 - z(h). Factor f(l).
4*(l - 3)*(l - 1)*(l + 1)
Let p(n) be the first derivative of 24*n + 2/3*n**3 + 13*n**2 + 6. Determine s so that p(s) = 0.
-12, -1
Let v(b) be the third derivative of 5/144*b**4 + 1 - 1/360*b**5 + 0*b - 1/6*b**3 - 23*b**2. Solve v(d) = 0.
2, 3
Let r(w) = w**3 + 37*w**2 - 38*w + 2. Let c be r(-38). Factor 0 - 8 - k**c - 283*k + 0 + 289*k.
-(k - 4)*(k - 2)
Let w(r) be the first derivative of 10*r**6/3 + 7*r**5 - 5*r**4/2 - 40*r**3/3 - 5*r**2 + 5*r - 938. Suppose w(c) = 0. What is c?
-1, 1/4, 1
Factor 27441*b**2 + 4*b**3 - 339 - 151 - 27381*b**2 + b**3 + 105*b.
5*(b - 2)*(b + 7)**2
Let f be 7 + 192/(-54) - (-8)/624*-26. Determine w so that 0 - 25/3*w**5 + f*w**3 - 10/9*w**4 + 8/9*w**2 + 0*w = 0.
-2/5, 0, 2/3
Let a = 224730 + -224730. Factor -8/3*q**3 + a*q + q**4 + 0 + 4/3*q**2.
q**2*(q - 2)*(3*q - 2)/3
Let u(l) = -9*l**3 - 7*l**2 - 5*l - 1. Let s(y) = -y**3. Suppose o + 1 = r - 0*o, 5*r - o = -3. Let c(x) = r*u(x) + 6*s(x). Determine h, given that c(h) = 0.
-1, -1/3
Let y(b) = -b**3 - 654*b**2 - 19325*b - 152337. Let z(c) = -330*c**2 - 9663*c - 76167. Let x(k) = -3*y(k) + 5*z(k). Factor x(r).
3*(r + 12)*(r + 46)**2
Let q(g) be the first derivative of -g**6/6 + g**5/5 + 3*g**4 + 2122. Factor q(o).
-o**3*(o - 4)*(o + 3)
Suppose 0 = 2*v - 5*b - 8, 8 = -7*v + 9*v + 2*b. Factor f - 2*f + f**3 - 10 + 2*f**2 + 4 + v.
(f - 1)*(f + 1)*(f + 2)
Let v(b) be the third derivative of -7/33*b**4 - 23/330*b**5 - 1/1155*b**7 + 0*b - b**2 - 51 - 2/165*b**6 - 4/11*b**3. Solve v(y) = 0.
-3, -2, -1
Suppose 0*l + 8/5*l**3 + 0 - 2/5*l**4 - 2/5*l**5 + 8/5*l**2 = 0. What is l?
-2, -1, 0, 2
Suppose 2/7*g**2 + 0 + 12/7*g = 0. What is g?
-6, 0
Suppose 4*f - 8 + 11 = -5*m, -4*f = -3*m + 11. Let o be (5/15)/(f/(18/(-15))). Factor -3/5 - 1/5*q**2 - o*q**3 + q.
-(q - 1)**2*(q + 3)/5
Let h(v) be the first derivative of v**6/240 - v**5/30 - 5*v**4/48 - 115*v**2/2 - 12. Let u(s) be the second derivative of h(s). Let u(q) = 0. What is q?
-1, 0, 5
Let f(d) be the first derivative of 16/9*d**3 + 0*d - 1/3*d**4 + 0*d**2 + 83 - 2/15*d**5. Determine c so that f(c) = 0.
-4, 0, 2
Let q(g) be the third derivative of -g**6/24 - 8*g**5/3 - 935*g**4/24 - 250*g**3 - 1245*g**2. Solve q(w) = 0.
-25, -4, -3
Let g(r) = -35*r + 5. Let l be g(0). Let w(n) be the third derivative of -1/60*n**l - 1/3*n**3 + 0*n + n**2 + 1/8*n**4 + 0. Factor w(v).
-(v - 2)*(v - 1)
Let v = 5411/12468 + -18/1039. Let z(r) be the third derivative of 1/12*r**5 + 1/24*r**6 + 0 + 0*r**3 + 0*r - v*r**4 + 8*r**2. Solve z(p) = 0 for p.
-2, 0, 1
Let g(q) be the second derivative of -2*q**7/21 + 22*q**6/15 - 48*q**5/5 + 104*q**4/3 - 224*q**3/3 + 96*q**2 + 285*q. Factor g(r).
-4*(r - 3)*(r - 2)**4
Factor -1/5*z**4 - 18/5*z**2 + 52/5*z - 13/5*z**3 + 88/5.
-(z - 2)*(z + 2)**2*(z + 11)/5
Factor -98 + 2/9*q**3 + 394/3*q - 302/9*q**2.
2*(q - 147)*(q - 3)*(q - 1)/9
Let d(r) be the second derivative of -147*r - 1/78*r**4 + 0 + 14/39*r**3 - 33/13*r**2. Suppose d(k) = 0. What is k?
3, 11
Let p(k) be the third derivative of k**5/90 + 25*k**4/6 - 304*k**3/9 + 7481*k**2. Solve p(q) = 0.
-152, 2
Let b be 7/(-3) + 93 + 15517/(-177). Let -12*u - 10/3 - 16/3*u**b - 14*u**2 = 0. Calculate u.
-1, -5/8
Factor 10*d + 517 + 2*d + 0*d**2 - 175 + 2*d**2 - 662.
2*(d - 10)*(d + 16)
Let x(a) be the second derivative of a**5/160 + a**4/12 - 199*a**3/48 + 95*a**2/8 + 4*a - 647. Suppose x(k) = 0. What is k?
-19, 1, 10
Let z(b) be the first derivative of -14/33*b**3 - 9/11*b**2 + 57 - 4/11*b. Factor z(q).
-2*(q + 1)*(7*q + 2)/11
Let s be (-630)/(-180) + (-4)/(-1) + 3. Factor -49/4*z**2 - 9/4 + s*z.
-(7*z - 3)**2/4
Factor -h**3 - 59 - 233/2*h**2 + 353/2*h.
-(h - 1)*(h + 118)*(2*h - 1)/2
Let i = 136 - 130. Let p be (-220)/770*(-1 - 8/i). Factor 2/3*s - 2/9 - p*s**2 + 2/9*s**3.
2*(s - 1)**3/9
Let v(k) = 2*k**5 + 18*k**4 - 36*k**3 - 8*k**2 - 12*k. Let n(i) = i**4 - i**3 - 4*i**2 - 2*i. Let c(q) = -6*n(q) + v(q). Factor c(h).
2*h**2*(h - 1)**2*(h + 8)
Let v(k) be the first derivative of k**3/9 - 103*k**2/6 - 104*k/3 - 4256. Factor v(z).
(z - 104)*(z + 1)/3
Let t(x) be the first derivative of 1/50*x**4 - 6/25*x**3 + 0*x**2 + 0*x - 32. Factor t(v).
2*v**2*(v - 9)/25
Let j(t) = 12*t**4 - 22*t**3 - 38*t**2 + 8*t - 20. Let y(u) = 10*u**4 - 22*u**3 - 39*u**2 + 6*u - 15. Let q(b) = 3*j(b) - 4*y(b). Solve q(s) = 0.
-3/2, 0, 7
Let v(s) be the first derivative of s**4/9 - 34*s**3/27 + 4*s**2/3 + 14*s - 6203. Factor v(q).
2*(q - 7)*(q - 3)*(2*q + 3)/9
Suppose 0 = 7*o - j + 6*j - 5809, 0 = 4*o + 2*j - 3322. Suppose -24*y - 784 + o = 0. Find h, given that 0 - 4/5*h - 4/5*h**3 + 22/15*h**y + 2/15*h**4 = 0.
0, 1, 2, 3
Let f(x) be the first derivative of 4*x**5/5 + 146*x**4 - 2380*x**3/3 + 1496*x**2 - 1200*x - 6729. Factor f(p).
4*(p - 2)*(p - 1)**2*(p + 150)
Let p(j) be the first derivative of 3*j**5/5 + 9*j**4/4 - 18*j**3 - 8. Solve p(s) = 0 for s.
-6, 0, 3
Let y be -11*837/341*1/3 - -13*1. Factor -3/2*g**y + 0 + 23/2*g**2 + 3*g + 7*g**3.
-g*(g - 6)*(g + 1)*(3*g + 1)/2
Factor 83*z**4 + 124500*z + 500*z**3 + 80*z**4 - 241*z**4 + 79*z**4 + 4580 + 62998*z**2 + 57421.
(z + 1)**2*(z + 249)**2
Suppose 0 = -118*n + 55*n + 189. Let s(o) be the third derivative of 0*o + 7/180*o**5 + 11/24*o**4 + 0 + 2*o**2 - 5/9*o**n. Find l, given that s(l) = 0.
-5, 2/7
Let j(i) be the third derivative of -i**6/24 + 1529*i**5/12 - 2442*i**2 - 3. Find g such that j(g) = 0.
0, 1529
Let y = -7031/13 + 56287/104. Suppose -1/2*q**2 + y*q**3 - 5/8*q + 1/4 = 0. What is q?
-1, 1/3, 2
Let 0 + 10*o**3 - 8/3*o**4 - 14*o - 4/3*o**2 = 0. Calculate o.
-1, 0, 7/4, 3
Let z(t) = -33*t**4 + 88*t**3 - 10*t**2 - 206*t - 3. Let k(l) = 270*l**4 - 705*l**3 + 80*l**2 + 1650*l + 25. Let f(y) = 3*k(y) + 25*z(y). What is s in f(s) = 0?
-4/3, 0, 2, 5
Let k(r) be the third derivative of -r**7/1260 - 109*r**6/720 + 47*r**5/24 + 1733*r**4/144 + 230*r**3/9 - 30*r**2 - 3*r - 1. Let k(m) = 0. Calculate m.
-115, -1, 8
Factor 200*m + 222*m**4 - 16 + 5*m**5 - 140*m**2 - 262*m**4 - 4 - 115*m + 110*m**3.
5*(m - 4)*(m - 1)**4
Let p(y) be the third derivative of y**5/30 - 151*y**4/4 - 456*y**3 + 2*y**2 - 2166. Factor p(n).
2*(n - 456)*(n + 3)
Factor 337*n**3 - 254*n**3 + 557*n**3 - 97344 - 26848*n**2 + 99840*n - 4*n**4.
-4*(n - 78)**2*(n - 2)**2
Let s = 83 - 85. Let x(l) = 24*l**2 + 53*l - 17. Let j(b) = 650*b**2 + 1430*b - 460. Let r(q) = s*j(q) + 55*x(q). Suppose r(v) = 0. What is v?
-3, 1/4
Suppose 5346 + 1154 = -25*a. Let b be a/(-117) - 4/18. Solve -6/5 + 4/5*q - 4/5*q**3 + 2/15*q**4 + 16/15*q**b = 0 for q.
-1, 1, 3
Suppose 0 = 5*g - 3*b - 804 - 426, -714 = -3*g - 3*b. Let s be -5 - (-1)/(45/g). Let 8/5*y**2 + 4/5 + s*y**3 + 2*y = 0. What is y?
-2, -1
Let m(w) be the third derivative of 5*w**7/252 - 19*w**6/144 + 8*w**5/45 - w**4/12 + 4936*w**2 - 2*w. Factor m(x).
x*(x - 3)*(5*x - 2)**2/6
Let w(n) be the first derivative of -1/12*n**4 - 32 + 2*n - 1/6*n**2 - 4/9*n**3. Factor w(z).
-(z - 1)*(z + 2)*(z + 3)/3
Let i = 157745 + -157742. What is t in 0 - 3/2*t**3 + i*t + 7/2*t**2 = 0?
-2/3, 0, 3
Suppose -3*v + 6 = -0*v. Suppose -13 = 6*i + 17. Let q(p) = -7*p**2 + 5*p. Let h(d) = -15*d**2 + 10*d. Let m(g) = i*q(g) + v*h(g). Let m(c) = 0. Calculate c.
0, 1
Let g(w) be the second derivative of -w**7/63 + 2*w**6 + 96*w**5/5 - 9846*w. Factor g(q).
-2*q**3*(q - 96)*(q + 6)/3
Let j(l) be the second derivative of -l**7/14 + 8*l**6/5 - 153*l**5/20 + 9*l**4 + 7*l - 414. Find m, given that j(m) = 0.
0, 1, 3, 12
Let k(b) be the second derivative of -b**5/20 - b**4/2 + b**3/6 + 4*b**2 + 10*b. Let v be k(-6). Factor 4*h**2 - 4*h**2 - v*h**2 + 12*h.
-2*h*(h - 6)
Let p(l) be the third derivative of 0*l**3 + 1/12*l**5 - 20*l**2 + 0*l**4 - 1 + 0*l + 2/21*l**7 - 5/24*l**6. Factor p(s).
5*s**2*(s - 1)*(4*s - 1)
Let i = 3369 - 3366. Let n(v) be the second derivative of 0 + 1/10*v**5 + 1/3*v**i + 17*v + 1/3*v**4 + 0*v**2. Let n(z) = 0. What is z?
-1, 0
Suppose -2195 = -5*v + 4*h, h = -4*v + 5*h + 1752. Determine n so that -v*n + 446*n + n**5 + 3 - 4*n**3 - 2*n**2 - 1 = 0.
-1, 1, 2
Let t be (((-16)/(-112))/(9/(-126)))/(4/(-6)). Factor -4/3*y**2 + 17/6*y + 1/6*y**t - 5/3.
(y - 5)*(y - 2)*(y - 1)/6
Let n(y) be the first derivative of -65/4*y**4 + 5*y - 52 + 4*y**5 - 35/2*y**2 + 25*y**3. Find p, given that n(p) = 0.
1/4, 1
Suppose -16 = -6*p