3
Let t be (-9)/12 - (-35)/(-28). Let z be (-28)/(-10) + t/(-10). Let 18*p**2 - z*p**2 - 10*p**2 - 20 = 0. Calculate p.
-2, 2
Factor -24/5*y**2 - 14/5*y**3 - 6/5*y + 4/5.
-2*(y + 1)**2*(7*y - 2)/5
Suppose 26*x = 12*x + 28. Let 3/5*r**x - 12/5*r + 12/5 = 0. Calculate r.
2
Let t(n) be the second derivative of -n**4/6 + 4*n**3 - 20*n**2 - 160*n + 1. Factor t(j).
-2*(j - 10)*(j - 2)
Let w(c) be the first derivative of 2*c**3/21 - 13*c**2/7 + 24*c/7 - 219. Factor w(l).
2*(l - 12)*(l - 1)/7
Find x such that 2/9*x**2 + 800/9 + 80/9*x = 0.
-20
Suppose 2 = -6*x + 7*x. Factor 196 - 18*w**x + 41*w**2 + 56*w - 19*w**2.
4*(w + 7)**2
Let h(v) = v**2 - 25*v + 114. Let d be h(6). Factor 0*j**2 + 0 + 0*j**3 + d*j - 1/3*j**4 + 1/3*j**5.
j**4*(j - 1)/3
Let q = 3/4 + -1/4. Let w = 886 + -882. Let -1/3*l**2 + 1/6*l**w + q*l + 1/6 + 1/2*l**5 - l**3 = 0. Calculate l.
-1, -1/3, 1
Let h(l) be the third derivative of -1/220*l**5 - 1/66*l**3 + 13*l**2 + 0*l + 1/88*l**4 + 1/1320*l**6 + 0. Factor h(r).
(r - 1)**3/11
Let k be ((-8)/((-160)/12))/(12/10). Let v = -7/9 - -23/18. Factor 0 - f - k*f**2 + v*f**3.
f*(f - 2)*(f + 1)/2
Factor 6*j**2 - 392/9 + 112/3*j + 2/9*j**3.
2*(j - 1)*(j + 14)**2/9
Let i = 45480/7 - 6496. Solve -i*g + 2/7*g**4 + 16/7*g**3 + 30/7*g**2 - 40/7 = 0.
-5, -2, 1
Let o = 4342 - 8681/2. Factor -6*m - 12*m**2 - o*m**4 + 0 - 15/2*m**3.
-3*m*(m + 1)*(m + 2)**2/2
Suppose 17*j + 6 = 40. Solve 10*f - 36 - 14*f + 136*f - 116*f**2 - 5*f**j = 0.
6/11
Let l = 495 - 492. Let b(t) be the first derivative of 1/15*t**l + 0*t - 7 + 1/5*t**2. Let b(v) = 0. What is v?
-2, 0
Let h be 5*((-90)/40 + 15/6). Let c(v) be the second derivative of 3/5*v**5 - 4*v + 0*v**2 + v**3 + h*v**4 + 0 + 1/10*v**6. Factor c(p).
3*p*(p + 1)**2*(p + 2)
Let x(b) = -b**3 - 74*b**2 - 141*b + 218. Let h be x(-72). Factor 0*f**3 + 2/3*f**5 + 0 + 0*f**h + 2/3*f**4 + 0*f.
2*f**4*(f + 1)/3
Let h(u) = -8*u**2 - 8*u + 20. Let z(s) = -s**3 - 8*s**2 - 5*s + 19. Let a(r) = -5*h(r) + 4*z(r). Factor a(m).
-4*(m - 3)*(m - 1)*(m + 2)
Let c be (-3 - -1) + 4 + 4. Let w be 2/6*(-4)/((-32)/c). Factor 3/2*t**3 + 0 + 1/4*t + w*t**5 + t**4 + t**2.
t*(t + 1)**4/4
Suppose 0 = -2*r + 5*a + 8, 23 = -5*r - 4*a + 43. Factor 3/7*s**r + 3/7*s**3 + 0 - 3/7*s**2 - 3/7*s.
3*s*(s - 1)*(s + 1)**2/7
Let k(n) be the third derivative of -3/4*n**3 + 0*n - 1/40*n**5 + 0 + 5/16*n**4 - 1/80*n**6 + 12*n**2. Find d such that k(d) = 0.
-3, 1
Factor 2/13*v**2 - 2/13*v + 2/13*v**3 - 2/13*v**4 + 0.
-2*v*(v - 1)**2*(v + 1)/13
Factor -32 + 28*g**3 + 34*g**2 - 63*g**2 - 69*g - 5*g**4 - 11*g**2 - 43*g + 17*g**4.
4*(g - 2)*(g + 2)**2*(3*g + 1)
Let l be 118/60 - (-1)/2. Let j = -9/5 + l. Let -1/3*g - 1/3*g**4 - 1/3 - 1/3*g**5 + j*g**2 + 2/3*g**3 = 0. Calculate g.
-1, 1
Factor -16 + 1/2*c**3 + 0*c + 3*c**2.
(c - 2)*(c + 4)**2/2
Suppose 50 = -3*x - 19. Let o = 70/3 + x. Solve -o + 2/3*p + 1/3*p**2 - 2/3*p**3 = 0 for p.
-1, 1/2, 1
Let p be ((-16)/(-320))/((-1)/(-12)). Solve -1/5*m**5 + p*m**3 - m**2 + 2/5*m + 1/5*m**4 + 0 = 0.
-2, 0, 1
Let s(x) = -2*x**2 - 25*x - 67. Let d be s(-8). Let c(m) be the third derivative of 0 + 1/36*m**4 + 0*m**3 + 1/36*m**5 + 0*m - 7/360*m**6 - d*m**2. Factor c(r).
-r*(r - 1)*(7*r + 2)/3
What is i in -16 + 83/2*i**2 + 5/2*i**3 + 23*i = 0?
-16, -1, 2/5
Let k = -146 - -96. Let j be (k/(-15) - 2/6) + 0. Factor 6/7*x**2 + 0*x**j - 3/7*x**4 + 0*x - 3/7.
-3*(x - 1)**2*(x + 1)**2/7
Let f(h) = -2*h + 9. Let t be f(6). Let r be (-92)/t - (-12)/9. Let 1 - 10 - 4 + 20*i**2 - 3 + r*i = 0. Calculate i.
-2, 2/5
Let y(g) be the third derivative of -g**8/1512 - 2*g**7/945 + 13*g**6/540 + 7*g**5/135 - 2*g**4/9 + 53*g**2 + 4. Suppose y(v) = 0. What is v?
-4, -2, 0, 1, 3
Let q(v) = 2*v**2 - 65. Let b be q(-9). Let i = 0 - -3. Solve -4*s**i - b*s + 48*s**2 - 149*s + 256 + 54*s = 0 for s.
4
Factor -45 - 3/2*p**2 + 39/2*p.
-3*(p - 10)*(p - 3)/2
Let v(j) be the second derivative of -j**7/280 - j**6/40 - 17*j**3/6 + 6*j. Let o(s) be the second derivative of v(s). Determine l, given that o(l) = 0.
-3, 0
Let s(r) = -r**2 + 5*r - 13. Let t be s(8). Let z = t + 39. Suppose -2/3*y**4 - 2*y**3 + z*y - 2/3*y**2 + 4/3 = 0. What is y?
-2, -1, 1
Let l(k) be the third derivative of -k**5/140 - k**4/14 - 2*k**3/7 - 26*k**2 - 2. Factor l(v).
-3*(v + 2)**2/7
Let b(t) be the first derivative of t**6/6 - t**5 + 3*t**4/2 + 2*t**3/3 - 7*t**2/2 + 3*t - 19. Factor b(n).
(n - 3)*(n - 1)**3*(n + 1)
Let x be (-1)/(-3) - 8/60. Let v be 1*((-6)/(-4) - (-156)/(-120)). Find r such that v - x*r**2 + 0*r = 0.
-1, 1
Solve 287/4*k**2 + 35/4 - 123/2*k + 138*k**3 - 4*k**4 = 0.
-1, 1/4, 35
Let c = 5213/7021980 - -2/39011. Let t(k) be the third derivative of c*k**7 + 0*k + 0*k**4 + 0 + 1/360*k**5 - 3*k**2 + 1/360*k**6 + 0*k**3. Factor t(o).
o**2*(o + 1)**2/6
Find s such that -26/5*s**2 - 2/5*s**3 - 46/5*s - 22/5 = 0.
-11, -1
Let -2/15*r**4 + 16/5*r - 96/5 - 4/15*r**3 + 46/15*r**2 = 0. What is r?
-4, 3
Factor -74*g + 2*g**2 - 4*g**3 - 7 - g**5 + 73*g + 6 + 3*g**3 + 3*g**3 - g**4.
-(g - 1)**2*(g + 1)**3
Let j(q) be the third derivative of -1/2*q**3 + 0*q + 0 - 1/12*q**5 + 1/120*q**6 + 13*q**2 + 7/24*q**4. Solve j(w) = 0.
1, 3
Let a = 128 + -120. Let w(y) be the third derivative of 0*y + 0*y**4 + 0*y**3 - 1/70*y**7 + 1/20*y**5 + 0 - 1/40*y**6 - 6*y**2 + 1/112*y**a. Factor w(z).
3*z**2*(z - 1)**2*(z + 1)
Let x(h) be the third derivative of h**8/20160 - h**7/1260 + h**6/240 - h**5/20 + 9*h**2. Let j(a) be the third derivative of x(a). Factor j(t).
(t - 3)*(t - 1)
Suppose 0 = -l - 4*c + 3 - 17, 0 = -3*c - 12. Let s be l + -3 + (-6)/(-2). Let 0*x - 3/2*x**s + 0*x**3 + 3/4*x**4 + 3/4 = 0. What is x?
-1, 1
Let m(q) = -2*q + 5*q - 2*q + 7*q**2. Let r(z) = -6*z**2 - 2*z. Let s(x) = 2*m(x) + 3*r(x). Find h such that s(h) = 0.
-1, 0
Let h(d) = 2*d**3 - 29*d - 3 + 26*d + 2 - 6*d**2. Let s(g) = g**3 - 4*g**3 + 2*g**3 + g**2. Let v(r) = h(r) + 3*s(r). Solve v(i) = 0.
-1
Let h(q) be the first derivative of 1/66*q**4 + 1 + 4*q + 1/33*q**3 + 0*q**2 - 1/165*q**6 - 1/110*q**5. Let r(w) be the first derivative of h(w). Factor r(f).
-2*f*(f - 1)*(f + 1)**2/11
Let j(a) be the third derivative of a**8/336 - a**7/210 - a**6/40 + a**5/60 + a**4/12 - 21*a**2. Solve j(t) = 0 for t.
-1, 0, 1, 2
Let p(n) be the first derivative of 1/6*n**3 - 1/2*n**2 - 3 - 3/2*n. Factor p(a).
(a - 3)*(a + 1)/2
Factor -16*d**4 + 26*d**4 + 150 - 7*d**4 + 420*d + 207*d**2 + 150 + 42*d**3.
3*(d + 2)**2*(d + 5)**2
Let o(x) be the second derivative of -x**6/18 - 3*x**5/10 + 11*x**4/12 - 5*x**3/9 - x - 38. Factor o(y).
-y*(y - 1)*(y + 5)*(5*y - 2)/3
Let l(n) be the first derivative of -n**3 + 3*n**2/2 + 6*n + 7. Let l(k) = 0. What is k?
-1, 2
Let k be 0/(-2) + 1134/112. Factor 81/8*h - k - 27/8*h**2 + 3/8*h**3.
3*(h - 3)**3/8
Let z = -181 + 183. Let v = -76/33 - -51/11. Factor -v*j + j**z + 2/3.
(j - 2)*(3*j - 1)/3
Let n = 2312 + -11558/5. Find w such that n*w**2 + 0 + 2/5*w**3 - 2/5*w**5 + 0*w - 2/5*w**4 = 0.
-1, 0, 1
Determine l, given that -359*l**2 + 8 + 0 + 369*l**2 - 35*l + 12 + 5*l**3 = 0.
-4, 1
Let x(g) = 12*g - 168. Let d be x(14). Determine p so that d - 12/5*p - 1/5*p**4 - 16/5*p**2 - 7/5*p**3 = 0.
-3, -2, 0
Let j(o) be the second derivative of -o**6/1440 + o**5/480 + 4*o**3/3 - 31*o. Let z(y) be the second derivative of j(y). Factor z(p).
-p*(p - 1)/4
Let t = -45 - -47. Determine f so that -25*f**2 + 17*f - 2*f + 5*f - 5 + 10*f**t = 0.
1/3, 1
Let q = -43 - -47. Let j(x) = 4*x. Let s be j(4). Factor 8*p - 40*p + 4*p**4 - s + q*p**3 + 16*p**3 - 4*p**5 - 4*p**2.
-4*(p - 2)**2*(p + 1)**3
Let v(d) be the second derivative of 34*d - 1/50*d**5 + 0 + 1/30*d**4 + 8/5*d**2 + 2/3*d**3. Find f such that v(f) = 0.
-2, -1, 4
Let m(x) be the second derivative of 0 + 7/4*x**5 + 0*x**2 + 5/6*x**3 + 8*x + 25/12*x**4 + 1/2*x**6. Factor m(i).
5*i*(i + 1)**2*(3*i + 1)
Let c(w) be the second derivative of -81*w**5/40 + 133*w**4/8 + 5*w**3/2 + 4*w - 15. What is v in c(v) = 0?
-2/27, 0, 5
Solve 37*i**2 - 9 + 14 - 21*i**2 + 6*i - 15*i**2 = 0 for i.
-5, -1
Let r(x) = -33*x - 3. Let d be r(1). Let l = d - -39. Factor -1/4*n**l - 1/4*n**2 + 1/4*n**5 + 0*n + 0 + 1/4*n**4.
n**2*(n - 1)*(n + 1)**2/4
Let y(a) = 7*a**4 + 9*a**3 + 9*a**2 + 7*a. Let q = -181 - -187. Let x(b) = b + b**2 + b**4 + 2*b**3 - 2*b**3 + b**3. Let m(v) = q*x(v) - y(v). Factor