123
Let m(d) be the first derivative of -d**5 + 65*d**4/4 - 235*d**3/3 + 115*d**2/2 + 420*d - 1000. Find h, given that m(h) = 0.
-1, 3, 4, 7
Suppose -123 + 35 = -2*l. Let i(s) = 10*s**2 + 29*s + 8. Let r(h) = h**2 + h - 1. Let j(a) = l*r(a) - 4*i(a). Factor j(o).
4*(o - 19)*(o + 1)
Let k(s) be the third derivative of s**5/3 + 541*s**4/6 + 72*s**3 - 15*s**2 + 23*s. Find x such that k(x) = 0.
-108, -1/5
Let r(j) = 88*j - 41. Let o be r(6). Factor 25*z**2 - 220 + o*z + 267*z + 10*z**2 + 6*z.
5*(z + 22)*(7*z - 2)
Factor 50/13 - 128/13*c**3 - 210/13*c + 288/13*c**2.
-2*(c - 1)*(8*c - 5)**2/13
Suppose 5*o - 39*o = -136. Let r(m) be the first derivative of 16 - 8/27*m**3 - 1/6*m**o + 5/9*m**2 + 4/9*m. Suppose r(t) = 0. Calculate t.
-2, -1/3, 1
Let f = 3219/2 + -22179/14. Let h = f - 25. Factor -h + 2/7*a**3 - 6/7*a**2 + 6/7*a.
2*(a - 1)**3/7
Factor 115 + 48*n - 9*n - 41 + 5*n**2 - 4*n**2.
(n + 2)*(n + 37)
Let a(d) be the third derivative of -d**6/150 - 4*d**5/5 + 62*d**4/15 - 10*d**2 - 45*d. Solve a(y) = 0 for y.
-62, 0, 2
Let i = 450278/1359 + 4/1359. Let v = i + -331. Solve 0 - v*m + 1/3*m**3 - 5/6*m**4 + 5/6*m**2 = 0 for m.
-1, 0, 2/5, 1
Let w(x) be the second derivative of x**5/20 - x**4/2 + 5*x**3/6 - 11*x - 171. Factor w(s).
s*(s - 5)*(s - 1)
Let z = 169 + -161. Solve -5*h**3 + 0*h**3 - 7*h**2 - z*h**2 + 120*h - 140 = 0.
-7, 2
Let o = -216 + 207. Let m(y) = y**3 + 36*y**2 - 359*y + 580. Let s(r) = 5*r**3 + 144*r**2 - 1437*r + 2321. Let w(i) = o*m(i) + 2*s(i). Factor w(f).
(f - 17)**2*(f - 2)
Let n be ((-3024)/(-2457))/(-1 + 57/39). Let j be 1/(-3) + (-10)/(-15). Factor j*s**2 + 16/3 + n*s.
(s + 4)**2/3
Let h = 5763/355 + 26/71. Let z = h + -15. Let -z*n - 4/5*n**2 - 4/5 = 0. What is n?
-1
Let a(k) = -k**3 + 13*k**2 - 4*k - 188. Let b be ((-5)/(-3) - 2/2)*-6. Let y(t) = t**3 - 13*t**2 + t + 187. Let d(f) = b*y(f) - 5*a(f). Factor d(j).
(j - 8)**2*(j + 3)
Let v = -608 - -663. Let x be v/66 + (-3)/(-6). Factor x*o**5 + 4/3*o - 8/3*o**2 + 4/3 + 4/3*o**4 - 8/3*o**3.
4*(o - 1)**2*(o + 1)**3/3
Let t(v) be the second derivative of 4*v**7/21 + 103*v**6/15 - 3*v**5 - 103*v**4/6 + 26*v**3/3 - 3052*v. Let t(c) = 0. Calculate c.
-26, -1, 0, 1/4, 1
Suppose 4*i + 21 = -x + 39, 2*x - 27 = i. Suppose 0 = 2*w + 5*k + 6, 0 = 3*w + 7*k - 11*k - x. Factor 3/10*q + 1/10*q**3 - 2/5*q**w + 0.
q*(q - 3)*(q - 1)/10
Let j(s) = -5*s**2 - 79*s + 115. Let k(g) = g**2 + 26*g - 38. Let p be (22/(-44))/(1/4). Let v(q) = p*j(q) - 7*k(q). Suppose v(y) = 0. What is y?
2, 6
Let u(y) be the first derivative of -2*y**7/21 - y**6/2 - 4*y**5/5 - y**4/4 + y**3/3 + 185*y + 148. Let d(m) be the first derivative of u(m). Solve d(r) = 0.
-2, -1, 0, 1/4
Let k(s) be the third derivative of -s**7/420 + s**6/180 + s**5/30 - 17*s**3/6 - s**2 - 2. Let v(o) be the first derivative of k(o). What is m in v(m) = 0?
-1, 0, 2
Suppose 40*c + 40*c - 160 = 0. Let u(y) be the second derivative of -1/20*y**5 + 0 - 3/2*y**c + 5/6*y**3 - 1/12*y**4 - 17*y. Suppose u(m) = 0. Calculate m.
-3, 1
Find s such that 251*s + 158*s + 258 + 3*s**2 + 0*s**2 - s**2 - 149*s = 0.
-129, -1
Let v(p) be the second derivative of 2*p**6/5 - 81*p**5/20 + 21*p**4/4 + 67*p**3/2 + 45*p**2/2 + 5158*p. What is f in v(f) = 0?
-1, -1/4, 3, 5
Let s be -12 + ((-441)/288)/((-3)/24). Let -5/2*b**2 + 29/4*b + s*b**3 - 5 = 0. Calculate b.
1, 4, 5
Let f be (-400)/30*(-12)/(-8). Let u be (8/f)/((-3)/(5 + -2)). Factor 0 + 1/5*s**2 + u*s + 2/5*s**4 - s**3.
s*(s - 2)*(s - 1)*(2*s + 1)/5
Let y(d) = -24*d**2 + 168*d - 141. Let s(h) = -25*h**2 + 169*h - 146. Let v(z) = -3*s(z) + 4*y(z). Let v(u) = 0. What is u?
6/7, 7
Factor -256*a**2 + 4367*a**3 - 5015*a**3 - 20*a**4 - 7 + 7.
-4*a**2*(a + 32)*(5*a + 2)
Suppose 383 = 63*b - 373. Let w be (b/16)/((-18)/(-64)). Find z such that 2/3*z**5 + 0*z**2 + w*z + 0 - 10/3*z**3 + 0*z**4 = 0.
-2, -1, 0, 1, 2
Let j be 3/8 - ((-56)/(-84))/(16/(-39)). Let x(b) be the first derivative of 10 + 0*b - j*b**2 + 4/3*b**3. Determine c so that x(c) = 0.
0, 1
Let d(u) be the first derivative of -u**7/280 - 3*u**6/40 - 3*u**5/8 - 7*u**4/8 - 38*u**3 + 4. Let q(k) be the third derivative of d(k). Factor q(b).
-3*(b + 1)**2*(b + 7)
Determine h, given that 58/11*h - 2/11*h**2 + 0 = 0.
0, 29
Let v(p) = -p**4 + p - 1. Let y(j) = -3*j**4 + 33*j**3 + 15*j**2 - 135*j + 84. Let b(s) = 6*v(s) - y(s). Factor b(t).
-3*(t - 1)**2*(t + 3)*(t + 10)
Let g(a) be the second derivative of -2*a**7/231 + 35*a**6/33 + 134*a**5/55 - 43*a**4/33 - 266*a**3/33 - 89*a**2/11 - 34*a + 1. Let g(i) = 0. What is i?
-1, -1/2, 1, 89
Let h(a) be the first derivative of -4*a**3/9 + 404*a**2 - 122412*a + 446. What is r in h(r) = 0?
303
Let m = -871331/7 - -124477. Factor 1/7*f**2 - 1/7*f**3 + m*f - 12/7.
-(f - 2)**2*(f + 3)/7
Let b(i) be the first derivative of -1452*i**4 + 1848*i**3 + 261*i**2/2 + 3*i + 768. Solve b(n) = 0 for n.
-1/44, 1
Let m = -219/136 - -59/34. Let f(g) be the third derivative of 1/80*g**6 + 0*g**3 - m*g**4 + 14*g**2 + 0 + 0*g + 1/40*g**5. Factor f(a).
3*a*(a - 1)*(a + 2)/2
Let -19*r**3 + 12*r**2 + 130*r - 42*r - 45*r - 43*r + 8*r**4 - r**5 = 0. What is r?
0, 1, 3, 4
Let j(i) be the second derivative of 9*i**5/4 - 343*i**4/4 + 142*i**3 + 66*i**2 + 3041*i. Factor j(q).
3*(q - 22)*(q - 1)*(15*q + 2)
Solve -8*s**2 + 2116/3*s - 352/3 = 0 for s.
1/6, 88
Let j be (1244/2177)/((-2)/(-4)*(-2)/(-42)). Determine w, given that j - 9/4*w**2 + 69/2*w = 0.
-2/3, 16
Let t be 20/66*(147/(-7) + 1008/40). Let m be ((-21)/(-28))/(3/8). Factor -12/11 - 2/11*a**m + t*a.
-2*(a - 6)*(a - 1)/11
Let q(h) = -18*h - h**2 - 23*h + 40*h. Let n(a) = -a**2 + 14*a + 64. Let u(s) = -2*n(s) + 4*q(s). Factor u(y).
-2*(y + 8)**2
Factor 1263*w**2 - 97*w**2 + 1224*w - w**3 + 2*w**3 + 62*w**2 + 3*w**3.
4*w*(w + 1)*(w + 306)
Let r be 2/(-22) + (780/110 - 5). Factor -r*a**3 + 50/9 + 10/9*a - 14/3*a**2.
-2*(a - 1)*(3*a + 5)**2/9
Let j be -6*(22/(-4) + 5). Factor j + 11*r**2 + 0*r**2 - 4*r - 13*r**2 + 4*r**3 - r**4.
-(r - 3)*(r - 1)**2*(r + 1)
Let s(r) be the third derivative of r**6/8 - 17*r**5/12 + 35*r**4/6 - 10*r**3 + 2309*r**2. Let s(h) = 0. What is h?
2/3, 2, 3
Let z(o) be the second derivative of o**4/30 - 59*o**3/5 + o - 419. Suppose z(v) = 0. Calculate v.
0, 177
Let q(i) be the first derivative of 5*i**4/4 - 185*i**2/2 + 420*i - 499. Factor q(n).
5*(n - 4)*(n - 3)*(n + 7)
Let c(q) be the third derivative of 3*q**5/130 - 109*q**4/78 + 16*q**3/13 - 2248*q**2. Find y, given that c(y) = 0.
2/9, 24
Let x = -59096 + 59098. Factor 4/3*n**3 + 0*n + 0 + 16/3*n**x.
4*n**2*(n + 4)/3
Let m(p) be the third derivative of 0 + 9/20*p**5 - p**2 + 1/40*p**6 - 14*p + 0*p**3 + p**4. Factor m(t).
3*t*(t + 1)*(t + 8)
Suppose -2*q - 204 = -6*l + 4*l, -3*q - 3*l - 318 = 0. Let f = q + 116. Determine j so that -10*j**5 + 2*j**2 - 21*j**4 + 7*j**4 + f*j**4 + 10*j**3 = 0.
-1, -1/5, 0, 1
Let x(u) be the second derivative of -2/9*u**3 - 255*u + 0 + 0*u**2 + 1/36*u**4. Factor x(j).
j*(j - 4)/3
Suppose -10*z - 6*z + 144 = 0. Factor -1 - 28*v**3 - 20 + 188*v**2 - z - 2 + 88*v - 84*v**3.
-4*(v - 2)*(4*v - 1)*(7*v + 4)
Let n(b) be the third derivative of -b**6/540 + 17*b**5/135 - 65*b**4/36 + 6*b**3 - 9484*b**2. Factor n(y).
-2*(y - 27)*(y - 6)*(y - 1)/9
Let y(p) = 5*p**2 - p. Let l(f) = 29*f**2 - 104*f - 2401. Let h(g) = -l(g) + 6*y(g). Factor h(d).
(d + 49)**2
Let f(x) be the first derivative of -31*x**6/3 - 86*x**5 - 272*x**4 - 1168*x**3/3 - 208*x**2 + 32*x - 1447. Suppose f(a) = 0. Calculate a.
-2, -1, 2/31
Let w(f) be the third derivative of -f**7/420 + 19*f**6/240 + 151*f**5/120 - 19*f**4/48 - 25*f**3/2 - 14*f**2 - 2*f. What is n in w(n) = 0?
-6, -1, 1, 25
Let 155*t**2 + 0 + 104*t - 3/2*t**3 = 0. Calculate t.
-2/3, 0, 104
Let d(i) be the first derivative of -i**7/2520 + i**6/135 + 19*i**5/360 + 5*i**4/36 - i**3/3 - 29*i + 12. Let n(u) be the third derivative of d(u). Factor n(y).
-(y - 10)*(y + 1)**2/3
Let x(c) = 2*c - 10. Let w(o) = 3*o - 10. Let p(z) = 4*w(z) - 3*x(z). Let n be p(2). Solve -8/7*t + 4/7*t**n + 4/7 = 0 for t.
1
Let j be 1/4*60/(-9)*156/(-390). Solve -1/3*p**3 + p**2 + 1/3*p - j - 1/3*p**4 = 0 for p.
-2, -1, 1
Let u(h) be the third derivative of h**5/60 - 179*h**4/12 + 32041*h**3/6 - 290*h**2. Factor u(d).
(d - 179)**2
Let t(z) be the first derivative of -141/16*z**4 + 0*z - 13/10*