 d.
1, 4
Suppose -5*x + 75 - 35 = 0. Let f(p) = -p**3 - 2*p**2 + p + 1. Let j be f(-3). Determine k so that 4*k**2 - x*k + j*k**2 + 17*k**2 = 0.
0, 2/7
Let r(b) be the first derivative of 98*b**5/5 + 273*b**4/2 + 96*b**3 + 20*b**2 + 1290. Let r(n) = 0. Calculate n.
-5, -2/7, 0
Let x(m) be the first derivative of -4*m**5/15 - 11*m**4/3 - 20*m**3/3 + 18*m**2 - 599. Determine r so that x(r) = 0.
-9, -3, 0, 1
Let h(r) be the third derivative of r**6/1020 + 4*r**5/255 + r**4/12 + 10*r**3/51 - 26*r**2 - 2*r. Determine x, given that h(x) = 0.
-5, -2, -1
Let o(z) = -11 + 6 - 8 - 138*z - 141*z + 283*z. Let t be o(4). Determine w, given that 1 + 5*w**t - w - 11/4*w**2 - 11/4*w**4 + 1/2*w**5 = 0.
-1/2, 1, 2
Let z(g) be the second derivative of -5*g**4/48 - 55*g**3/4 - 325*g**2/8 - 1557*g. Determine m, given that z(m) = 0.
-65, -1
Let z = -1323472 + 1323559. Find k such that -z*k + 246/7 - 15/7*k**2 = 0.
-41, 2/5
Factor -121*y - 722/3 - 1/3*y**2.
-(y + 2)*(y + 361)/3
Factor -326*w + 410*w + 554*w - 2089 + 973*w - 1121 - 3*w**2.
-3*(w - 535)*(w - 2)
Factor -10*z + 4*z**5 + 16*z**2 - 4*z - 16*z**4 - 69*z**3 + 81*z**3 + z - 3*z.
4*z*(z - 2)**2*(z - 1)*(z + 1)
Let d(t) = 9*t + 32. Let h be d(7). Let w = -93 + h. Factor 8*i**2 - 5*i**2 + 10*i - 5*i**w.
-2*i*(i - 5)
Let r = -7081/10 + 10744/15. Factor 2*g**3 - 1/6*g**4 - 14*g - r - 11/3*g**2.
-(g - 7)**2*(g + 1)**2/6
Factor -97*r**2 + 26*r**2 - 105*r - 75*r + 67*r**2 - 176.
-4*(r + 1)*(r + 44)
Factor -2*f**3 - 21/2 + 44*f - 15/2*f**2.
-(f - 3)*(f + 7)*(4*f - 1)/2
Let b = 90991/20220 - 1/20220. Let a(c) be the first derivative of -9/4*c**4 + 3/5*c**5 + 33 + c**3 - 6*c + b*c**2. Find z, given that a(z) = 0.
-1, 1, 2
Let w be (-72)/168 + (5 - 2) + -2. Factor 2/7*n**3 - 2*n - w*n**2 - 8/7.
2*(n - 4)*(n + 1)**2/7
Let s(d) be the third derivative of -d**5/15 - 113*d**4/24 - 14*d**3/3 + 1120*d**2. Factor s(f).
-(f + 28)*(4*f + 1)
Let g = 653 + -653. Let v be 18/10 + -50 + 49. Factor 0*x**3 + v*x**4 + 0*x + g + 0*x**2 - 4/5*x**5.
-4*x**4*(x - 1)/5
Let s(a) = 18*a - 195. Let r be s(12). Find v such that -151*v**2 - 50*v**2 + 16*v**2 + 120 + 100*v**3 - 70*v + r*v**4 + 14*v**4 = 0.
-4, -6/7, 1
Let v = 18014 + -1026902/57. Let o = v + 60/19. Factor 2/9*x**3 + 16/9 + o*x**2 + 8/3*x.
2*(x + 2)**3/9
Suppose -66*w - 8196 = -78*w. Suppose i + 681 = w. Factor 2/7*r**i - 4/7 - 2/7*r.
2*(r - 2)*(r + 1)/7
Let f(n) be the first derivative of 5/2*n**2 + 0*n + 13/18*n**3 - 75 - 1/24*n**4. Factor f(a).
-a*(a - 15)*(a + 2)/6
Let y(k) be the first derivative of k**3/21 - 31*k**2/7 + 961*k/7 + 458. Factor y(j).
(j - 31)**2/7
Let i(s) be the first derivative of -2*s**5/75 + 4*s**4/5 - 86*s**3/45 - 8*s**2/5 + 88*s/15 - 321. Determine k so that i(k) = 0.
-1, 1, 2, 22
Suppose 0 = 48*t - 51*t + 9. Factor -42*o - 96 + 6*o**2 + 0*o**2 - 6*o + 3*o**t.
3*(o - 4)*(o + 2)*(o + 4)
Let l(r) = -r**2 + r. Let z(u) = -13*u**2 + 79*u - 126. Let v(c) = -10*l(c) + z(c). Suppose v(s) = 0. What is s?
2, 21
Let y(o) = 9*o**3 - 1811*o**2 - 616*o + 1216. Let p(b) = 9*b**3 - 1812*b**2 - 615*b + 1215. Let n(j) = 4*p(j) - 3*y(j). Factor n(l).
3*(l - 202)*(l + 1)*(3*l - 2)
Let v(o) be the second derivative of o**4/108 - 59*o**3/54 + 41*o**2 + 4541*o. Suppose v(f) = 0. Calculate f.
18, 41
Let t(w) = -65*w**3 + 1250*w**2 - 2340*w + 1190. Let m(n) = 11*n**3 - 208*n**2 + 389*n - 198. Let b(g) = -35*m(g) - 6*t(g). Find z, given that b(z) = 0.
1, 42
Let t(u) = -2*u**4 - u**2 + 1. Let a(x) = 13*x**4 - 230*x**3 + 13231*x**2 - 6. Let b(q) = -a(q) - 6*t(q). What is c in b(c) = 0?
0, 115
Let p(i) be the third derivative of i**7/210 + 19*i**6/120 + 37*i**5/30 - 55*i**4/6 - 100*i**3 - 1563*i**2. Solve p(j) = 0 for j.
-10, -2, 3
Let x(j) = -j**2 + 14*j - 12. Let q(g) = -4*g**2 - 418*g - 3048. Let u(t) = q(t) - 2*x(t). Factor u(i).
-2*(i + 7)*(i + 216)
Let y(m) be the third derivative of m**7/140 - m**6/16 - m**5/2 + 15*m**4/4 + 36*m**3 - 7310*m**2. Find j such that y(j) = 0.
-3, -2, 4, 6
Let s(q) be the third derivative of -1/120*q**6 + 7/24*q**4 + 0*q + 0*q**3 + 70*q**2 + 0 - 1/10*q**5. Factor s(y).
-y*(y - 1)*(y + 7)
Determine l, given that 0 - 104/9*l + 2/3*l**5 + 302/9*l**3 - 200/9*l**2 - 100/9*l**4 = 0.
-1/3, 0, 2, 13
Let s(a) be the first derivative of 3*a**5 + 935*a**4/4 + 17080*a**3/3 + 37240*a**2 - 3594. Factor s(m).
5*m*(m + 28)**2*(3*m + 19)
Suppose 0 = j - z - 19320 - 35750, 0 = 2*j - 5*z - 110140. What is q in j*q**4 - 22232*q**3 - 12150*q**2 - 948*q - 24 - 23695*q**3 + 3979*q**4 = 0?
-2/27, 1
Let i = 3737413/7 - 533913. Find b such that i*b**3 - 52/7*b**2 + 0 + 32/7*b - 2/7*b**4 = 0.
0, 1, 2, 8
Let b(v) = v**3 - 9*v**2 + 20*v + 7. Let q be b(6). Suppose 5*n = q + 41. Suppose 18*p - 38*p**3 - 24*p**2 - 26*p - 2*p**5 + n*p**3 - 12*p**4 = 0. Calculate p.
-2, -1, 0
Let u(a) be the second derivative of a**5/12 - 5*a**4/12 - 40*a**3/9 - 10*a**2 - a + 71. Factor u(w).
5*(w - 6)*(w + 1)*(w + 2)/3
Solve -12*r + r**2 + 32/3 + 1/3*r**3 = 0.
-8, 1, 4
Suppose -70 = -6*i - 28. Suppose 4*c - 9*m - 41 = -14*m, 0 = -3*c + m + i. Factor 0 - 6/5*o**3 + 9/5*o**2 - 4/5*o + 1/5*o**c.
o*(o - 4)*(o - 1)**2/5
Let d = 850 + -611. Suppose -d = v - 241. Suppose -1/5*k**3 + 0 - 2/5*k**v + 3/5*k = 0. What is k?
-3, 0, 1
Let n be (88/(-10))/(35/(-175)). Factor -27*l**3 + 3*l**5 + 9*l - n*l**2 + l**5 - 4*l**4 + 8*l**3 - 25*l - 17*l**3.
4*l*(l - 4)*(l + 1)**3
Let v be ((-48)/420)/(216/(-84))*21. Find x such that -22/15*x**2 - 2/3*x - v*x**3 + 0 - 2/15*x**4 = 0.
-5, -1, 0
Suppose -77*z + 160 + 230 = -51*z. Let r(o) be the first derivative of 0*o - 1/8*o**2 + 1/24*o**3 - z. Factor r(i).
i*(i - 2)/8
Suppose 5289*x + 468 = 5445*x. Find t, given that 25*t**2 + 7/3*t**x - 12 + 104/3*t = 0.
-9, -2, 2/7
Let g = -3562 - -1925. Let s = 8188/5 + g. Factor 3/5 - 6/5*r**2 - 6/5*r**3 + 3/5*r**4 + 3/5*r + s*r**5.
3*(r - 1)**2*(r + 1)**3/5
Let a = 39528/5465 + -36/1093. Factor -a*w + 0 + 2/5*w**4 + 42/5*w**2 - 16/5*w**3.
2*w*(w - 3)**2*(w - 2)/5
Let i(u) = -13*u**3 + 980*u**2 - 1936*u + 979. Let r(p) = 15*p**3 - 981*p**2 + 1935*p - 981. Let m(z) = -6*i(z) - 5*r(z). Factor m(n).
3*(n - 323)*(n - 1)**2
Let j(f) = -f**3 + 26*f - 34. Let r be j(3). Let u(n) be the first derivative of r - 1/7*n**2 + 0*n - 2/21*n**3. Factor u(x).
-2*x*(x + 1)/7
Let d(b) be the third derivative of 2/3*b**4 - 4/3*b**3 - 1/12*b**6 + 0*b + 3*b**2 + 12 + 1/168*b**8 - 1/30*b**5 + 1/105*b**7. Suppose d(g) = 0. Calculate g.
-2, 1
Let a(m) be the second derivative of m**6/30 + 4*m**5/5 + 79*m**4/12 + 14*m**3 - 90*m**2 + 1825*m. Determine d, given that a(d) = 0.
-6, -5, 1
Let b(a) = -3*a**2 - 29*a - 26. Let j(v) be the first derivative of 5*v**3 + 72*v**2 + 129*v - 264. Let m(l) = -21*b(l) - 4*j(l). Solve m(q) = 0.
-10, -1
Let t(r) = -r**2 + 22*r + 170. Let i be t(28). Suppose -239*k**3 - 9860*k - 505*k**2 - 93*k**i + 161*k**2 + 3364 + 227*k**3 - 255*k**2 = 0. Calculate k.
-29, 1/3
Let u(v) = -v**2 - 9*v + 1. Let g be u(-7). Suppose 0 = -18*n + 33 + 3. Factor -g*q - 4*q**n + 8*q**2 - q**2.
3*q*(q - 5)
Let q = -2/551143 - -2204578/1653429. Let 1/3*r**3 - 4/3*r**4 + 16/3*r**2 + 0 - q*r = 0. What is r?
-2, 0, 1/4, 2
Let l(n) be the third derivative of -n**8/6720 + n**7/420 - n**6/80 - n**5/60 + 23*n**3/3 - 30*n**2. Let v(c) be the third derivative of l(c). Factor v(r).
-3*(r - 3)*(r - 1)
Let k be (-48)/72 - (42/105)/(6/(-85)). Factor 0 - 32/5*h**3 - 1/5*h**k + 11/5*h**4 + 0*h + 28/5*h**2.
-h**2*(h - 7)*(h - 2)**2/5
Let g be 8/(12/6) + -2. What is j in 12*j**g + 11*j**3 - 4*j**5 - 15*j**3 - 6*j**4 + 8*j - j**4 - 5*j**4 = 0?
-2, -1, 0, 1
Let s(j) be the first derivative of -41/7*j**2 - 80/21*j**3 + 1/14*j**4 + 0*j + 229. Solve s(d) = 0 for d.
-1, 0, 41
Let s(u) be the second derivative of -2*u**6/5 - 43*u**5/5 - 34*u**4 + 176*u**3/3 - 4*u - 263. Determine j, given that s(j) = 0.
-11, -4, 0, 2/3
Let d(p) be the second derivative of 35/6*p**3 + 5/6*p**4 + 15*p**2 + 0 + 241*p. Solve d(q) = 0.
-2, -3/2
Let b be (5 - 6/3) + -1. Let z = -27797/4 - -6950. Let -3/4*m - z*m**b + 0 = 0. What is m?
-1, 0
Let j(u) = -u**3 + 3*u**2 + 4*u + 5. Suppose -q - 3 = 3*l + 4*q, 1 = 4*l + 5*q. Let i be j(l). Solve -b - 23*b - 4*b**2 + i*b**2 - 5*b**2 = 0.
-6, 0
Factor 1016 - 2*d**2 - 1315*d + 841*d + 14*d**2 - 1058*d.
4*(d - 127)*(3*d - 2)
Suppose 276 = -7*i + 38. Let