*w**2 + 36*w + 24*w**4 + 4*w**5 + 0 + 8 + w**2 + 12*w**2 + 56*w**3.
4*(w + 1)**4*(w + 2)
Factor -70*o - 10*o**2 - 8*o**3 + 11*o**3 + 144 - 17*o**2 - 4*o - 46*o.
3*(o - 12)*(o - 1)*(o + 4)
Let a(t) be the second derivative of 3*t**5/70 + 821*t**4/14 + 3272*t**3/7 + 9804*t**2/7 - 7820*t. Factor a(c).
6*(c + 2)**2*(c + 817)/7
Let u(r) be the first derivative of r**4 - 4*r**3 - 2*r**2 + 12*r - 3773. Factor u(w).
4*(w - 3)*(w - 1)*(w + 1)
Let x(z) be the first derivative of -z**6/2160 - z**5/45 - 7*z**4/36 + 20*z**3/3 - 118. Let u(a) be the third derivative of x(a). Factor u(g).
-(g + 2)*(g + 14)/6
Let j(a) be the second derivative of 3*a**5/20 - a**4 + 3*a**3/2 + 3035*a. Factor j(o).
3*o*(o - 3)*(o - 1)
Let n(g) be the first derivative of -2*g**5/75 + 49*g**4/6 - 4428*g**3/5 + 531196*g**2/15 + 1102736*g/15 + 1257. Suppose n(z) = 0. What is z?
-1, 82
Let m = -360 + 265. Let u = m + 100. Factor 27/2*w**3 + 3/2*w**u + 0 + 3*w - 15/2*w**4 - 21/2*w**2.
3*w*(w - 2)*(w - 1)**3/2
Determine r, given that -111 + 5*r**3 + 167 - 16*r - 72 + 3*r**5 + 8*r**2 - r**4 - 4*r**5 + 3*r**3 = 0.
-2, -1, 2
Suppose 2*r - 11*n = -7*n + 18, -2*n - 10 = 0. Let o be (1 - r)*36/126. Factor 0 + 0*s - o*s**2 + 2/7*s**3.
2*s**2*(s - 2)/7
Factor 20*c**2 - 1678*c**4 - 8*c**3 + 19*c + 5*c + 3361*c**4 - 1687*c**4.
-4*c*(c - 2)*(c + 1)*(c + 3)
Let v(l) be the first derivative of -3*l**4/20 + 6*l**3/5 + 24*l**2/5 - 288*l/5 + 11831. Suppose v(o) = 0. What is o?
-4, 4, 6
Let p(d) be the third derivative of 4/3*d**3 - 1/12*d**4 + 1/240*d**6 + 0 + 3*d - 14*d**2 - 1/30*d**5. Factor p(x).
(x - 4)*(x - 2)*(x + 2)/2
Let p(u) be the third derivative of 1/735*u**7 + 0 - 24*u**2 + 9/7*u**3 + 1/210*u**6 - 2/35*u**5 + 0*u - 3/14*u**4. Factor p(q).
2*(q - 3)*(q - 1)*(q + 3)**2/7
Let c(t) = -23*t**2 + 170*t + 409. Let j(n) = -4*n**2 + 34*n + 82. Let x(h) = 4*c(h) - 22*j(h). Factor x(r).
-4*(r + 3)*(r + 14)
Let j(i) = 2*i**2 + 43*i + 23. Let x be 4 - (-6 + -6 + 38 + -1). Let a be j(x). Factor 16*c**3 - 1/2 - 12*c**a + 4*c - 8*c**4.
-(2*c - 1)**4/2
Let s(d) = 2*d**4 - 32*d**3 + 172*d**2 - 380*d + 280. Let h(b) = b**2 - b + 2. Let l(q) = -4*h(q) - s(q). Factor l(k).
-2*(k - 6)**2*(k - 2)**2
Suppose h + 16 = -4*o, 8*o = h + 5*o + 23. Let z = 39 + h. Suppose 900*x**4 - 76*x**2 - 115 + 1448*x**3 + 144*x**5 - 135*x - 48 + z - 537*x = 0. What is x?
-3, -2/3, -1/4, 2/3
Let l(n) = -3*n**2 + 166*n - 975. Let c(j) = 8*j**2 - 416*j + 2436. Let d(h) = -5*c(h) - 12*l(h). Factor d(g).
-4*(g - 12)*(g - 10)
Suppose -45369*j - 110 = -45424*j. Factor 1/3 - 8/3*y**j - 2/3*y**3 + 5/9*y**4 - 10/9*y.
(y - 3)*(y + 1)**2*(5*y - 1)/9
Let q(h) be the first derivative of 87/10*h**5 + 95 + 9/4*h**6 + 99/8*h**4 + 15/2*h**3 + 0*h + 3/2*h**2. Suppose q(k) = 0. What is k?
-1, -2/9, 0
Let x(a) = 7*a. Let h(n) = -123*n + 531. Let l(k) = h(k) + 5*x(k). Let j be l(6). Factor 2/7*f**5 + 12/7*f - 38/7*f**2 + 6*f**j + 0 - 18/7*f**4.
2*f*(f - 6)*(f - 1)**3/7
Let t(w) be the third derivative of w**5/4 + 125*w**4/24 + 20*w**3/3 - 1084*w**2. Suppose t(l) = 0. Calculate l.
-8, -1/3
Let d(r) be the second derivative of 3*r**5/80 - 5*r**4/16 - 7*r**3/4 + 27*r - 1. Suppose d(n) = 0. Calculate n.
-2, 0, 7
Let m be (-2 - (-2951)/1326) + (-1)/6. Let z = 259/68 - m. Determine q, given that -z*q**3 - 3 + 21/4*q**2 + 6*q = 0.
-1, 2/5, 2
Let h(c) = c**2 + 12*c + 1. Suppose 4 = -4*w, 2*r + 2*r + w = 127. Let k(y) = -17*y - 11*y + r*y. Let o(s) = 2*h(s) - 7*k(s). What is j in o(j) = 0?
1
Suppose -r + 4*z = 4, -z - 2*z = r - 3. Let c be ((-4)/(-12))/((4 - r)/36). Factor 9*l**2 - 3*l**2 + 2*l**3 - 18*l**c - 4*l + 14*l**2.
-4*l*(l - 1)*(4*l - 1)
Let 151/4*i**4 - 59/2*i + 4 + 17/4*i**5 + 101/4*i**3 - 167/4*i**2 = 0. Calculate i.
-8, -1, 2/17, 1
Let a(w) = -2*w**2 - 207*w - 4410. Let d be a(-30). Factor 1/3*x**3 + d*x + 0 - 5*x**2.
x**2*(x - 15)/3
Let n = 17 - -54. Let i = n + -69. Find d, given that 6 + 18 + 5*d**i + 20*d - 9 = 0.
-3, -1
Let q(z) = 27*z - 72. Let d be q(8). Factor -2*o**3 - 7*o**2 + 19*o**2 + 55 + 18*o**2 - d*o + 169.
-2*(o - 7)*(o - 4)**2
Let p(r) be the first derivative of -147*r**5/5 + 3129*r**4/4 + 2316*r**3 - 13632*r**2 + 17664*r - 1721. Suppose p(q) = 0. What is q?
-4, 8/7, 23
Let f be (189 - 189)*(0 - (-1)/2). Let v be f - (-13)/((-39)/(-6)). Factor 6/11*j + 2/11*j**v - 8/11.
2*(j - 1)*(j + 4)/11
Suppose 2*s = -219 - 187. Let r = s + 203. Factor -n**2 + r + 0*n - 1/2*n**4 + 11/6*n**3.
-n**2*(n - 3)*(3*n - 2)/6
Let v be (-2)/5 + 16601/65. Let t = v - 253. Factor 0 - 3/4*z - 1/4*z**3 + z**t.
-z*(z - 3)*(z - 1)/4
Let c(s) = s**3 - 18*s**2 - 63*s + 11. Let i be c(21). Suppose 11*v = i + 33. Find a such that 2*a**4 - 5*a**3 + a**3 - 39*a**2 + 37*a**2 + v*a = 0.
-1, 0, 1, 2
Let -1389/8*t - 27/8*t**3 + 2097/8*t**2 + 231/8 = 0. Calculate t.
1/3, 77
Let q(f) be the second derivative of 34*f + 3 + 35/12*f**4 - 75/2*f**2 - 35/6*f**3 - 1/4*f**5. Factor q(j).
-5*(j - 5)*(j - 3)*(j + 1)
Let x(u) be the third derivative of -1/4*u**4 + 1/15*u**6 + 0 - 4/15*u**5 - 2*u**2 + 3*u**3 - u. Suppose x(o) = 0. Calculate o.
-1, 3/2
Factor 204897 - 3357 + 272780 + 5*n**2 - 3080*n.
5*(n - 308)**2
Let d = 4/45 + 26/45. Let s = 171265 + -171263. Factor -d*j**2 - 4/3 - s*j.
-2*(j + 1)*(j + 2)/3
Suppose c - 5*c = 3*l - 12, -5*c + 20 = 5*l. Suppose -l*o - 206 + 214 = 0. Factor 16*y**o + y - 17*y**2 + 0*y + 6 - 4.
-(y - 2)*(y + 1)
Factor 2684/3 + 2680/3*j - 4/3*j**2.
-4*(j - 671)*(j + 1)/3
Factor -12213 + p**3 + 11973 + 10*p**2 - 46*p - 16*p**2 + 45*p**2.
(p - 3)*(p + 2)*(p + 40)
Let t(c) be the first derivative of c**5/10 - 47*c**4/8 + 263*c**3/3 + 168*c**2 - 576*c + 1624. What is a in t(a) = 0?
-2, 1, 24
Let c(q) = 2*q**3 - 21*q**2 - 9*q + 4. Let z be c(11). Let v = 42 - z. Solve v*a**4 - 11*a**3 + 2*a**2 - 7*a**5 - 8*a**5 + 8*a**5 = 0 for a.
0, 2/7, 1
Let i = -789 - -800. Suppose -i*y + 335 = 302. Factor -1/3*d**y - 175/9*d - 44/9*d**2 - 98/9.
-(d + 7)**2*(3*d + 2)/9
Factor 4965/7*p - 8550/7 + 1/7*p**4 - 323/7*p**2 - 13/7*p**3.
(p - 15)**2*(p - 2)*(p + 19)/7
Let a = -1159574/33 + 105460/3. Factor -306/11*c + a*c**2 + 150/11 - 6/11*c**3.
-6*(c - 25)*(c - 1)**2/11
Let k = 5 - 1. Let v be (-1 + 2)/(2 - 7/k). Solve 2*l + 38*l**v + 0 - 39*l**4 + 1 - 2*l**3 = 0.
-1, 1
Let s(a) be the first derivative of 102 - 8*a**2 + 0*a + 8/3*a**3 + a**4 - 2/5*a**5. Factor s(g).
-2*g*(g - 2)**2*(g + 2)
Suppose -10 = 5*l + 2*m, -39*l + 37*l - m = 5. Suppose 2 + l + 264*d + 19*d**3 - 6 - 2*d**5 - 276*d + d**2 - 2*d**5 = 0. What is d?
-2, -1/2, 1, 2
Let t(f) = 16*f**4 + 2624*f**3 + 10348*f**2 + 12888*f + 5141. Let o(k) = 5*k**4 + 874*k**3 + 3449*k**2 + 4296*k + 1714. Let d(b) = 7*o(b) - 2*t(b). Factor d(c).
3*(c + 1)**2*(c + 2)*(c + 286)
Factor -156 + 73/7*z**2 - 404/7*z + 1/7*z**3.
(z - 7)*(z + 2)*(z + 78)/7
Let r(p) = -p**2 + p + 2. Let c(m) be the second derivative of m**4/2 + 7*m**3/2 - 33*m**2/2 + 67*m. Let i(y) = -c(y) - 3*r(y). Factor i(u).
-3*(u - 1)*(u + 9)
Let n be 156/(-520)*(3/(63/(-392)) - 0). What is j in -12/5 + j**2 + n*j = 0?
-6, 2/5
Let b(u) be the first derivative of -4*u**5/15 - 112*u**4/3 - 2564*u**3/9 - 1060*u**2/3 + 1389. Let b(z) = 0. Calculate z.
-106, -5, -1, 0
Let s = -31538 - -31568. Let a(f) be the first derivative of -8/3*f**3 + s + 0*f**2 - f**4 + 0*f. Suppose a(d) = 0. Calculate d.
-2, 0
Let q(u) be the second derivative of u**7/1260 - 17*u**6/360 + u**5/2 + u**4/6 - 39*u**2/2 - 2*u - 6. Let z(d) be the third derivative of q(d). Factor z(y).
2*(y - 15)*(y - 2)
Let s = 323 + -316. Factor -4*g - 15*g**2 - s*g - 9*g + 10*g.
-5*g*(3*g + 2)
Suppose -2275*h + 2232*h + 129 = 0. Let k(b) be the first derivative of 2/5*b**h - 24/5*b + 9/5*b**2 - 29. Factor k(v).
6*(v - 1)*(v + 4)/5
Let h(d) be the third derivative of d**8/1008 - d**7/18 - 13*d**6/30 + 1511*d**2. Factor h(u).
u**3*(u - 39)*(u + 4)/3
Let c(w) be the second derivative of w**6/45 - 11*w**5/120 - w**4/24 + 6*w - 66. Factor c(o).
o**2*(o - 3)*(4*o + 1)/6
Let x be (-20*65/286 - 12/(-8)*2)*-16. Let -2/11*f**2 - x*f - 9248/11 = 0. Calculate f.
-68
Solve -3645*l**3 - 2*l**5 - 3817*l**3 - 352*l + 7636*l**3 - 8*l**4 + 188*l**2 = 0.
-11, -2, 0, 1, 8
Let q(n) = -219*n - 219. Let a be q(-1). Let y(s) be the second derivative of 1/16*s**4 + 0*s**2 + 9/80*s**5 - 1/4*s**3 + a - s. Factor y(c).
3*c*(c + 1)*(3*c - 2