7)
Suppose 92 = 4*l + 80. Suppose 0 = b - l*c - 7, 3*b = 4*c + 17 - 1. Factor -8/5*r + 2/5*r**b + 8/5*r**3 - 8/5 + 6/5*r**2.
2*(r - 1)*(r + 1)*(r + 2)**2/5
Let c(n) = -2*n - 6. Let g be c(0). Let s = g - -10. Suppose 74*r**3 + 81*r**3 - 285*r**s - 2*r + 135*r**5 - 8*r + 5*r**2 = 0. Calculate r.
-2/9, 0, 1/3, 1
Let b(n) be the first derivative of -25*n**6/3 - 88*n**5 + 168*n**4 + 736*n**3/3 + 80*n**2 - 2260. What is s in b(s) = 0?
-10, -2/5, 0, 2
Let c(h) be the second derivative of 2*h**7/35 + 61*h**6/50 - 2259*h**5/100 + 508*h**4/5 - 682*h**3/5 - 144*h**2 - 5790*h. What is y in c(y) = 0?
-24, -1/4, 2, 5
Let w = -52 - -58. Suppose 30 - w = 12*r. Factor -41*u - 5*u**2 + 29*u + u**r + 0*u**2 + 16.
-4*(u - 1)*(u + 4)
Let l(d) be the first derivative of -9*d**2 + 3/5*d**5 + 99 - 7*d**3 + 0*d**4 + 0*d. Factor l(x).
3*x*(x - 3)*(x + 1)*(x + 2)
Let j be (-1)/(16/4)*(2 - 238). Determine u so that 59*u**3 - 76*u + 1 + 4*u**2 - j + 15 + 19 - 12*u**4 - 15*u**3 = 0.
-1, -1/3, 2, 3
Find f such that -3*f**4 - 15*f + 45*f**2 - 203 + 319 + 15*f**3 - 158 = 0.
-2, -1, 1, 7
Let k = -691623 + 691629. Factor -81/2*p - k*p**2 + 21/2.
-3*(p + 7)*(4*p - 1)/2
Let y(h) be the second derivative of h**4/48 + 5*h**3/6 + 25*h**2/2 + 3462*h. Solve y(j) = 0.
-10
Let n = -525714 - -1577144/3. What is m in 0 - n*m + 1/3*m**2 + 1/3*m**3 = 0?
-2, 0, 1
Let y(g) = -2*g - 5*g + 0*g**2 + 5*g - 2*g**2. Let x(w) = -3*w**2 - 2*w + 1. Let v(i) = 3*x(i) - 5*y(i). Factor v(c).
(c + 1)*(c + 3)
Let n be (-30)/(-8) - (-6)/(-8). Suppose -o - 2 = b, 2*b = n*o + 24 - 3. Find i such that -i**4 - 2*i**3 - 2*i**3 - i + 3*i**3 + b*i**2 - 2 + 2*i**3 = 0.
-1, 1, 2
Suppose -5*b + 9*b = 24. Suppose 0 = -2*z + b - 2. Solve 374*o**2 - 35 - 13 + 272*o - 514*o**z - 784*o**3 = 0 for o.
-3/4, 2/7
Let m = 53356 + -53354. Factor -4/7*q**m + 0*q + 36/7.
-4*(q - 3)*(q + 3)/7
Let m(t) be the first derivative of 2*t**7/105 + t**6/15 - t**5/5 - 4*t**4/3 - 8*t**3/3 - 110*t**2 + 12. Let x(c) be the second derivative of m(c). Factor x(p).
4*(p - 2)*(p + 1)**2*(p + 2)
Let 2414*m + 70574/5 + 2/5*m**3 + 298/5*m**2 = 0. Calculate m.
-71, -7
Suppose -80/7*u - 4/7*u**2 + 176/7 = 0. Calculate u.
-22, 2
Let g(t) = 12*t**2 + 920*t - 932. Let r(h) = 10*h**2 + 924*h - 934. Let b(x) = -4*g(x) + 5*r(x). Suppose b(s) = 0. What is s?
-471, 1
Let r be ((-897)/338)/(5*(-9)/(-16)). Let q = -18/65 - r. Factor -q*t**3 + 0 - 1/3*t**4 + 0*t - 1/3*t**2.
-t**2*(t + 1)**2/3
Let n(u) = -395*u + 1584. Let x be n(4). Let b(v) be the third derivative of -1/12*v**5 + 0 + 5/24*v**x + 13*v**2 + 5/3*v**3 + 0*v. Let b(r) = 0. Calculate r.
-1, 2
Let w = 111 + -113. Let p be 42/(-6)*w/7. Let 11*v**3 + v**p + 0*v**2 - 10*v**3 = 0. Calculate v.
-1, 0
Let f(b) = -b**3 + 6*b**2 - b. Let k be f(5). Suppose -g + k = g. Factor -4 - 5*z + 9*z**3 + 6*z + 7*z + 27*z**2 + g*z**3 + 4*z**4.
(z + 1)*(z + 2)**2*(4*z - 1)
Let q(s) be the second derivative of -s**6/120 + 7*s**5/80 + 3*s**4/16 - 7*s**3/24 - s**2 + 437*s. Solve q(r) = 0 for r.
-1, 1, 8
Let s = 67092 + -67092. Suppose s - 8/9*a - 2/9*a**2 = 0. What is a?
-4, 0
Let b be (0 - -2)/((-4)/(-10)). Suppose -2*h + b + 5 = 0. Factor 3*g**3 + 5*g**3 - 16*g + 4*g**3 + 16*g**2 - 4*g**h - 8*g**4 + 0*g**3.
-4*g*(g - 1)**2*(g + 2)**2
Let m = -306 - -303. Let t be (2 - (2 + m))/(36/8). Suppose -5/3*c**2 + t*c + 0 = 0. Calculate c.
0, 2/5
Let u(x) be the first derivative of -2*x**3/21 - 5*x**2/7 + 184*x - 1022. What is d in u(d) = 0?
-28, 23
Let k be (644/2415)/((-1)/1 + 5). Let m(t) be the third derivative of 7*t**2 + k*t**5 + 0 + 8/3*t**3 - 5/6*t**4 + 0*t. Determine p, given that m(p) = 0.
1, 4
Let w be ((-183328)/42)/(-4)*(-21)/198. Let l = w - -1278/11. Let -4/3*x - 16/9*x**2 + 0 - l*x**3 = 0. Calculate x.
-3, -1, 0
Let b(w) be the first derivative of -91/9*w**3 + 17/3*w**2 - 49/36*w**6 - 4/3*w - 64 + 143/24*w**4 + 14/15*w**5. Find o, given that b(o) = 0.
-2, 2/7, 1
Let n(f) = f**3 + 38*f**2 - 129*f - 37. Let p be n(-41). Let i be 16/p + 7/399*6. Solve -2/11*k**2 - 2/11*k + 2/11*k**3 + i = 0.
-1, 1
Factor 3*i**4 - 5*i**4 + 5*i**4 + 74*i**3 - 386*i**3 - 6*i**4.
-3*i**3*(i + 104)
Let b = 175 - 173. Factor 30 - 66*z**b - 57*z**3 - 111*z - 60 + 48*z**3.
-3*(z + 2)*(z + 5)*(3*z + 1)
Suppose 2*y - 3*o - 36 = -2*y, y - 9 = -2*o. Let g be y/2 - 5/10. Factor -3*b**3 + 2*b**4 - 2*b - 2*b**g - 5*b**2 + b**4 - 14*b**5 + 15*b**5.
b*(b - 2)*(b + 1)**3
Let y be (-1068)/(-182) + 7*24/(-1092). Solve -y*u - 18/7*u**4 - 86/7*u**3 - 124/7*u**2 + 16/7 = 0 for u.
-2, -1, 2/9
Solve -1723776 - 2144*s - 2/3*s**2 = 0.
-1608
Let z(x) = -2*x**2 - 354*x - 1408. Let n(f) = -3*f - 8. Let o(a) = -6*n(a) - z(a). Determine p, given that o(p) = 0.
-182, -4
Let w(d) be the third derivative of -d**5/210 - 5*d**4/6 - 2*d**2 + 608*d - 2. What is z in w(z) = 0?
-70, 0
Let m(q) = 20*q**2 + 268*q + 96. Let n(s) = s**2 - 4*s + 6. Let w(y) = m(y) - 16*n(y). Factor w(a).
4*a*(a + 83)
Let g(m) be the first derivative of m**6/33 - 134*m**5/11 + 13775*m**4/11 + 169340*m**3/33 + 85345*m**2/11 + 57122*m/11 - 1375. Find h such that g(h) = 0.
-1, 169
Let i(q) = -30*q**4 - 595*q**3 - 16150*q**2 + 77465*q + 93015. Let b(d) = 5*d**4 + d**3 + 2*d**2 + d + 2. Let y(s) = 5*b(s) + i(s). Factor y(x).
-5*(x - 5)*(x + 1)*(x + 61)**2
Let i(b) be the first derivative of b**5/2 + 265*b**4/4 + 260*b**3 + 775*b**2/2 + 515*b/2 + 5682. Factor i(q).
5*(q + 1)**3*(q + 103)/2
Let l(a) be the first derivative of a**5 - 49*a**4 - 122*a**3 - 62*a**2 + 41*a + 26. Factor l(y).
(y - 41)*(y + 1)**2*(5*y - 1)
Let i(q) be the first derivative of q**3/3 - 257*q**2/2 + 1012*q + 5. Factor i(f).
(f - 253)*(f - 4)
Determine h so that -5191 - 3325*h - 2930 + 5*h**2 + 11441 = 0.
1, 664
Let s be 0/36*(6 + 11/(-2)). Let p(y) be the third derivative of -29*y**2 + s*y - 1/126*y**5 - 1/42*y**4 + 0 - 1/1260*y**6 + 0*y**3. What is m in p(m) = 0?
-3, -2, 0
Suppose -3*b = 3*z, -1 + 9 = -z - 5*b. Let l(r) = 3. Let p(g) = g**3 - 7*g. Let j(k) = z*l(k) - p(k). Factor j(i).
-(i - 3)*(i + 1)*(i + 2)
Suppose -6*d = -d - 5*i - 10, -2*d - 2*i = -20. Suppose -d + 8 = w. Suppose 16*u**2 - 208*u**w - 4*u**4 + 228*u + 28*u + 57*u**3 - 9*u**3 = 0. Calculate u.
0, 4
Let k be ((-5)/40)/((-18)/108*2). Suppose -27/4 + k*r**2 + 9/8*r = 0. What is r?
-6, 3
Suppose -2/13*d - 980/13 + 980/13*d**2 + 2/13*d**3 = 0. What is d?
-490, -1, 1
Suppose -3*w - 1141 = p, -p - 5*w + 9*w = 1169. Let r = 1153 + p. Factor 1/7 - 1/7*x**2 + r*x.
-(x - 1)*(x + 1)/7
Let -2/7*a**5 + 24*a - 80/7 - 34/7*a**3 - 76/7*a**2 + 24/7*a**4 = 0. What is a?
-2, 1, 2, 10
Let q = 563821/9 - 62645. Factor 2/9*w**3 + 32/9 - 14/9*w**2 + q*w.
2*(w - 4)**2*(w + 1)/9
Let t be ((-36)/(-84))/((-2)/(-7))*2. Let i be (-2)/(-10)*0 + (-2 - -4). Determine r so that 0*r + 2/11*r**t + 0 + 4/11*r**i = 0.
-2, 0
Let x(b) be the third derivative of -125*b**8/336 + 85*b**7/6 + 31*b**6/4 - 407*b**5/3 + 665*b**4/3 - 160*b**3 + 35*b**2. Find k such that x(k) = 0.
-2, 2/5, 1, 24
Let z(o) be the third derivative of -o**6/24 + 23*o**5/60 - 5*o**4/6 - 2*o**3 - 1920*o**2. Factor z(r).
-(r - 3)*(r - 2)*(5*r + 2)
Let t be (9/24)/((-6363)/(-288) + -22). Suppose 3/2*y**3 - 13/2*y**2 + t*y + 6 = 0. What is y?
-2/3, 2, 3
Suppose -2/3*k**2 - 456 - 110/3*k = 0. What is k?
-36, -19
Let h(z) be the second derivative of 3*z**5/20 + 19*z**4 - 317*z**3/2 + 360*z**2 + 361*z. Determine w so that h(w) = 0.
-80, 1, 3
Suppose -480*x**2 + 84*x + 52 + 28 + 496*x**2 = 0. Calculate x.
-4, -5/4
Let c(q) be the second derivative of 1/12*q**3 - 5/12*q**4 + 3/2*q**2 + 3/40*q**5 + 6*q - 2. Suppose c(r) = 0. What is r?
-2/3, 1, 3
Let p(n) = 735*n - 20. Let g be p(6). Factor g*m + 4*m**3 - 1 - 3*m**3 + m**2 - 4391*m.
(m - 1)*(m + 1)**2
Let d(m) be the second derivative of m**7/21 + 19*m**6/5 - 248*m**5/5 + 764*m**4/3 - 688*m**3 + 1040*m**2 + 13634*m. Factor d(k).
2*(k - 2)**4*(k + 65)
Let n = 620 - 618. Determine b so that 28*b + 2 - 2 - 16*b**n + 30*b**2 - 10*b**2 = 0.
-7, 0
Let f(b) be the third derivative of b**6/120 + 7*b**5/20 + 43*b**4/12 + 16*b**3 + 2199*b**2. Find l, given that f(l) = 0.
-16, -3, -2
Suppose 5*v - 4*d + 46 = 0, v - 2*d = 41 - 67. Suppose 64/5*i**5 - 36/5 + 204/5*i - 288/5*i**4 + 516/5*i**3 - 92*i**v = 0. Calculate i.
3/4, 1
Let t(g) be the first derivative of 161 - 20*g**2 + 10/3*g**3 + 25/4*g**