 2
Determine v, given that 175/4 - 87/2*v - 1/4*v**2 = 0.
-175, 1
Let w = -71 - -75. Factor -10*r - 25*r**2 + r - 14*r**3 + 145*r**4 - 3*r - 146*r**w.
-r*(r + 1)**2*(r + 12)
Let o(b) = 2*b**2 - 10*b - 4. Let i(n) = n. Let p(h) = -2 + 3 + 4 - h + 0*h. Let a be p(-3). Let l(t) = a*i(t) + o(t). Factor l(g).
2*(g - 2)*(g + 1)
Suppose -5*f - 147*p + 31 = -148*p, 4*f = -3*p - 36. Determine i, given that 1/4*i**f + 0 + 21/4*i - 5/2*i**2 = 0.
0, 3, 7
Let d(x) = 19*x**2 - 58*x - 310. Suppose 0 = 14*n + 17*n + 155. Let a(j) = -13*j**2 + 38*j + 206. Let w(q) = n*d(q) - 7*a(q). What is z in w(z) = 0?
-3, 9
Let x(h) be the first derivative of -5*h**3/9 + 745*h**2/2 + 2240*h/3 + 815. Factor x(y).
-5*(y - 448)*(y + 1)/3
Factor -63/5 + 37/5*n**2 + 2/5*n**3 - 108/5*n.
(n - 3)*(n + 21)*(2*n + 1)/5
Solve -5*w**2 - 817*w + 245 + 1283*w - 706*w = 0.
-49, 1
Let b(o) be the third derivative of -o**6/240 - o**5/40 + o**4/48 + o**3/4 - 1736*o**2. Factor b(z).
-(z - 1)*(z + 1)*(z + 3)/2
Let d(b) be the first derivative of b**3/24 + 101*b**2/8 + 201*b/8 - 1308. Suppose d(z) = 0. Calculate z.
-201, -1
Let d(b) be the second derivative of -b**5/4 - 2635*b**4/12 - 5255*b**3/6 - 2625*b**2/2 + 150*b + 8. Suppose d(a) = 0. Calculate a.
-525, -1
Let q = 111 - 107. Let -5*y**q - 10*y**3 - 60*y + 164*y - 30*y + 25*y**2 - 44*y = 0. What is y?
-3, -1, 0, 2
Let j(s) be the first derivative of -1/8*s**2 + 1/8*s**4 + 1/4*s - 1/24*s**6 - 1/6*s**3 - 59 + 1/20*s**5. Suppose j(m) = 0. Calculate m.
-1, 1
Find d, given that -64*d**3 - 558*d**2 + 72*d**4 + 68*d - 7*d**5 - d**5 + 4*d**5 + 486*d**2 = 0.
-1, 0, 1, 17
Let v = 70211 - 70206. Factor 0*f**3 - 1/4*f**v + 0 + 0*f**2 + 0*f + 0*f**4.
-f**5/4
Let c(b) = 5*b**3 + b**2 + 3*b - 2. Let y be c(1). Suppose 16*d = 10*d + y*d. Factor -3/4*s**2 + 0*s - 3/4*s**3 + d.
-3*s**2*(s + 1)/4
Let v(y) = -79*y + 9798. Let l be v(124). Determine x, given that -130*x**4 - 15*x**5 - 500/3*x + 1300/3*x**l - 545/3*x**3 + 0 = 0.
-5, 0, 2/3
Let w = 200 - 201. Let d be 10 + (w + 6 - 12). Factor -2/5*n**2 + 0 - 1/5*n**d - 1/5*n.
-n*(n + 1)**2/5
Let v be ((-63)/84)/((-30)/(-32))*-1. Let j(h) be the first derivative of 0*h**2 - v*h**5 + 15 + 8/3*h**3 + 0*h + h**4. Find r, given that j(r) = 0.
-1, 0, 2
Suppose 4*d - 17 - 27 = 0. Suppose 20 = 3*t + d. Let o(m) = -3*m. Let p(j) = -j**2 + 8*j + 1. Let n(a) = t*p(a) + 8*o(a). Factor n(l).
-3*(l - 1)*(l + 1)
Find k, given that 197*k**2 + 288*k + 9*k**4 + 1/2*k**5 + 144 + 123/2*k**3 = 0.
-6, -4, -3, -1
Let x(m) be the first derivative of -5*m**3/3 - 1690*m**2 - 6740*m - 6167. Suppose x(h) = 0. Calculate h.
-674, -2
Let a(m) = 2*m**4 + 4*m**3 + 2*m**2 + m - 2. Let x(i) = 28*i**4 - 46*i**3 - 1142*i**2 + 343*i - 14. Let q(u) = 14*a(u) - 2*x(u). Determine g so that q(g) = 0.
-7, 0, 2/7, 12
Let b(i) be the first derivative of 2*i + 1/10*i**5 + 2/3*i**3 + 12 - 1/2*i**4 + 0*i**2. Let g(p) be the first derivative of b(p). Factor g(d).
2*d*(d - 2)*(d - 1)
Let h(b) = b**3 + 8*b**2 + 9*b - 10. Let d be h(-6). Factor 53 - 317 + 3*v**4 + 156*v + 54*v**2 - 41*v**3 + d*v**3 - 6*v**3.
3*(v - 11)*(v - 2)**2*(v + 2)
Let i be ((-190)/5)/(-1 - 3 - -2). Suppose 5*a + 4 = i. Solve -4*o**a + 3*o**4 - 2*o**2 - o**2 + 6 + 4*o - 5*o**2 - o**4 = 0 for o.
-1, 1, 3
Determine c, given that -56/3 + 32/3*c - 2/3*c**2 = 0.
2, 14
Let c(f) be the first derivative of -27*f**6 - 450*f**5 + 1999*f**4 - 3148*f**3 + 2355*f**2 - 850*f + 2879. Solve c(z) = 0.
-17, 5/9, 1
Let d(n) be the first derivative of 2/45*n**3 + 16/15*n - 252 + 1/30*n**4 - 2/3*n**2. Determine u so that d(u) = 0.
-4, 1, 2
Let q(a) be the third derivative of -a**7/70 + 11*a**6/40 + a**5/20 - 11*a**4/8 + 1410*a**2. Factor q(i).
-3*i*(i - 11)*(i - 1)*(i + 1)
Let z(a) be the second derivative of a**7/14 + 239*a**6/15 + 15*a**5/2 - 120*a**4 - 1433*a**3/6 - 159*a**2 + 38*a + 23. Suppose z(x) = 0. What is x?
-159, -1, -1/3, 2
Let z be (-2)/7 + (-60)/(-14). Let s = 669 - 669. What is c in z*c**2 + 0*c**2 + 8*c + s*c**2 + 0*c**2 = 0?
-2, 0
Let c(j) = -27*j + 300. Let f be c(11). Let n(d) be the second derivative of -1/9*d**4 + 4/9*d**f + 0*d**2 + 5*d - 1/15*d**5 + 0. Factor n(w).
-4*w*(w - 1)*(w + 2)/3
Let q(y) be the third derivative of y**5/4 + 205*y**4/6 + 90*y**3 + 3381*y**2. Solve q(z) = 0 for z.
-54, -2/3
Let t(p) be the third derivative of -p**5/12 - 25*p**4/8 + 85*p**3/3 + p**2 - 47. Factor t(d).
-5*(d - 2)*(d + 17)
Let x(u) be the third derivative of u**8/30240 - u**7/2100 - u**6/675 + 7*u**5/60 - u**3/3 + u**2 + 4. Let k(g) be the third derivative of x(g). Factor k(p).
2*(p - 4)*(5*p + 2)/15
Let b(n) be the first derivative of 4*n**5/5 + 7*n**4 - 4*n**3 - 110*n**2 + 200*n + 2293. Factor b(f).
4*(f - 2)*(f - 1)*(f + 5)**2
Solve 20/3*v**3 - 76/3*v**2 - 80*v - 48 = 0.
-6/5, -1, 6
Let x(r) be the second derivative of -5*r**7/42 + 3*r**6/2 + 33*r**5/4 - 1085*r**4/12 - 680*r**3 - 1440*r**2 - 15*r + 68. Suppose x(z) = 0. What is z?
-3, -1, 8
Let z(h) be the first derivative of -2*h**5/45 + 13*h**4/18 - 62*h**3/27 - 5*h**2 + 143. Factor z(n).
-2*n*(n - 9)*(n - 5)*(n + 1)/9
Suppose 2*d = -2 + 10. Suppose -3*z - 8 = -c - d*z, 3*c + 4*z = 25. Factor 8*p**3 - c*p**4 + 18*p**3 - 8*p**2 - 8*p**3 + 12*p**3.
-p**2*(p - 4)*(7*p - 2)
Let k = 84883/14 + -6063. Let u(a) be the first derivative of 5/7*a**2 - 4/7*a - 8/21*a**3 + k*a**4 - 4. Determine n so that u(n) = 0.
1, 2
Suppose -63 + 231 = 21*n. Suppose 0 = 2*c - 2*x, 3*x - n*x + 2 = -4*c. Determine m so that -c*m + 0 - 1/3*m**2 = 0.
-6, 0
Let k(c) be the third derivative of 7*c**5/180 + 17*c**4/36 + 13*c**3/6 - 79*c**2 - 1. What is o in k(o) = 0?
-3, -13/7
Let n(h) = -850*h - 7650. Let v be n(-9). Let a(j) be the second derivative of 81*j**2 - 6*j**3 + 1/6*j**4 + 10*j + v. What is r in a(r) = 0?
9
Suppose 16/11 + 74/11*w**2 + 2*w**3 + 68/11*w = 0. Calculate w.
-2, -1, -4/11
Let k = 5243/346 - 2535/173. Factor k*x**5 + 3*x**4 + 11/2*x**3 + 0*x + 0 + 3*x**2.
x**2*(x + 1)*(x + 2)*(x + 3)/2
Factor 26*v**3 + 35655*v**5 - 10*v**4 + 16*v**2 + 21*v**4 - 35654*v**5.
v**2*(v + 1)*(v + 2)*(v + 8)
Factor -108*w**3 + 705*w**4 - 5400*w - 544 - 4456 - 1658*w**2 - 1417*w**4 + 710*w**4.
-2*(w + 2)**2*(w + 25)**2
Factor -128/5*m**2 - 322/5*m**4 + 98/5*m**5 + 0 + 0*m + 352/5*m**3.
2*m**2*(m - 1)*(7*m - 8)**2/5
Let w = -33015 + 33019. Let m(p) be the second derivative of -2/3*p**2 - 16*p + 0 + 1/18*p**w - 1/9*p**3. Factor m(f).
2*(f - 2)*(f + 1)/3
Suppose -3*y + 11 = 5*f - 0*y, 2*f - 3*y = 17. Suppose -36*l = -35*l - f. Solve l*k + 10*k**2 - 8*k**2 + 4*k = 0.
-4, 0
Let k be (-4)/(-2)*-86*-7. Let v be -6 - k/(-77)*3/6. Factor 2/11*q**2 + 50/11 - v*q.
2*(q - 5)**2/11
Let u(t) be the second derivative of 0 + 0*t**2 - 1/84*t**7 + 1/20*t**6 + 12*t + 0*t**3 - 1/20*t**5 + 0*t**4. Factor u(y).
-y**3*(y - 2)*(y - 1)/2
Let p(y) be the third derivative of y**8/110880 + y**7/1980 + 41*y**5/60 - 233*y**2. Let k(r) be the third derivative of p(r). Factor k(i).
2*i*(i + 14)/11
Let v(i) be the third derivative of -7/4*i**4 - 43/160*i**6 + 0*i - 73/80*i**5 - 1/448*i**8 - 11/280*i**7 + 0 - 2*i**3 - 322*i**2. Let v(d) = 0. Calculate d.
-4, -1
Factor 20*w**2 + 46*w**2 + 25*w + 192*w + 4*w**3 + 560 + 10*w**2 + 199*w.
4*(w + 2)*(w + 7)*(w + 10)
Suppose 0 = -i + 4*s - 16, 3 - 9 = i - 2*s. Factor 0 - 21*a + 1 + 0*a**5 - 26*a**3 + 9*a**i + 34*a**2 + 4 - a**5.
-(a - 5)*(a - 1)**4
Suppose -53*v + 6 = -51*v - 4*o, o - 12 = -4*v. Let b = 117/74 - 3/37. Let 1/2*n**v + n + 0 - b*n**2 = 0. Calculate n.
0, 1, 2
Let x be (-62)/(-24) - 19*(-98)/(-798). Let a(m) be the second derivative of 14*m + 0 + 1/8*m**4 - 3/2*m**2 + x*m**3. Determine l so that a(l) = 0.
-2, 1
Factor -6*k**2 + k**3 + 2*k - 168 + 150*k**2 - k**3 + 24 - 2*k**3.
-2*(k - 72)*(k - 1)*(k + 1)
Factor 8/15*i - 136 + 2/15*i**2.
2*(i - 30)*(i + 34)/15
Let 2977566 - 898*o - 794*o**3 - 758*o - 3144*o**2 - 2977790 + 162*o**5 + 1080*o**4 = 0. What is o?
-7, -1, -4/9, -2/9, 2
Let w(l) be the first derivative of -l**6/12 - 59*l**5/10 - 53*l**4/8 + 287*l**3/6 - 87*l**2/2 - 2454. Suppose w(h) = 0. What is h?
-58, -3, 0, 1
Suppose 0 = -233*v + 107*v. Let b(s) be the second derivative of 15*s + v*s**3 + 1/54*s**4 + 0*s**2 + 0. Factor b(q).
2*q**2/9
Solve 0*h + 1/9*h**5 + 0*h**2 + 0 + 40/9*h**3 - 13/9*h**4 = 0 for h.
0, 5, 8
Let h(r) = 10*r**2 + 70*r + 12