 1, 2
Let k(q) = q**3 - 15*q**2 - 65*q - 9. Let d be k(19). Factor -5309 + 1084 - 4*p**2 + d*p + 208*p - 6179.
-4*(p - 51)**2
Let l(j) be the first derivative of -4*j**3/3 + 632*j**2 - 2512*j + 2087. Determine r, given that l(r) = 0.
2, 314
Let w be ((-51)/6 + 2)*312/(-3). Factor -3*f**3 - 93*f**3 - 8*f**3 + w*f**2 + 4*f**4.
4*f**2*(f - 13)**2
Determine t so that -2/9*t**2 - 64/9*t + 64/9*t**3 + 2/9*t**4 + 0 = 0.
-32, -1, 0, 1
Let 2803 - 1600*b + 3*b**2 + 2*b**2 + 1713 - 1336 = 0. What is b?
2, 318
Let f(v) be the second derivative of v**5/4 + 175*v**4/12 + 340*v**3 + 3960*v**2 - 1704*v. Factor f(c).
5*(c + 11)*(c + 12)**2
Let t(g) be the second derivative of g**7/63 + 71*g**6/45 + 911*g**5/15 + 9817*g**4/9 + 67873*g**3/9 - 89401*g**2/3 + 8358*g. Determine j, given that t(j) = 0.
-23, -13, 1
Let v(g) be the third derivative of -4*g - 1/27*g**4 + 0 - 1/270*g**5 + 3*g**2 + 5/27*g**3. Factor v(c).
-2*(c - 1)*(c + 5)/9
Let o(b) = 9*b**3 + 135*b**2 - 279*b + 135. Let p(i) = -26*i**3 - 404*i**2 + 835*i - 405. Let q(h) = 17*o(h) + 6*p(h). Factor q(z).
-3*(z - 1)**2*(z + 45)
Let j = 203 + -178. Suppose -27 = -26*k + j. Determine w so that 0 - 1/7*w - 1/7*w**3 - 2/7*w**k = 0.
-1, 0
Let m(z) be the first derivative of -3*z**5/5 - 549*z**4/2 - 34213*z**3 - 198738*z**2 - 393132*z + 362. Factor m(b).
-3*(b + 2)**2*(b + 181)**2
Let v be 4 + -13 + (-410)/(-2). Suppose 113*b - v - 11*b - 6*b**2 + 2*b**2 + 98*b = 0. Calculate b.
1, 49
Let i be -2 - (-308)/165 - ((-390)/225 - 2/5). Factor 12 + 27/2*c + 3/2*c**i.
3*(c + 1)*(c + 8)/2
Determine j so that -212*j**2 - 93*j**2 - 490*j + 145 - 245 - 70*j - 25*j**3 = 0.
-10, -2, -1/5
Let a(j) = j**4 - j**3 + j**2 + 1. Let l = -68 - -79. Let x(p) = -3*p + p + 90*p**3 - 79*p**3 - 9 - 7*p**4 - l*p**2. Let h(k) = -18*a(k) - 2*x(k). Factor h(s).
-4*s*(s - 1)*(s + 1)**2
Suppose -o + 2*o = 280. Suppose 3*x = -4*x + o. Factor 23 + 22 - 5*c**2 - x.
-5*(c - 1)*(c + 1)
Let h(n) = 16*n**2 + 111*n + 489. Let j(u) = -3*u**2 - 22*u - 98. Let r = 77 - 110. Let o(d) = r*j(d) - 6*h(d). What is x in o(x) = 0?
-10
Suppose -9085 - 5115 = -309*q + 4830 - 1417. Find p, given that 54*p**3 - 100/3*p - q*p**2 - 4 = 0.
-2/9, 3/2
Let l be (-954)/(-1590)*20/6. Suppose -c - c = 0. Factor 2/17*b**4 + 0*b**l + c + 0*b + 0*b**3.
2*b**4/17
Let v(a) be the first derivative of -3*a**5/5 + 21*a**4/2 - 69*a**3 + 210*a**2 - 300*a - 152. Suppose v(m) = 0. Calculate m.
2, 5
Let s(w) be the second derivative of -w**4/3 + 70*w**3/3 + 400*w**2 + 1415*w + 2. Determine v so that s(v) = 0.
-5, 40
Let d = -501471 + 501475. Factor 0*t - 6*t**2 + 9/2*t**3 + 3/2*t**d + 0.
3*t**2*(t - 1)*(t + 4)/2
Let i(p) be the first derivative of -15/2*p**4 + 24 - p**5 - 15*p**3 - 10*p**2 + 0*p. Factor i(m).
-5*m*(m + 1)**2*(m + 4)
Let q be (-1)/((-14)/4) - (-260)/70. Suppose 5*s = q*r - 0*s - 64, -4*r - 4*s + 64 = 0. Factor -8*a**2 + 5*a**2 + 4*a - r*a + 6*a**2.
3*a*(a - 4)
Let l(w) = w**3 + 442*w**2 + 71158*w + 3652264. Let r(o) = -o**3 - 446*o**2 - 71156*o - 3652264. Let a(z) = 4*l(z) + 5*r(z). Factor a(x).
-(x + 154)**3
Let c = -1798 - -1798. Let q(i) be the second derivative of c + 5/3*i**3 - 1/6*i**4 + 22*i + 0*i**2. Factor q(n).
-2*n*(n - 5)
Let h(o) = 8*o**2 - 10352*o + 6708228. Let z(f) = -23*f**2 + 31058*f - 20124652. Let s(u) = -11*h(u) - 4*z(u). Factor s(l).
4*(l - 1295)**2
Let d(s) be the second derivative of -1/84*s**4 + 271*s - 504*s**2 + 0 + 4*s**3. Factor d(p).
-(p - 84)**2/7
Let a(b) = -4*b**2 - 440*b - 1308. Let c(w) = 4*w**2 + 438*w + 1306. Let i(d) = 7*a(d) + 6*c(d). Factor i(f).
-4*(f + 3)*(f + 110)
Let a = -48659/44 - -4425/4. Factor -2/11*w**5 - 2/11*w**3 + 0*w + 0*w**2 + 0 - a*w**4.
-2*w**3*(w + 1)**2/11
Let g = 114/161 - 250/483. Let s(z) be the second derivative of -g*z**3 - 2/35*z**5 - 1/7*z**2 + 41*z - 1/105*z**6 + 0 - 1/7*z**4. Factor s(h).
-2*(h + 1)**4/7
Let a(g) be the first derivative of 3*g**5/20 + 249*g**4/32 - 11*g**3/2 - 249*g**2/16 + 63*g/4 - 582. What is d in a(d) = 0?
-42, -1, 1/2, 1
Determine f, given that -57/7 - 16/7*f + 1/7*f**2 = 0.
-3, 19
Let n(t) be the second derivative of t**5/20 + 19*t**4/2 - t**3/6 - 57*t**2 + 357*t. Factor n(d).
(d - 1)*(d + 1)*(d + 114)
Let v(s) = -2172*s + 10862. Let o be v(5). Factor 18/7*q + 6/7*q**3 - 20/7*q**o - 4/7.
2*(q - 2)*(q - 1)*(3*q - 1)/7
Suppose 2*w - 8 = 0, 5*d + 6 = 3*w - 6. Suppose -4*n - x + 3 + d = 0, 5*n + 3*x = 9. Factor 0*k**2 + 0*k - 2/13*k**3 + 2/13*k**5 + n*k**4 + 0.
2*k**3*(k - 1)*(k + 1)/13
Let o(w) be the first derivative of -w**5/5 + 7*w**4/3 + 2*w**3/3 - 14*w**2 + 3*w - 98. Let m(l) be the first derivative of o(l). Factor m(x).
-4*(x - 7)*(x - 1)*(x + 1)
Let g(n) be the third derivative of 5*n**7/42 + 59*n**6/12 + 31*n**5 - 2555*n**4/3 + 3920*n**3/3 + 386*n**2. Solve g(y) = 0.
-14, 2/5, 4
Let a(r) be the first derivative of 3*r**4/4 - 28*r**3 + 573*r**2/2 - 1140*r + 4293. Determine i, given that a(i) = 0.
4, 5, 19
Let f(k) = -63*k - 250. Let o be f(-4). Factor 11027 - 6306 + o*g**2 + 332*g + 9057.
2*(g + 83)**2
Suppose 2/15*v**2 + 184/15*v + 238/3 = 0. What is v?
-85, -7
Determine p, given that -31752/11 - 10*p**4 - 15570/11*p**2 + 45360/11*p + 2070/11*p**3 + 2/11*p**5 = 0.
1, 6, 21
Suppose 184*t**3 - 320*t**2 + 1491*t - 1875*t - 2 + 2 - 4*t**4 - 16*t**4 = 0. What is t?
-4/5, 0, 4, 6
Let z = 5389 - 5386. Let v(j) be the first derivative of -1/3*j**z + j**2 - 8 + 0*j. What is f in v(f) = 0?
0, 2
Let x be 385/875*-15 + 1*7. Determine i so that 0 - 2/5*i**2 - x*i = 0.
-1, 0
Let m be -32 + (-5799)/(-180) - (-1 + (-8)/(-10)). Let l(f) be the second derivative of -m*f**4 + 10*f**2 + 0*f**3 + 31*f + 0. Let l(t) = 0. What is t?
-2, 2
Let r be -6*(4 + (-434)/84) - 4. Factor 0 + 16/5*q + 4*q**2 + 2/5*q**r - 2/5*q**4.
-2*q*(q - 4)*(q + 1)*(q + 2)/5
Suppose -40*k - 345 = -45*k. Let -267*x**3 + 9*x + 327*x**3 - 20 - 5*x**2 + 25*x**4 - k*x = 0. Calculate x.
-2, -1, -2/5, 1
Let i(k) be the first derivative of k**6/24 - 13*k**5/20 - 3*k**4/16 + 41*k**3/12 - 13*k**2/4 - 6869. Let i(o) = 0. Calculate o.
-2, 0, 1, 13
Suppose 0 = -82*r + 80*r + f - 1, -4*r = -4*f + 4. Let h(n) be the first derivative of 42 + 0*n + 1/20*n**5 + r*n**4 + 0*n**2 + 0*n**3. Factor h(w).
w**4/4
Factor -199 - 78*b - 3*b**2 - 2*b**2 + 4*b**2 + 225*b + 53.
-(b - 146)*(b - 1)
Let n(r) = 12*r**3 - 87*r**2 - 1824*r - 6918. Let s(d) = 3*d**3 + 4*d**2 + d - 3. Let q(m) = n(m) - 3*s(m). Factor q(w).
3*(w - 47)*(w + 7)**2
Let x(j) be the first derivative of -j**4/2 + 64*j**3/3 - 208*j**2 + 768*j - 729. Let x(z) = 0. What is z?
4, 24
Let i(l) be the third derivative of l**6/210 - 44*l**5/35 + 125*l**4/6 - 2*l**2 - 556*l. Factor i(b).
4*b*(b - 125)*(b - 7)/7
Let v(g) be the third derivative of g**7/105 + 32*g**6/15 + 127*g**5/30 + 2512*g**2. Factor v(f).
2*f**2*(f + 1)*(f + 127)
Suppose 0 = -40*v + 8*v - 64. Let a be v/(-72) - (56/36)/(-7). Let -a*j**5 - 5/4*j**3 + j**4 + 0 + 0*j + 1/2*j**2 = 0. Calculate j.
0, 1, 2
Let n(w) = -40*w**4 + 288*w**3 + 1163*w**2 - 259*w - 1268. Let v(t) = 22*t**4 - 160*t**3 - 646*t**2 + 144*t + 704. Let p(k) = -16*n(k) - 29*v(k). Factor p(d).
2*(d - 1)*(d + 1)*(d + 8)**2
Let w(z) be the first derivative of z**3/15 - 21*z**2/2 - 106*z/5 + 1273. Factor w(o).
(o - 106)*(o + 1)/5
Let c be 1892*10/80*4/(-6). Let w = c + 159. Suppose 0*z**2 + 0*z - w*z**3 + 2/3*z**4 + 0 = 0. Calculate z.
0, 2
Let c(p) be the first derivative of -25*p**4/24 + 245*p**3/18 - 95*p**2/3 + 80*p/3 - 3489. Solve c(r) = 0 for r.
4/5, 1, 8
Let b be (2/14)/(((-1)/120)/((-17574)/1010)). Factor -6/7*c**3 - b*c - 1296/7 - 220/7*c**2.
-2*(c + 18)**2*(3*c + 2)/7
Suppose r = 4*b + 3, -b + 3*r - r - 6 = 0. Let u(m) be the second derivative of -6*m - m**3 + b + 9/2*m**2 + 1/12*m**4. Factor u(o).
(o - 3)**2
Solve 870 - 4276*c - 627 + 4640*c**2 - 1418*c**3 - 1114*c**4 + 1181 + 1476*c**4 - c**5 - 731*c**3 = 0 for c.
1, 2, 356
Let x(t) be the first derivative of -t**7/56 - t**6/20 - 3*t**5/80 - 31*t - 3. Let q(p) be the first derivative of x(p). Factor q(s).
-3*s**3*(s + 1)**2/4
Let f(n) be the first derivative of 2*n**3/33 + 98*n**2/11 + 4802*n/11 + 566. Suppose f(k) = 0. What is k?
-49
Let j(x) be the third derivative of x**7/105 + 7*x**6/5 - 57*x**5/10 + 43*x**4/6 - 6*x**2 - 67*x - 3. Factor j(s).
2*s*(s - 1)**2*(s + 86)
Suppose -8976*v**2 - 271 +