4*g**l - 5*g.
(g - 10)**2/4
Let x(v) be the third derivative of -4*v**2 + 77/30*v**5 - 4/15*v**6 - 49/6*v**4 - 12 + 0*v**3 + 0*v + 1/105*v**7. Factor x(p).
2*p*(p - 7)**2*(p - 2)
Let n(y) be the third derivative of -1/160*y**6 - 5*y**2 - 16 + 0*y + 9/2*y**3 + 5/8*y**4 - 17/80*y**5. Suppose n(t) = 0. What is t?
-18, -1, 2
Suppose -20 = 5*z, 102 = -14*p + 4*z + 146. Let d(q) be the third derivative of -1/24*q**6 + 0*q + 0 - 5/6*q**3 + 5/24*q**4 - 6*q**p + 1/12*q**5. Factor d(h).
-5*(h - 1)**2*(h + 1)
Find p, given that 260/7 - 1/7*p**2 + 128/7*p = 0.
-2, 130
Let q = 450 + 176. Let s = 626 - q. Determine r so that -3/4*r**2 - 15/4*r + s = 0.
-5, 0
Let h(d) be the first derivative of 7*d**3/12 - 475*d**2/8 + 117*d - 8400. Factor h(b).
(b - 1)*(7*b - 468)/4
Let l(y) be the second derivative of y**4/12 - y**3/6 - 2*y + 6. Let m(g) = 2*g**2 - 7*g - 4. Let v(j) = 15*l(j) - 5*m(j). Factor v(s).
5*(s + 2)**2
Let v(o) be the second derivative of -o**6/1800 + 7*o**5/150 - 5*o**3/6 + o. Let w(q) be the second derivative of v(q). Determine a so that w(a) = 0.
0, 28
Let g(k) = -k**3 - 26*k**2 + 29*k + 45. Let r be g(-27). Let b be (r/(-27))/(3*3/54). Suppose 1/4*u**4 - 6*u - b*u**3 + 11/2*u**2 + 9/4 = 0. What is u?
1, 3
Let t(a) be the first derivative of 12*a**5/5 - 115*a**4 + 48*a**3 + 152*a**2 - 3447. Solve t(s) = 0.
-2/3, 0, 1, 38
Let x = -21666 + 21668. Let h(y) be the third derivative of -1/10*y**6 - 1/112*y**8 + 0*y**4 + 1/14*y**7 + 0*y**3 + 0 + 0*y**5 + 0*y - 6*y**x. Factor h(r).
-3*r**3*(r - 4)*(r - 1)
Let o(x) be the first derivative of 135*x**3 + 7470*x**2 + 137780*x - 97. Determine r so that o(r) = 0.
-166/9
Let g(n) be the first derivative of -4*n**3/3 - 242*n**2 + 984*n + 1788. Factor g(x).
-4*(x - 2)*(x + 123)
Let t(j) be the third derivative of -j**5/240 + 19*j**4/32 - 55*j**3/12 - 3*j**2 + 88. Factor t(a).
-(a - 55)*(a - 2)/4
Let z(i) = -i**5 + 2*i**4 - 3*i**3 + 9*i + 3. Let k(p) = -p**4 + p**3 + 3*p + 1. Let l(g) = 3*k(g) - z(g). What is m in l(m) = 0?
0, 2, 3
Let j = 10837/52248 - -2/2177. Let u(i) be the third derivative of 5/12*i**3 - j*i**4 + 0 + 0*i - 4*i**2 + 1/24*i**5. Factor u(v).
5*(v - 1)**2/2
Let k(y) be the first derivative of 2*y**3/15 + 2*y**2/5 - 5295. Factor k(m).
2*m*(m + 2)/5
Determine c so that -1/2*c**5 - 924*c**3 + 36*c**4 - 31944*c + 0 + 9680*c**2 = 0.
0, 6, 22
What is n in -27/5*n**3 + 0 - 108/5*n + 492/5*n**2 = 0?
0, 2/9, 18
Let n(f) be the third derivative of -f**8/1008 + f**7/14 + 241*f**6/360 + 443*f**5/180 + 29*f**4/6 + 50*f**3/9 - 3686*f**2. Find d such that n(d) = 0.
-2, -1, 50
Suppose -2*k + 55 = 60007*i - 60010*i, 2*k = 2*i + 38. Factor -450*f**k - 16875 - 20*f**3 - 1/3*f**4 - 4500*f.
-(f + 15)**4/3
Suppose j + 28 = t, -t - 3*t = -j - 37. Let s be ((-35)/j)/(-7)*-15. Factor 8*f**2 + f**3 + 0*f - f - 3*f**3 - 8 + s*f.
-2*(f - 4)*(f - 1)*(f + 1)
Let i(l) be the second derivative of -2*l**6/15 - 11*l**5/5 + l**4/3 + 22*l**3/3 + 10*l + 33. Determine h, given that i(h) = 0.
-11, -1, 0, 1
Suppose 5*j - 113 + 13 = 4*n, -2*j + 37 = -n. Suppose 3*d + 7 - j = 0. Suppose -8*x + 16*x**3 - 10*x**d - 4*x**3 + 2*x**2 + 4*x = 0. What is x?
-2, 0, 1
Let x(c) be the first derivative of 4*c**3/3 - 73*c**2 - 228*c + 8952. Find s, given that x(s) = 0.
-3/2, 38
Let n be 5*8/10 - -44. Factor 5*w**3 - 51 - 21*w**3 + 28*w**3 + n*w**2 + 42*w**3 + 3*w**4 - 54*w.
3*(w - 1)*(w + 1)**2*(w + 17)
Let h be (-5)/22*561/(-1530). Let u(a) be the first derivative of 1/4*a**4 - h*a**6 - 2/3*a**3 + a - 1/4*a**2 + 48 + 1/5*a**5. Solve u(t) = 0.
-1, 1, 2
Solve -79840/3*t**4 - 934624/3*t**3 + 132098/3 + 1523696/3*t**2 - 1600/3*t**5 - 782308/3*t = 0.
-257/10, 1/2
Let x(g) be the first derivative of -3*g**4/4 + 224*g**3 + 1353*g**2/2 + 678*g - 1664. Factor x(c).
-3*(c - 226)*(c + 1)**2
Find w such that -6187*w + 3089*w + 127*w**4 - 705*w**3 + 3056*w - 155*w**2 - 196*w**2 - 19*w**4 = 0.
-1/4, -2/9, 0, 7
Let f(y) be the third derivative of 0*y - y**2 - 5/24*y**4 - 1/12*y**5 - 5 + 10*y**3. Suppose f(g) = 0. What is g?
-4, 3
Suppose -10*i + 13*i = 6. Factor -72*j + 65*j**2 - 137*j - 18*j**i + 265*j + 7*j**3 - 20.
(j + 2)*(j + 5)*(7*j - 2)
Solve -3/5*q**2 + 1062/5*q + 213 = 0 for q.
-1, 355
Let x(q) be the third derivative of -q**5/96 + 87*q**4/64 - 51*q**3/8 - 2479*q**2. Factor x(n).
-(n - 51)*(5*n - 6)/8
Let f = -31 - -29. Let t be (f - -4 - -11) + -4. Determine q, given that 18*q**3 + 4*q**3 + 3*q + t*q**4 + 5*q - 15*q**4 - 24*q**2 = 0.
0, 2/3, 1, 2
Let p(z) be the first derivative of 2*z**5/35 - 2726*z**4/7 + 7431076*z**3/7 - 10128556588*z**2/7 + 6902611314722*z/7 - 8732. Factor p(a).
2*(a - 1363)**4/7
Let j = 59448 + -118891/2. Factor -1/2*k**2 - 2 - j*k.
-(k + 1)*(k + 4)/2
Suppose 4*t + z + 10 = 0, -10*z + 5*z = t + 12. Let f be t - ((-12)/4 - (-25)/45). Let -f*a**3 + 2/9*a**5 + 8/9*a**2 + 2/9*a - 4/9*a**4 - 4/9 = 0. Calculate a.
-1, 1, 2
Factor -49/5 + 293/5*a - 239/5*a**2 - a**3.
-(a - 1)*(a + 49)*(5*a - 1)/5
Suppose -i + v - 24 = 6*v, -4*i + 19 = -3*v. Let d be (-1679)/138 + 1/6. Let r(l) = l. Let s(n) = -10*n**2 - 4*n + 8. Let m(p) = d*r(p) + i*s(p). Factor m(z).
-2*(z + 2)*(5*z - 2)
Let r be 3/(-63)*11/(1188/(-63)). Let s(o) be the third derivative of 5/72*o**4 + 0*o**3 + 0*o + 9*o**2 - r*o**5 + 0. Suppose s(w) = 0. Calculate w.
0, 1
Solve -4/7*g**3 + 0 + 4/7*g**2 + 120/7*g = 0.
-5, 0, 6
Factor -1/4*z**4 + 15*z - 41/4*z**2 + 0 - 9/2*z**3.
-z*(z - 1)*(z + 4)*(z + 15)/4
Let y(z) be the first derivative of 209*z**4/2 + 1252*z**3/3 - 3*z**2 - 404. Let y(t) = 0. Calculate t.
-3, 0, 1/209
Let s(m) = -3*m + 7. Let g(o) = -o + 3. Let i(x) = 5*g(x) - 2*s(x). Let d(c) = -c**2 + 153*c - 5471. Let k(l) = d(l) - 5*i(l). Factor k(r).
-(r - 74)**2
Let r(n) = -n**3 - 5*n**2 - n. Let y(u) = -u**3 - 31*u**2 - 77*u + 88. Let q(k) = 3*r(k) - y(k). Factor q(t).
-2*(t - 11)*(t - 1)*(t + 4)
Suppose 0 = 693*f - 783*f. Factor f - 1/8*l**4 + 1/8*l**2 + 1/2*l**3 - 1/2*l.
-l*(l - 4)*(l - 1)*(l + 1)/8
Let r(w) = 3*w + 147. Let f be r(-16). Determine b so that -37*b**4 - 642*b**2 + 31*b**3 - 512 - 893*b + 35*b**4 - f*b**3 - 195*b = 0.
-16, -1
Let o = 2588/15 + 18629/30. Factor 3/8*j**2 + o + 69/2*j.
3*(j + 46)**2/8
Suppose 6 = -351*m + 354*m. Let d(a) be the first derivative of 27 + 0*a**m + 4/39*a**3 - 3/26*a**4 + 1/39*a**6 + 0*a + 0*a**5. Factor d(w).
2*w**2*(w - 1)**2*(w + 2)/13
Let w(i) = -574*i + 65436. Let u be w(114). Determine p so that u + 1/4*p**4 + 5/4*p**2 + 3/2*p**3 + 0*p = 0.
-5, -1, 0
Suppose -5*q = 4*l + 47, -4*l + 0*l = q + 3. Let z be (187/(-4))/q + -4. What is p in 9/4*p**2 + 5/4*p + z + 1/2*p**4 + 7/4*p**3 = 0?
-1, -1/2
Let t = -169 + 163. Let c be (-1 + 8 + -7)*3/t. Factor -2/3*d + 0 + c*d**2 + 2/3*d**3.
2*d*(d - 1)*(d + 1)/3
Suppose 150*d - 374*d = -672. Let 2/11*r**5 - 2/11 + 4/11*r**2 - 4/11*r**d + 2/11*r - 2/11*r**4 = 0. Calculate r.
-1, 1
Let z(n) = -n**3 - 7*n - 4. Let k be (-1 - 2)/(-4*6/32). Let f(x) = x**3 + x**2 + 8*x + 5. Let w(d) = k*f(d) + 5*z(d). Solve w(b) = 0 for b.
0, 1, 3
Suppose 281 = -3*r - 391. Let z = r + 1126/5. Factor -17/5*p + z - 3/5*p**2.
-(p + 6)*(3*p - 1)/5
Let v(q) = -15*q**2 + 11*q - 34. Let s(j) = -4*j**2 - 2*j + 2. Let o(p) = -4*s(p) + v(p). Suppose o(w) = 0. Calculate w.
-21, 2
Let z(y) be the second derivative of y**5/80 - 6*y**4 + 6815*y**3/8 + 21025*y**2/4 + 341*y. Let z(h) = 0. Calculate h.
-2, 145
Let o(a) be the first derivative of -361*a**3 - 342*a**2 - 108*a - 1448. Determine p, given that o(p) = 0.
-6/19
Let h(c) = 12*c**2 - 2867*c - 239. Let f be h(239). Let 6/19*j**2 + 0*j**3 + 4/19*j - 2/19*j**4 + f = 0. What is j?
-1, 0, 2
Let k(t) be the third derivative of 1/210*t**7 + 0*t + 3/2*t**3 - 176*t**2 + t**4 + 1/15*t**6 + 11/30*t**5 + 0. Factor k(w).
(w + 1)**2*(w + 3)**2
Let l be ((-368)/(-506))/(18/33). Let a(r) be the first derivative of -2/3*r**4 - 2/3*r**3 + 5 - l*r + 3*r**2. Determine d, given that a(d) = 0.
-2, 1/4, 1
Determine c, given that 1520*c - 2373*c**2 - 17 + 2377*c**2 + 34 - 17 = 0.
-380, 0
Find t such that -2*t**4 + 34/3*t**2 - 82/3*t**3 + 82/3*t - 28/3 = 0.
-14, -1, 1/3, 1
Let w = 842 + -833. Suppose 28*l**2 - 20*l**3 - 5*l**2 - 16*l + 4*l**4 + w*l**2 = 0. What is l?
0, 1, 2
Let j(d) be the first derivative of -2*d**5/5 + 73*d**4 + 296*d**3 + 446*d**2 + 298*d - 15682. Factor j(g).
-2*(g - 14