p + 47. Let y be s(-6). Let x be ((-108)/168)/(1/(2/y)). Suppose x*g - 3/7*g**3 + 6/7*g**2 + 0 = 0. What is g?
-1, 0, 3
Let h(w) be the first derivative of w**6/21 + 4*w**5/7 - 39*w**4/14 + 8*w**3/21 + 52*w**2/7 + 1755. Determine t so that h(t) = 0.
-13, -1, 0, 2
Let c(b) be the second derivative of -8*b - 1/378*b**7 + 1/54*b**4 + 1/90*b**5 - 1/18*b**2 + 0 - 1/270*b**6 - 1/54*b**3. Solve c(q) = 0 for q.
-1, 1
Let v be 1/(-3) + 40420/516. Suppose -40*b - 78 = -v. Factor 0*j + 0 + b*j**3 + 1/6*j**2 - 1/6*j**4.
-j**2*(j - 1)*(j + 1)/6
Suppose 0 = 9*d + 58 - 202. Let c(i) be the second derivative of 0*i**2 + 1/60*i**4 - 1/100*i**5 - d*i + 0*i**3 + 0. Solve c(p) = 0 for p.
0, 1
Let w(k) = 3*k**3 - 6*k**2 + 3906*k + 4058. Let v(s) = -2*s**3 - 4*s**2 - 1952*s - 2028. Let n(y) = 11*v(y) + 6*w(y). Suppose n(l) = 0. What is l?
-34, -1, 15
Suppose -8*h = -6 - 10. Let f(y) = 62*y - 126 + 14*y - 21 - 12*y**h. Let j(v) = -4*v**2 + 25*v - 49. Let x(n) = 3*f(n) - 8*j(n). Determine c so that x(c) = 0.
7/2
What is b in 789*b**3 + 37851/5*b + 62967/5*b**2 + 5766/5 + 63/5*b**4 = 0?
-31, -1/3, -2/7
Let j be (-1558)/120 - (-101 + 88). Let a(z) be the third derivative of -1/210*z**7 + 0*z**4 + 0 + 0*z**3 - 11*z**2 + 1/60*z**6 - j*z**5 + 0*z. Solve a(k) = 0.
0, 1
Factor -295/2 - 1/4*d**2 + 123/4*d.
-(d - 118)*(d - 5)/4
Let w(c) = c**3 - 4*c**2 - c + 5. Suppose -4 = -23*m + 22*m. Let q be w(m). Find f, given that 4*f**2 - q - 6 - 4*f + 7 = 0.
0, 1
Let d be 24/(-324) + (26/(-12) - -2) + 5380/2160. Let 0 - d*b**3 - 3/4*b**4 + 1/4*b**5 + 0*b - 5/4*b**2 = 0. What is b?
-1, 0, 5
Let x = 162/583 + 50882/9911. Suppose 162/17 + x*l**2 + 2/17*l**4 - 32/17*l**3 + 288/17*l = 0. What is l?
-1, 9
Let i be 435024/(-399) + (0 - 2). Let j = i + 1094. Factor -24/7*r + 9/7*r**2 + j.
3*(r - 2)*(3*r - 2)/7
Let h(u) = -22*u**3 - 562*u**2 - 410*u + 10. Let s(w) = -2*w**3 - w**2 + 14*w + 1. Let o(k) = 2*h(k) - 20*s(k). Determine q so that o(q) = 0.
-275, -1, 0
Let h = -33 + 38. Suppose 120 = h*c - n - 69, 3*c - 131 = 5*n. Solve 0*p**2 - 10 - 4*p**2 + c*p - p**2 - 22*p = 0 for p.
1, 2
Let p(g) be the third derivative of 7/45*g**5 - 11/18*g**4 + 10/9*g**3 + 0 + 0*g - 1/90*g**6 + 23*g**2. Let p(c) = 0. Calculate c.
1, 5
Let d(w) = -116*w - 452. Let t be d(-4). What is f in 152*f**2 - 4/5*f**5 + 324/5 - 180*f - 24*f**3 - t*f**4 = 0?
-9, 1
Let w = -2 - -5. Suppose -4*b + 7 + 17 = 4*t, -5*b = -3*t - 6. Factor -30*j - 3*j**w + 5*j + 30*j**2 - 4*j**t + 2*j**3.
-5*j*(j - 5)*(j - 1)
Factor -8/5 + 8*z - 18/5*z**2.
-2*(z - 2)*(9*z - 2)/5
Let i(g) be the third derivative of -g**5/300 - g**4/120 - 4627*g**2. Suppose i(d) = 0. What is d?
-1, 0
Factor 621 + 101 - 589*g + 274*g + 55*g**2 + 678 - 495*g.
5*(g - 2)*(11*g - 140)
Determine d, given that 105 - 33*d**3 + 33*d - 64 + d**4 - 7 - 167*d**2 + 132*d**2 = 0.
-1, 1, 34
Suppose -u + 10*u = 9. Let s(h) be the first derivative of -3*h + 9 - 17*h**3 + 15*h**2 - 8*h**3 + u. Factor s(z).
-3*(5*z - 1)**2
Factor -536 + 4822/9*d + 2/9*d**2.
2*(d - 1)*(d + 2412)/9
Let -277/2*x + 84 - 5/2*x**2 = 0. Calculate x.
-56, 3/5
Let s(p) be the second derivative of -49/30*p**4 + 0*p**2 - 1/75*p**6 + 0 + 0*p**3 - 7/25*p**5 + 63*p. Factor s(d).
-2*d**2*(d + 7)**2/5
Suppose -2*k - 6 = -141*h + 142*h, -4*k = -3*h + 12. Suppose h - 12/5*n - 33/5*n**3 - 72/5*n**2 = 0. What is n?
-2, -2/11, 0
Factor -3/2*p**2 - 27*p + 57/2.
-3*(p - 1)*(p + 19)/2
Let g(w) be the third derivative of 1/240*w**5 + 61 - 1/12*w**4 + 2*w**2 + 0*w + 7/24*w**3. Solve g(o) = 0 for o.
1, 7
Suppose 0 = 13*g - 5 + 70. Let l be g/((-27)/(-12)*(-8)/6). Suppose 5/6*u**4 + 0 + l*u + 25/6*u**2 + 10/3*u**3 = 0. Calculate u.
-2, -1, 0
Let r(b) be the third derivative of b**6/540 - b**5/360 - b**4/72 + 5*b**3/3 - 39*b**2 - b. Let j(y) be the first derivative of r(y). What is x in j(x) = 0?
-1/2, 1
Let s(d) be the first derivative of d**6/27 - 8*d**5/45 + 20*d**3/27 - d**2/9 - 4*d/3 - 10806. What is w in s(w) = 0?
-1, 1, 2, 3
Let v be ((-51)/(-12) + -2)*(-3 + 23). Factor -35*m - 4*m**2 - v*m - m**2.
-5*m*(m + 16)
Solve -220/3 + 225*b**3 - 120*b + 135*b**2 = 0.
-2/3, 11/15
Let h(a) be the third derivative of -a**6/60 - 449*a**5/10 - 201601*a**4/4 - 90518849*a**3/3 + 700*a**2. Find u such that h(u) = 0.
-449
Let i(v) be the second derivative of v**5/15 - 29*v**4/6 + v**2/2 + 116*v. Let h(y) be the first derivative of i(y). Factor h(c).
4*c*(c - 29)
Let u(p) = -p**3 - 8*p**2 - 15*p - 13. Let i be u(-6). What is s in 5*s**2 + 16 + 9*s**4 - 4*s - 47*s**2 - 8*s**3 + i*s**4 = 0?
-1, 4/7, 2
Let t(u) be the second derivative of -u**7/420 + 29*u**6/300 - 67*u**5/50 + 34*u**4/5 - 48*u**3/5 - 4*u - 26. Let t(i) = 0. Calculate i.
0, 1, 4,