441*c**2/8 + 393*c. Factor y(k).
(k - 21)**2*(4*k + 1)/4
Let g = 76 - -95. Factor -90*d**2 + 320*d**3 + 30*d**5 + g - 540*d + 155*d**4 - 52*d**5 - 36 + 24*d**5 + 18*d**5.
5*(d - 1)*(d + 3)**3*(4*d - 1)
Let c(p) = 50*p**3 - 15*p - 15. Let h(u) = 7*u**3 - 2*u - 2. Let y(z) = -z**3 - 5*z**2 - 4*z + 15. Let t be y(-4). Let o(w) = t*h(w) - 2*c(w). Factor o(b).
5*b**3
Let m(l) = l**2 + 31*l + 4683. Let b(g) = -5*g**2 - 120*g - 14050. Let v(r) = -3*b(r) - 10*m(r). Factor v(n).
5*(n - 26)*(n + 36)
Let b(r) be the first derivative of 23*r**6/39 + 14*r**5/65 - 8*r**4/13 - 3806. Determine i so that b(i) = 0.
-1, 0, 16/23
Let 108/5*s - 3/5*s**2 - 672/5 = 0. What is s?
8, 28
Suppose 0 = -612*g + 609*g + 6. Let m(p) be the third derivative of 1/420*p**5 - 1/21*p**3 + 0 - 30*p**g + 1/168*p**4 + 0*p. Factor m(q).
(q - 1)*(q + 2)/7
Factor 1/7*y**3 - 4/7*y + 10/7*y**2 - 1/7*y**4 - 24/7.
-(y - 3)*(y - 2)*(y + 2)**2/7
Factor -147*x**4 + 112 + 143*x**4 - 59 - 53 + 4*x**2 + 1352*x - 1352*x**3.
-4*x*(x - 1)*(x + 1)*(x + 338)
Let w be (36/12 + -9)*1/(-150). Let n(k) be the first derivative of -6 + 1/20*k**4 + 2/15*k**3 + 0*k**2 + 0*k - w*k**5. Find t such that n(t) = 0.
-1, 0, 2
Let u(m) be the third derivative of 0*m**5 + 0*m**3 + 10*m**2 - 5/24*m**4 + 0*m**7 + 1/12*m**6 - 5/336*m**8 + 0 + 0*m. Suppose u(x) = 0. Calculate x.
-1, 0, 1
Let q(n) be the third derivative of n**7/210 + n**6/24 - 2*n**5/15 - 2*n**4 + 31*n**2 + 3*n + 1. Let q(o) = 0. What is o?
-4, 0, 3
Suppose -58*g**4 + 249*g**2 + 860*g - 50*g**4 - 18 + 240*g**3 - 845*g = 0. What is g?
-1/2, 2/9, 3
Let n(i) = -18*i - 36. Let k be n(-2). Let l = k + 2. Factor 0 - 4/9*p**3 - 2/9*p - 1/9*p**4 - 5/9*p**l.
-p*(p + 1)**2*(p + 2)/9
Suppose -240 = -19*p - 5*p. Let -17*f**5 - 9 - 4 + 7*f**5 + 20*f + 25*f**4 + 8 - p*f**3 - 20*f**2 = 0. What is f?
-1, 1/2, 1
Let n be (-5)/10*(-5 - 3). Let 236*d**3 - 92*d**n + 192*d**2 - 20*d + 12*d**5 - 68*d - 4*d**5 - 56*d = 0. Calculate d.
-1, 0, 1/2, 6
Let r(k) = -k**2 + 6*k + 7 - 8 + 3 + k**3. Let g be r(0). Find p, given that 0 - 8/5*p - 36/5*p**g + 0*p**4 + 16/5*p**5 - 44/5*p**3 = 0.
-1, -1/2, 0, 2
Let i = 819 - 817. Let x = 5 + -3. Factor 12 - x*a**3 + 0*a**3 - 24*a + 14*a**2 + a**i - a**3.
-3*(a - 2)**2*(a - 1)
Let a(x) be the second derivative of -27/2*x**2 + 0 - 9/2*x**3 + 3/2*x**4 + 1/42*x**7 - 7/30*x**6 + 249*x + 1/2*x**5. Find z, given that a(z) = 0.
-1, 3
Let t = -31 - -55. Suppose 2*a - t = 46. Suppose 7*i + 2*i - 41 - 3*i**3 + a = 0. What is i?
-2, 1
Let n(s) be the third derivative of 1/75*s**5 + 0 + 0*s - 34*s**2 + 1/30*s**3 - 1/24*s**4. Factor n(a).
(a - 1)*(4*a - 1)/5
Let f(u) = -u**2 - 3*u + 499. Let a be f(0). Let q = a + -495. Factor 0 + 8/5*y - 2/5*y**q + 2*y**3 - 16/5*y**2.
-2*y*(y - 2)**2*(y - 1)/5
Let l be 32*(10/(-16))/(4/(-16)). Let f be ((-1)/(-1) - -4)/(l/64). Factor 0 + 6/5*x**f + 6/5*x**3 + 0*x + 2/5*x**2 + 2/5*x**5.
2*x**2*(x + 1)**3/5
Suppose -39519*c**3 + 160*c**2 + 6*c**5 - 34*c**4 + 64*c - 112 - 39544*c**3 + 16 + 79023*c**3 = 0. What is c?
-2, -1, 2/3, 2, 6
Let i(j) be the first derivative of -j**4 + 4*j**3 + 50*j**2 + 84*j - 771. Solve i(f) = 0 for f.
-3, -1, 7
Let s(x) be the first derivative of 147*x**4/4 + 287*x**3 - 564*x**2 + 336*x - 1215. Find k, given that s(k) = 0.
-7, 4/7
Let m(s) = -s**2 + 26*s + 6. Suppose 0 = -12*f + 3*f + 234. Let y be m(f). Find l such that y + 2/3*l**2 + 4*l = 0.
-3
Let t(c) be the second derivative of -c**7/105 + c**6/25 - 3*c**5/50 + c**4/30 + 839*c. Find q, given that t(q) = 0.
0, 1
Let k(i) be the second derivative of -i**5/4 - 10*i**4/3 - 95*i**3/6 - 30*i**2 - 21*i + 5. Factor k(d).
-5*(d + 1)*(d + 3)*(d + 4)
Let q(k) be the third derivative of -1/1155*k**7 + 32/33*k**3 + 0 + k + 2/55*k**5 + 10/33*k**4 - 1/330*k**6 + 9*k**2. Solve q(l) = 0 for l.
-2, 4
Suppose 190790*n = 190889*n - 198. Factor -13/4*c**3 + 3 + 13/4*c - 1/4*c**4 - 11/4*c**n.
-(c - 1)*(c + 1)**2*(c + 12)/4
Let m(z) = 2*z**2 - 10*z + 20. Let f be m(6). Suppose -6*t - 2*t = -f. Factor 14 + 4*q**3 + 4*q**2 - 7 - t*q**4 - 7 - 4*q**5.
-4*q**2*(q - 1)*(q + 1)**2
Let r(c) be the first derivative of -c**4/12 - 11*c**3/6 + 6*c**2 + 129*c - 184. Let j(i) be the first derivative of r(i). Solve j(d) = 0 for d.
-12, 1
Let j(l) be the second derivative of 0 + 8/9*l**3 + 0*l**2 - 1/36*l**4 - 103*l. Factor j(c).
-c*(c - 16)/3
What is y in 986*y**2 - 52 - 32*y + 1001*y**2 - 2*y**3 - 50*y - 2019*y**2 = 0?
-13, -2, -1
Suppose 4 + 8 = 3*b. Let t(c) = -c + 54. Let l be t(52). Factor -12*i + 48*i**l - 10*i - 52*i**3 + 6*i + 4*i**b + 20*i**4 - 4*i**5.
-4*i*(i - 2)**2*(i - 1)**2
Let r(t) = -t**3 + 4*t + 4. Let n be r(-3). Solve -20*m**3 + 14*m**2 - 4*m**4 - 7*m**2 + 4*m**5 - n*m**2 = 0 for m.
-1, 0, 3
Suppose 448*u + 99 = 439*u. Let f be u/((-77)/(-14))*(-3 + 2). Let 2/15*z**f + 0 + 2/5*z = 0. What is z?
-3, 0
Let o(l) = 5*l**3 - 35*l - 15. Let i(u) be the first derivative of -u**2/2 - u - 46. Let k(m) = -15*i(m) + o(m). Factor k(q).
5*q*(q - 2)*(q + 2)
Let v(s) = -55*s**2 - 590*s - 13690. Let p(x) = -34*x**2 - 296*x - 6846. Let g(b) = 5*p(b) - 3*v(b). Factor g(h).
-5*(h - 76)*(h + 18)
Let w(j) be the first derivative of -j**3/4 + 239*j**2/8 - 79*j/2 + 1401. Determine y, given that w(y) = 0.
2/3, 79
Let j(i) = -4*i**2 + 12*i + 3. Let w(b) = -7*b**2 + 23*b + 5. Let p = -190 - -187. Let s(m) = p*w(m) + 5*j(m). Factor s(h).
h*(h - 9)
Factor 148/9*k + 0 + 2*k**3 - 166/9*k**2.
2*k*(k - 1)*(9*k - 74)/9
Let s(x) be the second derivative of -73*x**6/75 + 373*x**5/100 + 199*x**4/60 - 2*x**3/5 - 931*x - 8. Determine b so that s(b) = 0.
-1/2, 0, 4/73, 3
Let t = -3391 - -3393. Let s(j) be the first derivative of 0*j**t + 2 + 0*j - 4/15*j**3. Solve s(i) = 0 for i.
0
Determine u so that 33 + 17 + 29 - 16 - 3*u**2 + 45 = 0.
-6, 6
Suppose 0 = 102*d - 112*d + 50. Factor 22*z**5 - 32*z**4 - 67*z**5 + 49*z**d.
4*z**4*(z - 8)
Suppose -4*q + 6 = -2*q. Let z(v) be the third derivative of 0 - 1/4*v**4 - 1/20*v**5 + 0*v - 1/2*v**q - 17*v**2. Factor z(m).
-3*(m + 1)**2
Let c = 11 - 50. Let h be ((-2)/3)/(13/c). Factor -9*r**5 + 12*r**3 + 3*r**5 - 2*r**h - 6*r**2 - 8*r**4 + 8*r**5 + 2*r.
2*r*(r - 1)**4
Factor -3*g**4 + 57*g - 729*g**2 + 5767*g**5 + 189*g**3 - 5770*g**5 + 753*g.
-3*g*(g - 3)**3*(g + 10)
Let g(n) be the third derivative of n**7/504 + n**6/108 - n**5/72 - 5*n**4/36 + n**3/2 - 2*n**2 + 8*n. Let z(s) be the first derivative of g(s). Factor z(y).
5*(y - 1)*(y + 1)*(y + 2)/3
Let d(j) be the first derivative of 4*j**3/3 + 126*j**2 - 520*j - 1751. Factor d(g).
4*(g - 2)*(g + 65)
Let d(b) be the first derivative of -2*b**7/105 + b**6/15 - b**5/15 - 41*b**2 + 28. Let k(a) be the second derivative of d(a). Factor k(u).
-4*u**2*(u - 1)**2
Let z(h) be the third derivative of -h**6/300 + 7*h**5/50 - h**4/3 + 56*h**2 + 8*h. Find q, given that z(q) = 0.
0, 1, 20
Determine w so that -4050*w**2 + 1589*w + 3192 - 3552 + 2575*w + 63*w**4 + 183*w**3 = 0.
-10, 2/21, 1, 6
Let r(j) be the third derivative of j**5/36 + 665*j**4/72 - 3*j**2 - 346. Determine q so that r(q) = 0.
-133, 0
Let z(g) be the second derivative of -11*g**6/195 - 4*g**5/13 - 9*g**4/13 - 32*g**3/39 - 7*g**2/13 + 62*g - 6. Determine p, given that z(p) = 0.
-1, -7/11
Let q(x) be the third derivative of x**5/270 + 421*x**4/54 + 2*x**2 + 21*x - 19. Factor q(m).
2*m*(m + 842)/9
Determine n so that -375*n - 1/4*n**2 - 140625 = 0.
-750
Let v = -232 - -252. Let 28 + 17 - 9*a**2 - v*a + 18 - 3 + 4*a**2 = 0. Calculate a.
-6, 2
Factor -1568*n**2 + 756*n**3 + 27/2*n**5 - 76832/3 - 46648/3*n + 198*n**4.
(n - 4)*(3*n + 14)**4/6
Let b(a) be the third derivative of 15*a**4 + 59*a**2 - 1/6*a**7 - 41/12*a**6 + 0 + 0*a - 19*a**5 + 0*a**3. What is k in b(k) = 0?
-6, 0, 2/7
Suppose -1359 + 1089 = -5*i. Suppose 0 = -3*y + 3*x + 3, -53 = -y - x - i. Find l, given that -4/9*l**3 + y*l**4 + 2/9*l**5 + 0*l**2 + 0 + 2/9*l = 0.
-1, 0, 1
Let o(d) be the second derivative of d**7/1050 + d**6/225 - d**5/150 - d**4/15 + 12*d**3 + 126*d. Let g(x) be the second derivative of o(x). Factor g(z).
4*(z - 1)*(z + 1)*(z + 2)/5
Let r(f) be the first derivative of -2*f**3 + 155*f**2/3 + 84*f + 841. Suppose r(v) = 0. Calculate v.
-7/9, 18
Let j = 159/799 + 2083/5593. Let 25/7*x**2 + 8/7 + 38/7*x + j*x**3 = 0. What is x?
-4, -2, -1/4
Solve -37/10*g**3 - 1/10*g**4 - 672