+ d. Let m(w) = v*c(w) + f(w). Find j such that m(j) = 0.
4/51, 2/7
Let b(c) be the third derivative of 0*c + 5/24*c**4 - 1/210*c**7 - 1/24*c**6 + 2/3*c**3 + 32*c**2 - 1/20*c**5 + 0. Factor b(z).
-(z - 1)*(z + 1)**2*(z + 4)
Suppose 9*a - 8 = 10. Suppose 6 + g - 11*g - a*g**2 + 15*g - g**3 = 0. What is g?
-3, -1, 2
Let s(t) be the first derivative of -9 - 3/2*t - 5/8*t**4 + 1/4*t**2 + 7/6*t**3. Solve s(x) = 0 for x.
-3/5, 1
Let t(f) be the third derivative of f**5/240 + 1207*f**4/96 - 151*f**3/3 + 380*f**2 + 2*f + 3. Factor t(r).
(r - 1)*(r + 1208)/4
Let w(a) be the first derivative of -a**5/78 + 3*a**4/52 + 2*a**3/39 + 35*a**2/2 + 10. Let c(q) be the second derivative of w(q). Factor c(d).
-2*(d - 2)*(5*d + 1)/13
Suppose 3*d - 3 = -4*u + 6*u, -5*u - 2*d + 2 = 0. Suppose 5*c = 2*g - 16, 4*g + 8*c - 8 = 6*c. Factor -p**g - 1/2*p**2 + 0 + u*p - 1/2*p**4.
-p**2*(p + 1)**2/2
Factor 3*s - 20/7*s**2 - 9/7*s**3 + 0.
-s*(s + 3)*(9*s - 7)/7
Let t(i) = 45*i**3 - 5155*i**2 + 79330*i - 190015. Let s(o) = -2*o**3 + 234*o**2 - 3606*o + 8637. Let n(m) = -65*s(m) - 3*t(m). Factor n(g).
-5*(g - 24)**2*(g - 3)
Let f(k) be the second derivative of -3*k + 0 - 10/9*k**3 + 1/36*k**4 + 50/3*k**2. Factor f(z).
(z - 10)**2/3
Let z(c) be the second derivative of -68*c - 37/114*c**4 - 3/38*c**5 - 11/19*c**3 - 9/19*c**2 - 2/285*c**6 + 0. Let z(u) = 0. What is u?
-3, -1, -1/2
Let u(v) be the first derivative of -2*v**5/55 + 37*v**4/22 - 310*v**3/11 + 2119*v**2/11 - 3380*v/11 + 66. Solve u(m) = 0.
1, 10, 13
Suppose -2*p + 16 = 6. Find n such that -324*n - 117*n**5 + 555*n**2 + 80*n**4 + 447*n**2 + 113*n**p - 282*n**2 - 472*n**3 = 0.
0, 1, 9
Suppose -2*g = 5*j - 10, -g = 2*j - 0*g - 4. Factor 39*h - 10 - 5*h**j + 50 - 86*h + 37*h.
-5*(h - 2)*(h + 4)
What is h in -4357/2*h**2 - 1358*h**3 - 910*h - 114 + 49/2*h**4 = 0?
-1, -2/7, 57
Let a(w) be the first derivative of w**3/12 - 361*w**2/8 + 90*w + 75. Factor a(t).
(t - 360)*(t - 1)/4
Suppose -5*i + 80 = 4*p, 88*i - 92*i = 5*p - 73. Let 440/13*r**3 + 160/13*r**2 - 98/13*r**p - 192/13*r - 42/13*r**4 + 32/13 = 0. Calculate r.
-2, -1, 2/7, 2
Let o(c) = c**3 + c**2 - 9*c + 4. Let j(b) = -32*b**2 - 216*b - 171. Let t(y) = -j(y) + o(y). Find w such that t(w) = 0.
-25, -7, -1
Let c(i) be the third derivative of -i**5/80 - 45*i**4/16 - 261*i**3/8 + i**2 - i - 7. Find o, given that c(o) = 0.
-87, -3
Factor 5/3*k**3 + 260/3 + 115/3*k**2 - 380/3*k.
5*(k - 2)*(k - 1)*(k + 26)/3
Let p(t) be the first derivative of -3/4*t**4 - 1029*t - 21*t**3 - 76 - 441/2*t**2. Solve p(r) = 0.
-7
Determine x so that -2025*x + 5*x**4 - 75*x**3 + 2*x**4 + 621*x**2 + 1458 - 50*x**2 - 4*x**4 + 68*x**2 = 0.
1, 6, 9
Let f(b) be the third derivative of b**5/180 + 35*b**4/36 + 118*b**2 + 3*b. Suppose f(h) = 0. What is h?
-70, 0
Factor 259*r**3 - 773*r**3 + 258*r**3 + 258*r**3 + 26*r - r**2 - 27*r**2.
2*r*(r - 13)*(r - 1)
Let r(i) be the second derivative of -i**4/18 + 19*i**3/9 - 16*i**2 + 819*i. Factor r(j).
-2*(j - 16)*(j - 3)/3
Factor 104*p**2 + 0*p**3 + 52146*p + 51*p**2 - 52566*p - 7*p**3 + 2*p**3.
-5*p*(p - 28)*(p - 3)
Factor 848/5*w + 616/5*w**2 + 212/5*w**3 + 34/5*w**4 + 2/5*w**5 + 448/5.
2*(w + 2)**3*(w + 4)*(w + 7)/5
Let k(j) be the second derivative of 4/3*j**3 - 3*j**2 + 0 - 1/8*j**4 + 343*j - 1/40*j**5. Solve k(b) = 0.
-6, 1, 2
Let w(s) = -9*s + 49. Let t be w(5). Suppose -3*j + 0*j - 59 = -5*h, -2*h + 14 = 2*j. Suppose -6*q - t*q - 12*q**2 - h*q + 8 = 0. Calculate q.
-2, 1/3
Suppose 0 = -18*w + 19*w + o + 469, -o = -4*w - 1886. Let l = w - -1414/3. Factor -1 + 4/3*h - l*h**2.
-(h - 3)*(h - 1)/3
Let 216*n + 18475 - 16805 - 1041*n - 5*n**2 = 0. Calculate n.
-167, 2
Let x(k) be the first derivative of -k**5/5 + 13*k**4/4 - 17*k**3 + 63*k**2/2 - 949. Factor x(a).
-a*(a - 7)*(a - 3)**2
Let b = 55404 + -55402. Factor -3/4*f**b - 12 - 15/2*f.
-3*(f + 2)*(f + 8)/4
Let m be 13916/568*3/63. Let j(b) be the second derivative of 0 + m*b**3 + 17/24*b**4 - 34*b - 2*b**2 - 1/8*b**5. Let j(x) = 0. Calculate x.
-1, 2/5, 4
Let t(l) = -7*l + 81. Let f be t(11). Suppose -f*z + 0*s + 28 = 5*s, 2*z - 4*s + 12 = 0. Factor -17/5*p**z + 0 - 6/5*p - p**3.
-p*(p + 3)*(5*p + 2)/5
Let x be -28*(6/68)/((-9)/12). Let m(s) be the first derivative of -4/17*s + 40/17*s**4 - x*s**3 + 1 + 23/17*s**2 + 128/85*s**5. Factor m(a).
2*(a + 2)*(4*a - 1)**3/17
Let p = -10 - -14. Suppose 8*t - 7*t = 38. Factor 42*n**3 - n**p - t*n**3 + 6*n**4 - n**4.
4*n**3*(n + 1)
Let v = -95 - -1997/21. Let r(d) be the first derivative of 0*d + 7 - v*d**3 + 0*d**2 - 1/7*d**4 - 2/35*d**5. Factor r(w).
-2*w**2*(w + 1)**2/7
Let d(z) = -49*z. Let f be d(6). Let l be 49/f - 5/(-3). Factor -4/3*b**2 + b - 1/6*b**4 + l - b**3.
-(b - 1)*(b + 1)*(b + 3)**2/6
Suppose 26569 = -186*k + 27127. Factor 2/5*j**4 + 46/5*j**k + 0 - 288/5*j + 48*j**2.
2*j*(j - 1)*(j + 12)**2/5
Let w = -90 - -121. Suppose 2*p + 20 = 10*t - 5*t, -5*p = -3*t + w. Factor -9/2*l - 3/4*l**t - 6.
-3*(l + 2)*(l + 4)/4
Let s(n) be the second derivative of -n**6/120 + n**5/40 + 7*n**4/48 - 5*n**3/6 + 3*n**2/2 + 6306*n. Let s(g) = 0. Calculate g.
-3, 1, 2
Let c(u) = 2*u**3 + 18*u**2 + 5*u + 2. Let p be c(-5). Let x = p + -175. Suppose 2/5 + 4/5*z + 2/5*z**x = 0. Calculate z.
-1
Determine m, given that 236 - 140*m - 5*m**4 - 295 + 165*m**2 - 241 = 0.
-6, -1, 2, 5
Suppose -3*l = -51 + 9. Suppose -n + 2*q - 4 = 0, n - 5*n + l = 2*q. Suppose 8*x + 14/5*x**3 - 52/5*x**n + 16/5 = 0. What is x?
-2/7, 2
Let a be -2*3/(-2)*1052/530997. Let c = a - -5372/2019. Let -31/3*d - 4/3*d**2 + c = 0. What is d?
-8, 1/4
Let v = -2/151439 + 5906135/1060073. What is r in 3/7*r**3 - 3*r**2 - 18/7 - v*r + 3/7*r**4 = 0?
-2, -1, 3
Let i(l) = -10*l**2 + 6195*l + 6425. Let u(h) = -5*h**2 + 3097*h + 3234. Let f(r) = -3*i(r) + 5*u(r). Factor f(d).
5*(d - 621)*(d + 1)
Let k(h) be the second derivative of h**6/210 - 2*h**5/35 - h**4/12 + 25*h**3/21 + 24*h**2/7 - 1281*h. Solve k(p) = 0.
-2, -1, 3, 8
Factor 339/2*n - 495 - 3/2*n**2.
-3*(n - 110)*(n - 3)/2
Let r(q) be the third derivative of q**7/12600 - q**6/1200 + q**4/12 + 37*q**3/6 + q**2 - 15*q. Let n(i) be the second derivative of r(i). Factor n(j).
j*(j - 3)/5
Let h(d) be the third derivative of -d**8/672 - 2*d**7/105 + 13*d**6/120 + 7*d**5/5 - 147*d**4/16 - 4842*d**2. Factor h(y).
-y*(y - 3)**2*(y + 7)**2/2
Let k(x) be the first derivative of -6*x**3/5 - 73*x**2 + 748*x/5 + 801. Let k(a) = 0. Calculate a.
-374/9, 1
Let v(c) be the first derivative of c**4/3 + 4*c**3 - 14*c**2 - 240*c - 131. Let n(l) be the first derivative of v(l). Determine i, given that n(i) = 0.
-7, 1
Let f = -686 - -689. Let y(p) be the second derivative of 0 - 10/3*p**f + 12*p + 4*p**2 - 7/3*p**4. Factor y(s).
-4*(s + 1)*(7*s - 2)
Suppose 5*c - 4*r + 4 = 0, -3*c = -125*r + 121*r + 4. Let o = -3/13 + 207/52. Factor -5/4*i**2 + c - o*i.
-5*i*(i + 3)/4
Let n(l) = 598*l + 362*l + 60*l**3 - 720 + 3567*l**2 - 4022*l**2. Let h(f) = -5*f**3 + 38*f**2 - 80*f + 60. Let p(k) = 35*h(k) + 3*n(k). Factor p(j).
5*(j - 3)*(j - 2)**2
Let x(v) be the first derivative of -3/4*v**4 + 36*v**3 - 648*v**2 + 125 + 5184*v. Suppose x(m) = 0. Calculate m.
12
Suppose -20*y + 72 + 40 = 36*y. Let z(v) be the first derivative of 43 - 8/9*v**y + 1/6*v**4 - 46/27*v**3 + 0*v. Factor z(d).
2*d*(d - 8)*(3*d + 1)/9
Let p(o) be the first derivative of 13/7*o**3 + 9/28*o**4 + 0*o - 15/7*o**2 + 141. Factor p(t).
3*t*(t + 5)*(3*t - 2)/7
Let i(m) be the second derivative of 2/21*m**3 + 1/42*m**4 + 0*m**2 + m - 1/105*m**6 + 31 - 1/35*m**5. What is f in i(f) = 0?
-2, -1, 0, 1
Let u be 6 + 1 + 1 + 6/(-3). Let d(f) = f - 3. Let o be d(u). Solve -2*s**5 - 5*s + 10*s**2 - 3*s**5 + 118 + 10*s**o - 5*s**4 - 123 = 0.
-1, 1
Suppose 3*k = u + 12, -3*u + 3 = 3*k - 7*u. Let -h**3 + 14*h - 21*h + k*h - 3*h**2 = 0. What is h?
-2, -1, 0
Let p(s) = -s**3 + 10*s**2 - 16*s - 8. Let d be p(7). Solve -h - 4*h**4 + 29*h**5 + 0*h**2 - h - d*h**5 + 4*h**2 = 0 for h.
-1, 0, 1
Let m(s) = 2*s**4 + 10*s**2 - s - 1. Let v(b) = 5*b**4 + 71*b**3 + 102*b**2 - 3*b - 3. Let f(p) = 6*m(p) - 2*v(p). Factor f(i).
2*i**2*(i - 72)*(i + 1)
Suppose -4*v + 0*v + 12 = 0. Let x be (19 - (7 - -6)) + 456/22. Solve x*i**v + 0 + 6/11*i + 84/11*i**2 = 0.
-1/7, 0
Let a be ((-4)/(-162)*-3)/((12730/3192)/(-335)). Let 2/9*j**3 - 676/9 - a*j**2 + 442/