, 1, 3
Let y(g) = 2*g**2 - 24*g - 108. Let r be y(-7). Suppose 174 - r = 8*h. Factor 0 + 3*w + 1/3*w**h.
w*(w + 9)/3
Let m(g) be the second derivative of 3/2*g**5 + 0 - g + 5*g**2 - 65/6*g**3 + 25/12*g**4. What is q in m(q) = 0?
-2, 1/6, 1
Let a be 1440/36 + -28 - (-1728)/40. Determine s so that 68/5 - 296/5*s**3 - 4/5*s**5 - a*s + 84/5*s**4 + 424/5*s**2 = 0.
1, 17
Let f(w) = w**3 - 2*w**2 - 3*w. Suppose -2*g = -4*a + 6, 3*a - 5*g + 4 + 2 = 0. Let o be f(a). Factor 0*u - 1/4*u**3 + o - u**2.
-u**2*(u + 4)/4
Let n(o) = -o**3 + 6*o**2 - 3*o - 4. Let r be n(5). Let d = r + 8. Factor 11*u + 5*u**3 + 9*u - 6*u**2 - d*u**2.
5*u*(u - 2)**2
Let 54/5*o - 2/5*o**3 + 0*o**2 + 108/5 = 0. What is o?
-3, 6
Let i be (-122)/305*25/(-2). Let k(w) = 2*w**2 - 5*w + 2. Let p be k(3). Suppose 0*c**5 - 10*c**3 - i*c**3 + p*c**5 + 10*c**2 = 0. What is c?
-2, 0, 1
Let q(y) be the first derivative of -191 - 5/7*y**2 - 8/7*y - 2/21*y**3. Factor q(k).
-2*(k + 1)*(k + 4)/7
Let z(v) = -160*v**3 + 320*v**2 - 140*v. Let n(x) = -x**4 - 318*x**3 + 639*x**2 - 270*x. Let u(w) = -2*n(w) + 5*z(w). Solve u(j) = 0.
0, 1, 80
Factor 2/5*q**2 - 544/5 + 52/5*q.
2*(q - 8)*(q + 34)/5
Let b(p) = -6*p**2 - 256. Let y(f) = 65*f**2 + 2560. Let g(z) = 21*b(z) + 2*y(z). Let g(w) = 0. What is w?
-8, 8
Let n(t) be the first derivative of t**8/84 - 4*t**7/105 + t**6/30 + 22*t**2 - 121. Let p(v) be the second derivative of n(v). Find f, given that p(f) = 0.
0, 1
Let w(u) be the first derivative of -u**6/36 - u**5/5 - 13*u**4/24 - 2*u**3/3 - u**2/3 - 5744. Determine q so that w(q) = 0.
-2, -1, 0
Suppose 4*z = 6*x - x + 5946, -x = -2. Let n = z - 4465/3. Let 0 + 10/3*f**2 - n*f**3 + 0*f = 0. Calculate f.
0, 5
Let i(f) = f - 16. Let j be i(30). Factor 6*y**5 + 14*y**3 - 8*y**5 + j*y + 38*y**2 + 8*y**4 + 2*y**2 + 22*y**3.
-2*y*(y - 7)*(y + 1)**3
Let r(x) be the first derivative of 11*x + 0*x**2 + 0*x**3 + 1/20*x**6 - 3/20*x**5 + 1/8*x**4 + 28. Let y(t) be the first derivative of r(t). Factor y(v).
3*v**2*(v - 1)**2/2
Let 576/7 - 284/7*d - 2/7*d**2 = 0. What is d?
-144, 2
Let u(t) = t**4 + t**3 - t**2. Let k(x) = 6*x**4 - 57*x**3 + 36*x**2 + 342*x. Let h(z) = -k(z) + 3*u(z). Factor h(v).
-3*v*(v - 19)*(v - 3)*(v + 2)
Let f be 52/((-1716)/627) - -19. Suppose f + 6/5*o + 8/5*o**2 + 2/5*o**3 = 0. Calculate o.
-3, -1, 0
Let y(f) = 15*f**4 + 38*f**3 + 48*f**2 - 5*f - 9. Let i(l) = -63*l**4 - 153*l**3 - 194*l**2 + 19*l + 39. Let v(m) = -6*i(m) - 26*y(m). Factor v(p).
-2*p*(p + 2)*(p + 4)*(6*p - 1)
Let u = -70055 - -70057. Factor -1849/5*q**u - 172/5*q - 4/5.
-(43*q + 2)**2/5
Let z(t) = -t**3 + 10*t**2 - 2*t + 23. Let i be z(10). Factor -4*v**5 - 51*v**4 + 4*v**i + 4*v**2 + 22*v**4 + 25*v**4.
-4*v**2*(v - 1)*(v + 1)**2
Let i(h) be the first derivative of h**4/22 - 1018*h**3/33 + 5957*h**2 - 34914*h + 3067. What is t in i(t) = 0?
3, 253
Let j(x) be the first derivative of -x**5/240 + x**4/16 - 5*x**3/24 + x**2 + 153*x - 152. Let s(r) be the second derivative of j(r). Factor s(f).
-(f - 5)*(f - 1)/4
Let -182/3*r**4 - 6484/9*r - 3253/9*r**3 - 1/9*r**5 - 2344/3*r**2 - 240 = 0. Calculate r.
-540, -2, -1
What is l in 4336*l - 190*l**2 + 2350112 + 558*l**2 - 192*l**2 - 174*l**2 = 0?
-1084
Factor 4*d**2 - 163711*d + 149495*d + 6728182 + 5902734.
4*(d - 1777)**2
Let h(y) be the first derivative of 5*y**4/4 - 10*y**3/3 - 50*y**2 - 120*y - 1645. Factor h(d).
5*(d - 6)*(d + 2)**2
Let n(s) = -9*s**2 - 227*s + 240. Let z(w) = -w**2 - 17*w - 48. Let m be z(-13). Let q(u) = 8*u**2 + 229*u - 240. Let t(a) = m*q(a) + 3*n(a). Factor t(p).
5*(p - 1)*(p + 48)
Let n(i) = 14*i**2 - 67*i - 215. Let r be n(7). Factor -5/3*y**r + y + 1/3*y**4 + 1/3*y**3 + 0.
y*(y - 1)**2*(y + 3)/3
Let s(k) be the second derivative of 0 + 0*k**2 + 5/12*k**4 + 1/6*k**3 - 287*k - 3/10*k**5. Let s(z) = 0. Calculate z.
-1/6, 0, 1
Let p(a) be the second derivative of 5*a**5/4 - 205*a**4/6 + 830*a**3/3 - 300*a**2 - 1030*a + 1. Factor p(g).
5*(g - 10)*(g - 6)*(5*g - 2)
Factor 2599*v - 56 + 20*v**3 + v**4 - 2675*v - 21*v**3 - 30*v**2.
(v - 7)*(v + 2)**3
Suppose 48 - 499 = 11*k. Let y = -16 - k. Factor 23*u - 18*u + 15 + 5*u**2 - y*u.
5*(u - 3)*(u - 1)
Let p(g) be the first derivative of g**6/30 + g**5/5 + g**4/3 - 43*g + 27. Let v(z) be the first derivative of p(z). Let v(h) = 0. Calculate h.
-2, 0
Let q(i) be the second derivative of 117*i + 1/35*i**5 + 8/3*i**3 + 10/21*i**4 + 48/7*i**2 + 0. Factor q(p).
4*(p + 2)**2*(p + 6)/7
Let l = 46 - 32. Suppose -9*g + l*g - 240 = 0. Solve -44*x**2 + g*x**2 + 9*x**3 - 8*x - 4*x**5 + 3*x**3 - 4*x**4 = 0 for x.
-2, -1, 0, 1
Let c(p) be the second derivative of -9*p**5/140 + 19*p**4/28 + 39*p**3/7 + 12*p**2 + 7028*p. Let c(m) = 0. What is m?
-2, -1, 28/3
Let q(f) be the second derivative of -f**4/2 + 59*f**3/3 + 20*f**2 + 111*f + 5. Suppose q(k) = 0. What is k?
-1/3, 20
Let l = -616 - -613. Let z be 5/l*120/(-100). Factor 1/2*g + 1/6*g**z + 1/3.
(g + 1)*(g + 2)/6
Factor 262*v**3 + 69*v**2 - 165*v - 271*v**3 + 64*v**2 + 48*v**2 - 67*v**2.
-3*v*(v - 11)*(3*v - 5)
Let m(r) be the second derivative of -r**6/10 + 9*r**5/10 - 7*r**4/4 - 3*r**3 + 12*r**2 + 2*r - 893. Determine y so that m(y) = 0.
-1, 1, 2, 4
Let t be 62/(((-105)/14)/(-15)). Let d = t - 119. What is r in 18/13*r**4 - 6/13*r + 10/13*r**2 + 2*r**3 - 4/13 + 4/13*r**d = 0?
-2, -1, 1/2
Let m(r) be the second derivative of -5*r**4/12 - 305*r**3 - 167445*r**2/2 - 1526*r. Factor m(c).
-5*(c + 183)**2
Factor 0 + 2/3*t**3 + 89/6*t**2 - 23/2*t.
t*(t + 23)*(4*t - 3)/6
What is h in -1950*h**2 + 4053*h**2 + 20*h**3 + 330 + 635*h - 1828*h**2 = 0?
-11, -2, -3/4
Let y(k) be the second derivative of 169/10*k**2 + 0 - 41*k + 13/15*k**3 + 1/60*k**4. Solve y(n) = 0.
-13
Let i = 202450/151839 + 2/151839. Factor 16/3 + i*r**2 - 65/3*r.
(r - 16)*(4*r - 1)/3
Factor 5*t**4 + 20*t**3 - 21 - 90*t**2 - 15*t + 150*t + 6*t - 14 - 41*t.
5*(t - 1)**3*(t + 7)
Let d(z) = z**3 - 3*z**2 - 11*z + 48. Let b be d(5). Solve 5*n**2 - b*n + 9*n + 15*n - 50 + 4*n = 0 for n.
-2, 5
Let p(h) be the third derivative of 0*h + 0 - 1/180*h**6 + 5*h**2 + 1/6*h**4 - 1/60*h**5 + 1/2*h**3. Let r(t) be the first derivative of p(t). Factor r(m).
-2*(m - 1)*(m + 2)
Let y(m) = 6*m**5 + 32*m**4 + 104*m**3 + 216*m**2 + 154*m - 4. Let c(v) = v**5 + 2*v**4 - v**3 - 2*v - 1. Let k(z) = 4*c(z) - y(z). Factor k(r).
-2*r*(r + 3)**4
Factor 3554/13*p - 1420/13 - 10/13*p**2.
-2*(p - 355)*(5*p - 2)/13
Suppose 7442 - 5*y**3 + 3*y**3 + 3*y**3 + 124*y**2 + 513*y + 3452*y = 0. What is y?
-61, -2
Factor -28/11*u + 2/11*u**3 - 2/11*u**2 + 48/11.
2*(u - 3)*(u - 2)*(u + 4)/11
Suppose 5*g - 4*d = -1557, -2*g - 17*d + 15*d - 612 = 0. Let n = -309 - g. Let 2/3*p**3 + 0*p**4 - 1/3*p + n*p**2 - 1/3*p**5 + 0 = 0. Calculate p.
-1, 0, 1
Let y(b) be the second derivative of b**7/42 + 9*b**6/10 + 177*b**5/20 + 277*b**4/12 + 21*b**3 + 3*b + 1463. Factor y(j).
j*(j + 1)**2*(j + 7)*(j + 18)
Factor 116*l**3 - 189224*l**2 + 94473*l**2 + 16 + 94535*l**2 + 84*l.
4*(l - 1)**2*(29*l + 4)
Suppose 0 = 4*n - 15 - 9. Let k be n/((15/(-5))/(-3)). Solve -13*q**2 + 26*q**2 + k*q - 9 - 14*q**2 = 0.
3
Let o = -119/900 - -319/900. Factor 2/3*f - 4/9 - o*f**2.
-2*(f - 2)*(f - 1)/9
Let q(t) be the first derivative of -t**3/2 - 387*t**2/4 - 750*t + 3762. Factor q(m).
-3*(m + 4)*(m + 125)/2
Let f be -13 - ((-102)/6 - -2). Let i(p) be the second derivative of 0*p**f + 3/100*p**5 - 24*p - 1/20*p**4 - 1/5*p**3 + 0. Factor i(l).
3*l*(l - 2)*(l + 1)/5
Let r(u) be the first derivative of -116/9*u**3 + 0*u - 63 - 841/3*u**2 - 1/6*u**4. Factor r(j).
-2*j*(j + 29)**2/3
Let p(y) be the third derivative of y**8/5040 + 2*y**7/315 + 7*y**6/180 - 23*y**5/60 + 242*y**2. Let t(h) be the third derivative of p(h). Factor t(z).
4*(z + 1)*(z + 7)
Let j(f) be the third derivative of 9*f**7/70 + f**6/4 + 2*f**5/15 + 873*f**2. Factor j(s).
s**2*(3*s + 2)*(9*s + 4)
Let f(p) be the first derivative of p**3 - 39*p**2 - 168*p + 520. Factor f(i).
3*(i - 28)*(i + 2)
Let w(t) be the first derivative of t**4/18 + 196*t**3/9 + 2368*t**2 - 87616*t/9 + 3535. What is j in w(j) = 0?
-148, 2
Let z be (-6567)/(-4776) + ((-140)/(-32))/7. Factor 90/11 + 102/11*o**z + 6/11*o**3 + 186/11*o.
6*(o + 1)**2*(o + 15)/11
Let d = -21691 + 21694. Find y such that -1/2*y + 13/4*y**2 - y**5 + 17/4*y**4 + 0 - 6*y**d = 0.