18
Let l(a) = -a**4 - 3*a**2 - a + 3. Let u(j) = 7*j**4 - 39*j**3 + 177*j**2 - 221*j - 12. Let x(d) = 4*l(d) + u(d). Factor x(o).
3*o*(o - 5)**2*(o - 3)
Let s(p) = p**3 - 21*p + 2. Let m(o) = -o**2 - o - 1. Let r = -44 + 43. Let k(z) = r*s(z) + 6*m(z). Factor k(v).
-(v - 1)**2*(v + 8)
Suppose 2212*x - 18 = 2206*x. Let v(g) be the third derivative of -1/5*g**5 - 4/3*g**3 + 0 - 7/6*g**4 - x*g**2 + 0*g. Let v(w) = 0. What is w?
-2, -1/3
Let t(x) be the second derivative of 5*x**4/6 - 22*x**3 + 13*x**2 + 567*x. Factor t(j).
2*(j - 13)*(5*j - 1)
Let q = 197790/7 - 28254. Solve 8/7 + q*f + 4/7*f**2 = 0 for f.
-2, -1
Factor -1/4*t**4 - 95/4*t - 13/4*t**3 - 25/2 - 57/4*t**2.
-(t + 1)*(t + 2)*(t + 5)**2/4
Factor 81*g**2 - 2*g**4 - 26*g**3 + 51*g**2 - 16*g**2 + 19 + 138*g**3 - 133 - 112*g.
-2*(g - 57)*(g - 1)*(g + 1)**2
Let c be (6/4)/(-7 - (-7634)/1091). Let f = c + 547. Factor 1/2*p**3 + f*p + 0 + 2*p**2.
p*(p + 1)*(p + 3)/2
Let v(u) = -889*u**2 + 411*u + 1098. Let o(x) = -197*x**2 + 103*x + 274. Let s(i) = 9*o(i) - 2*v(i). Factor s(g).
5*(g + 3)*(g + 18)
Let y = 588 - 588. Let v(r) be the second derivative of -1/210*r**7 + 1/50*r**5 + 0 + 0*r**2 + 0*r**6 - 1/30*r**3 + 2*r + y*r**4. Factor v(s).
-s*(s - 1)**2*(s + 1)**2/5
Let b(n) be the third derivative of 0*n + 6 - 6/17*n**4 + 432/17*n**3 + 7*n**2 + 1/510*n**5. Solve b(i) = 0 for i.
36
Let s(m) be the second derivative of m**6/330 + 8*m**5/55 + 13*m**4/66 - 76*m**3/33 + 93*m**2/22 + 13*m + 16. Find a, given that s(a) = 0.
-31, -3, 1
Let u = -11708/455 - -336/13. Let c(j) be the first derivative of -5 + 0*j + 3/14*j**4 - 8/21*j**3 - 4/7*j**2 + u*j**5 - 1/21*j**6. Factor c(d).
-2*d*(d - 2)**2*(d + 1)**2/7
Let u(q) be the third derivative of -q**6/80 - 7*q**5/15 - 35*q**4/48 + 3*q**3/2 - 78*q**2 - 2*q. Solve u(o) = 0 for o.
-18, -1, 1/3
Let m(j) be the first derivative of 0*j - 45 + 28/9*j**3 - 4*j**2 - 1/3*j**4. Factor m(s).
-4*s*(s - 6)*(s - 1)/3
Let f(d) be the third derivative of d**8/2688 + d**7/420 - 7*d**5/240 - 17*d**4/192 - d**3/8 - 362*d**2. Let f(s) = 0. What is s?
-3, -1, 2
Let t be (-12)/3*6/(5 + -11). Suppose -2/13*b**5 + 0 - 6/13*b**3 + 0*b - 2/13*b**2 - 6/13*b**t = 0. What is b?
-1, 0
Let y be ((-4)/1)/(3*(-116)/435). Let k(n) be the second derivative of -3/20*n**y + 9*n - 17/4*n**4 - 96*n**2 - 40*n**3 + 0. Factor k(q).
-3*(q + 1)*(q + 8)**2
Let f(x) be the second derivative of x**7/70 - x**6/15 - x**5/50 + 4*x**4/15 - x**3/30 - 3*x**2/5 + 11*x + 24. Determine k so that f(k) = 0.
-1, -2/3, 1, 3
Let d be ((1 - -1)*-72)/1. Let v = 146 + d. Factor 2*h**4 + 185*h**3 - 6*h**v - 185*h**3 - 4*h.
2*h*(h - 2)*(h + 1)**2
Factor 16/3*m**2 - 20/3*m**3 + 124/3*m + 8.
-4*(m - 3)*(m + 2)*(5*m + 1)/3
Let a(z) be the first derivative of 7*z**4/4 - 258*z**3 + 1542*z**2/7 - 440*z/7 - 863. Suppose a(k) = 0. Calculate k.
2/7, 110
Let i be 20/90 + 295934/504. Let m = 2377/4 - i. Suppose 24/7*h**2 + 32/7 + m*h + 4/7*h**3 = 0. Calculate h.
-2
Let y(q) be the first derivative of -2*q**3/39 + 372*q**2/13 + 746*q/13 - 224. What is p in y(p) = 0?
-1, 373
Suppose 0 = 90*t - 89*t - 3. Let i(p) be the second derivative of 0*p**2 + 0 + 1/10*p**4 - 9/100*p**5 + t*p + 0*p**3 + 1/50*p**6. Factor i(r).
3*r**2*(r - 2)*(r - 1)/5
Let g = 173805 - 173803. Factor 1/2*j**g + 1/3*j + 0 + 1/6*j**3.
j*(j + 1)*(j + 2)/6
Let g(k) be the second derivative of -k**5/5 + 13*k**4/18 + k**3/3 - 10*k**2/3 + 316*k - 3. Factor g(t).
-2*(t - 2)*(t - 1)*(6*t + 5)/3
Let h(j) be the third derivative of 0 + 0*j**4 + 11*j**2 + 0*j**3 + 2/3*j**5 + 6*j + 1/10*j**6. Factor h(m).
4*m**2*(3*m + 10)
Let x(v) be the third derivative of -23*v**5/120 + 61*v**4/144 + 2*v**3/9 - 3*v**2 + 129*v. Factor x(m).
-(m - 1)*(69*m + 8)/6
Let k(t) = -t**2 - t. Let b(g) = 1764*g**5 + 2100*g**4 + 352*g**3 + 11*g**2 - 5*g. Let x(v) = b(v) - 5*k(v). Factor x(m).
4*m**2*(m + 1)*(21*m + 2)**2
Let 449/5*l + 3/5*l**2 + 0 = 0. What is l?
-449/3, 0
What is y in -10*y - 23/6*y**2 + 1/6*y**4 + y**3 - 16/3 = 0?
-8, -1, 4
Let f(v) be the first derivative of -3*v**4/4 - 5*v**3 + 9*v**2 - 149. Factor f(y).
-3*y*(y - 1)*(y + 6)
Let b(y) be the second derivative of y**7/231 - 6*y**6/11 + 2699*y**5/110 - 4485*y**4/11 - 900*y**3/11 + 27000*y**2/11 + 934*y. Suppose b(l) = 0. What is l?
-1, 1, 30
Let b = -72576 - -72580. Factor 2*m**3 - 1 - 3/2*m - 1/2*m**5 + m**2 + 0*m**b.
-(m - 2)*(m - 1)*(m + 1)**3/2
Let p(o) be the second derivative of o**7/378 + 19*o**6/270 - 37*o**5/180 - 355*o**4/108 - 50*o**3/9 + 4*o - 951. Solve p(v) = 0.
-20, -3, -1, 0, 5
Let a(j) be the first derivative of 4*j**3/3 - 1864*j**2 + 868624*j + 906. Solve a(n) = 0 for n.
466
Suppose 5*q**2 + 12*q**3 - 23*q**2 - 335 - 2*q**4 + 5*q + 335 + 3*q = 0. Calculate q.
0, 1, 4
Let q(j) = -3 + 2 - 2*j**2 + j**2 + j**3. Let r(p) = -16*p - 20*p**3 + 33 - 3*p**2 + 23*p**2 + 22*p + 14*p - 5. Let g(h) = 16*q(h) + r(h). Factor g(n).
-4*(n - 3)*(n + 1)**2
Let n(i) be the second derivative of 5*i**6/24 + 17*i**5/4 + 225*i**4/8 + 125*i**3/6 - 95*i**2/2 - 181*i. Let c(v) be the first derivative of n(v). Factor c(l).
5*(l + 5)**2*(5*l + 1)
Let j(f) be the third derivative of -f**6/480 - 101*f**5/30 + 1619*f**4/96 - 135*f**3/4 - 8*f**2 + 127*f. Let j(m) = 0. Calculate m.
-810, 1
Let h(f) = -2*f**4 + 148*f**3 + 6*f**2 - 148*f + 2. Let k(q) = q**4 - 148*q**3 - 7*q**2 + 148*q - 3. Let u(p) = 3*h(p) + 2*k(p). Suppose u(r) = 0. What is r?
-1, 0, 1, 37
Let t = 113427 - 113427. Factor 1/5*z**3 + t*z + 0*z**2 + 0.
z**3/5
Let u(i) be the second derivative of i**4/108 + 191*i**3/54 - 32*i**2/3 + 96*i - 2. Factor u(s).
(s - 1)*(s + 192)/9
Let j(p) = -4*p**4 + 7*p**3 - 14*p**2 + 5*p - 3. Let n(o) = o**4 + o**2 + 1. Let k = -584 - -569. Let m(i) = k*n(i) - 5*j(i). Factor m(u).
5*u*(u - 5)*(u - 1)**2
Suppose 19 - 9 = 5*k. Factor 3 + 28*m**3 - 14*m**3 - 3*m**4 + 9*m + 12*m**3 - 15*m**4 - 45*m**k + 25*m**3.
-3*(m - 1)**3*(6*m + 1)
Let a(t) = 2*t**2 - 9*t - 1. Let k be a(5). Let s be (3/k*(-9 + -15))/(-10). Factor -s - 3*x**2 + 3/5*x**3 + 21/5*x.
3*(x - 3)*(x - 1)**2/5
Let c(x) = -3*x**3 + 10*x + 4. Let p be c(-3). Let s = p - 437/8. Factor -s*o**5 - 3/8*o**3 + 0*o**2 + 0 + 3/4*o**4 + 0*o.
-3*o**3*(o - 1)**2/8
Let o(d) be the first derivative of 5/2*d**2 + 8/3*d**3 - 17 - 14*d + 1/4*d**4. Factor o(z).
(z - 1)*(z + 2)*(z + 7)
Let v(l) be the first derivative of -l**4/4 - 3*l**3 + 1169. Factor v(o).
-o**2*(o + 9)
Let z(p) be the second derivative of -1/6*p**6 + 5/12*p**4 + 0*p**2 + 1/4*p**5 - 5/6*p**3 - p + 11. Factor z(y).
-5*y*(y - 1)**2*(y + 1)
Let s(l) be the third derivative of l**6/24 + 103*l**5/12 + 620*l**4 + 13440*l**3 + 850*l**2 - l. Factor s(p).
5*(p + 7)*(p + 48)**2
Let t be 2*(1 - 0)*14/35. Suppose o = 5*g + 6*o + 5, 4*o + 18 = 3*g. Let 4/5*j + t*j**g + 0 = 0. Calculate j.
-1, 0
Let a be (32/10)/(-4)*(-168)/2016. Let s(w) be the third derivative of -8/15*w**3 - a*w**5 - 1/150*w**6 + 0 - 4/15*w**4 - w**2 + 0*w. Find o such that s(o) = 0.
-2, -1
Let n(t) be the second derivative of -t**6/10 + 3*t**5/10 + 37*t**4/4 + 41*t**3 + 72*t**2 + t - 1350. Let n(y) = 0. What is y?
-3, -2, -1, 8
Let a(m) be the first derivative of m**4/9 - m**3/2 + m**2/3 - 15*m - 31. Let j(l) be the first derivative of a(l). What is k in j(k) = 0?
1/4, 2
Let o(i) be the first derivative of -2*i**6/3 - 8*i**5 + 335*i**4 + 4560*i**3 - 56160*i**2 - 1168128*i - 1194. Factor o(n).
-4*(n - 13)**2*(n + 12)**3
Find i such that -7608*i**3 + 14470416*i**2 + 3/2*i**4 + 3877647022464 - 12232324992*i = 0.
1268
Let s(a) be the second derivative of 5*a**7/42 - 14*a**6/3 + 25*a**5 - 40*a**4 - 3*a + 296. Factor s(j).
5*j**2*(j - 24)*(j - 2)**2
Let j(k) be the third derivative of k**5/30 - k**4/4 - 60*k**3 + 22*k**2 + 41*k. Let j(p) = 0. Calculate p.
-12, 15
Let x(j) = -8*j**2 + 75*j - 86. Let a be x(8). Let h(c) be the second derivative of 1/4*c**a + 0 + 1/24*c**3 + 43*c - 1/16*c**4. Determine z so that h(z) = 0.
-2/3, 1
Suppose -46*k + 6 = -43*k. Factor 32*w**k + 4*w**4 + 3 - 14*w - 20*w**3 + 2*w - 4*w - 3.
4*w*(w - 2)**2*(w - 1)
Let g(p) be the third derivative of p**5/15 - 30*p**4 + 358*p**3/3 - 1218*p**2. Factor g(d).
4*(d - 179)*(d - 1)
Let m = 273515 + -1367548/5. Let -9/5*w - 3*w**2 - 3/5*w**3 + m = 0. Calculate w.
-3, 1
Suppose 0 = 2*j + 6, -3*c + 0*j = 3*j - 18. Suppose -c*f + 