 2, 4
Let g(l) be the third derivative of -l**6/540 - 214*l**5/15 - 45796*l**4 - 78402752*l**3 - 15*l**2 + 12*l. Factor g(x).
-2*(x + 1284)**3/9
Let l(v) be the second derivative of -v**5/4 - 1465*v**4/12 - 730*v**3/3 + 524*v. Determine o, given that l(o) = 0.
-292, -1, 0
Let m(d) be the first derivative of -d**4/2 + 10*d**3 + 126*d**2 - 373. Determine g so that m(g) = 0.
-6, 0, 21
Let j be (17 + 1476/(-90))*1. Factor -j*q**2 + 6/5*q + 0.
-3*q*(q - 2)/5
Let j = 106316 - 531576/5. Factor 0*t + 0 + 0*t**2 - j*t**3 + 3/5*t**4 + 1/5*t**5.
t**3*(t - 1)*(t + 4)/5
Let a(p) be the first derivative of -27*p**5/35 - 2088*p**4/7 - 214366*p**3/7 + 215760*p**2/7 - 72075*p/7 - 619. Suppose a(y) = 0. Calculate y.
-155, 1/3
Let b be 3360/128*2/(-7) + 10. Find v such that 1/2*v**5 - b*v**4 + 9/2*v**2 + 0*v + 3/2*v**3 + 0 = 0.
-1, 0, 3
Let k(s) = -15*s. Let v be k(4). Let x be (-1)/((-1)/(-5) + 22/v). Let 27*m**3 - 8 + x*m**2 - 49*m**3 + 24*m**3 = 0. Calculate m.
-2, 1
Let y = 62 + -58. Find o such that -205*o**3 + 2*o**5 - o**5 + o**y + 203*o**3 = 0.
-2, 0, 1
Let h be 180/30 - (-2 - (-2 - -2)). Let p(u) be the third derivative of h*u**3 + 1/20*u**5 + 8*u**2 - u**4 + 0*u + 0. Find n such that p(n) = 0.
4
Let o(l) = -4*l**4 + 12*l**3 - 20*l**2 - 28*l + 24. Suppose 1 = 5*z - 4*z. Let a(w) = w**4 + w**3 - w**2 + w. Let q(i) = z*o(i) + 8*a(i). Factor q(k).
4*(k - 1)**2*(k + 1)*(k + 6)
Suppose 3*l = 5*b - 6*b + 12, 4*l = 3*b + 16. Let g = 4578/5 - 915. Factor 0 + g*z**5 + 2/5*z**2 - 4/5*z**4 + b*z - 1/5*z**3.
z**2*(z - 1)**2*(3*z + 2)/5
Let a(p) be the third derivative of -p**6/1380 - 4*p**5/23 - 1599*p**4/92 - 63878*p**3/69 - p**2 - 145*p - 5. Find r, given that a(r) = 0.
-41, -38
Let o = -64 + 49. Let t = -1 - o. Determine q, given that -3 + 17*q**3 + q**3 + 3*q**2 - 32*q + t*q = 0.
-1, -1/6, 1
Let v = -189430/3 - -63152. Find d, given that 7/3*d**3 - 8/3*d + 0 + v*d**2 = 0.
-4, 0, 2/7
Let p(g) be the third derivative of g**6/30 - 178*g**5/5 + 15842*g**4 - 11279504*g**3/3 - 2*g**2 + 82*g + 3. Find v such that p(v) = 0.
178
Suppose 10512*a - 10592*a = 0. Factor a*t - 16/7*t**2 + 0 - 2/7*t**3.
-2*t**2*(t + 8)/7
Let t(w) be the first derivative of w**4/4 - 382*w**3/3 + 36481*w**2/2 + 2475. Let t(y) = 0. Calculate y.
0, 191
Let b(p) be the second derivative of p**7/2520 + p**6/144 - p**5/20 - p**4/6 + 3*p**2/2 - 48*p. Let w(h) be the third derivative of b(h). Factor w(m).
(m - 1)*(m + 6)
Let r(u) be the first derivative of 3/35*u**5 + 256/7*u**3 + 196 + 0*u + 0*u**2 + 24/7*u**4. Factor r(m).
3*m**2*(m + 16)**2/7
Solve -12*x**3 + x**4 - 180*x**2 - 227*x**2 + 122*x**2 - 1328*x + 2240 - 16*x**3 + 576*x**2 = 0 for x.
5, 7, 8
Let t(c) = 13*c**2 - 3906*c + 980109. Let g(r) = -3*r**2 + 978*r - 245027. Let l(j) = -9*g(j) - 2*t(j). Factor l(q).
(q - 495)**2
Let k be -11 + 7 - 4 - 0. Let v be ((-3)/4)/(k + 5). Determine z so that v*z - 1/4*z**2 + 1/2 = 0.
-1, 2
Factor 688017 + 145847*t**2 + 55995 - 135875*t**2 + 20*t**3 + 1245996*t.
4*(t + 249)**2*(5*t + 3)
Suppose 3*j + 88 = 5*w + 82, -4*j = -4*w. Determine u, given that 44/7*u - 4*u**2 - 20/7 + 4/7*u**j = 0.
1, 5
Let w(t) be the third derivative of t**6/1260 + 4*t**5/315 - t**4/21 - 16*t**3/7 - t**2 - 448*t. Factor w(g).
2*(g - 4)*(g + 6)**2/21
Suppose -u - u = -4*w, 0 = -u - 4*w + 6. Suppose -2*k = -4*m - 12, m = 3*k - 3*m - 16. Factor -9*f**u + 17*f**2 + k*f - 12*f**2.
-4*f*(f - 1)
Find q such that -2104*q**5 + 99199*q + 674210*q + 1984*q**3 - 9*q**4 + 2103*q**5 + 68096*q**2 + 62175*q + 3604480 = 0.
-16, 55
Let c(q) = 2*q**3 - 32*q**2 + 63*q - 1644. Let d be c(17). Suppose -1666/5*y**3 - 1242/5*y**4 + 1458/5*y**d + 1234/5*y**2 + 8/5 + 208/5*y = 0. Calculate y.
-1, -2/27, 1
Suppose -11*r + 304 = 73. Suppose 37*m = r*m. Let -8/9*i**2 + 2/9*i**3 + 0 + m*i = 0. Calculate i.
0, 4
Let j(p) be the second derivative of -p**5/70 - 41*p**4/42 - 40*p**3/21 + 880*p. Find t, given that j(t) = 0.
-40, -1, 0
Let o be (28 - 19) + 74/(-8) + (-9)/(-36). Let q(b) be the third derivative of 2/21*b**3 - 43*b**2 - 5/84*b**4 - 1/420*b**6 + 2/105*b**5 + o + 0*b. Factor q(p).
-2*(p - 2)*(p - 1)**2/7
Let p be (4/(-2))/(2/(-3)). Factor 2*h**3 - h**p - 19*h - 6*h**3 - 21*h - 30*h**2.
-5*h*(h + 2)*(h + 4)
Let c(y) be the second derivative of -y**7/210 + 8*y**6/45 - y**5/2 - 37*y**3/3 + y**2/2 + 71*y. Let q(u) be the second derivative of c(u). Factor q(s).
-4*s*(s - 15)*(s - 1)
Suppose -151/3*q + 185/6*q**2 - 61/6*q**4 + 19/2*q**3 + 1/6*q**5 + 20 = 0. What is q?
-2, 1, 60
Suppose 3*j + 2*a = 12, -j - 202*a + 8 = -200*a. Let n(p) be the first derivative of -36*p + 30*p**j - 15 + p**4 - 28/3*p**3. Factor n(z).
4*(z - 3)**2*(z - 1)
Suppose -d + 3*z - 2 = -13, 23 = 4*d - 5*z. Let r be -2 - (3 + -5 - (d + 38)). Let -195*x**3 - 40*x**4 - 5*x**4 - 180*x - r + 7 - 290*x**2 - 7 = 0. Calculate x.
-2, -1, -2/3
Let d(l) be the first derivative of l**5/100 - l**4/15 + 2*l**3/15 - l**2/2 + 96*l - 5. Let q(i) be the second derivative of d(i). Factor q(t).
(t - 2)*(3*t - 2)/5
Let c(j) be the first derivative of -5*j**3/3 - 10145*j**2 - 20584205*j + 7407. Determine z so that c(z) = 0.
-2029
Let b(r) = r**2 + 10*r + 11. Let f be b(-10). Suppose 0 = -14*j - 190 + 218. Solve -6*n + 0*n**2 + j*n - 3*n**2 - f*n = 0.
-5, 0
Factor -9*s**2 - 14 - 10*s**2 + 16*s - 11*s**2 + 28*s**2.
-2*(s - 7)*(s - 1)
Let o(q) be the first derivative of -q**8/672 - q**7/112 - q**6/72 - 17*q**3 - 49. Let p(w) be the third derivative of o(w). Solve p(x) = 0 for x.
-2, -1, 0
Let l(u) = -2*u**2 + 2*u - 1. Let p(q) be the second derivative of q**4 - 17*q**3/6 + 3*q**2 - 12*q. Let g(f) = 12*l(f) + 3*p(f). Factor g(h).
3*(h - 2)*(4*h - 1)
Let f be (-2)/6*-27 - 7. Let 5*c**2 - 5*c**2 - 27*c**f - 18*c**2 + 540 + 5*c**3 = 0. What is c?
-3, 6
Let l(d) = -5*d**4 + 948*d**3 + 707*d**2 - 136*d - 10. Let o(u) = -2*u**4 - u**3 - 11*u**2 - u - 1. Let i(f) = -l(f) + 10*o(f). Factor i(z).
-z*(z + 1)*(z + 63)*(15*z - 2)
Suppose -c - 3*n + 2 = 0, 13*n = 2*c + 10*n - 13. Determine b, given that -35*b - 2919 + 2919 + c*b**2 = 0.
0, 7
Let a = -13116/7 - -1881. Solve 33/7*d**2 + 159/7*d**3 - a*d**5 - 108/7*d + 12/7 - 45/7*d**4 = 0 for d.
-2, -1, 2/17, 1
Let i = 2 + -2. Let s(x) be the second derivative of -10*x + 1/3*x**3 + i*x**2 - 1/6*x**4 + 0. Factor s(h).
-2*h*(h - 1)
Let t(f) be the third derivative of -f**5/180 - 19*f**4/72 + 14*f**3 + 13723*f**2. Factor t(n).
-(n - 9)*(n + 28)/3
Let r(w) be the first derivative of 2*w**3/3 - 43*w**2 + 660*w + 1787. Suppose r(i) = 0. Calculate i.
10, 33
Suppose 798 = 30*m - 24*m. Factor 2*g**3 + 109*g - 29*g**2 + m*g**2 + 506*g + 737*g.
2*g*(g + 26)**2
Let a(v) be the third derivative of v**6/1080 + v**5/20 + 9*v**4/8 + 20*v**3 + 186*v**2. Let i(n) be the first derivative of a(n). Factor i(f).
(f + 9)**2/3
Let a(u) be the first derivative of -2*u**5/65 - u**4/13 + 2*u**3/39 + 2*u**2/13 + 756. Solve a(s) = 0.
-2, -1, 0, 1
Let q be (2 - (-406)/(-218))*(-333)/(-297). Let c = q + 3/109. Find r, given that -4/11*r - c*r**3 + 0 + 6/11*r**2 = 0.
0, 1, 2
Let h(i) = 7*i**2 - 23*i + 14. Suppose 0 = -4*p - 7 - 29. Let w(m) = -15*m**2 + 48*m - 27. Let v(d) = p*h(d) - 4*w(d). Factor v(u).
-3*(u - 3)*(u - 2)
Let s be (-7)/(7*(-13)/156). Let f be (340/(-136))/((-10)/s). Factor 0 + 1/6*p**4 + 2/3*p**f + 0*p + 2/3*p**2.
p**2*(p + 2)**2/6
Let w(t) be the first derivative of -4*t**3 + 27/2*t**2 - 1/4*t**4 - 31 + 9*t. Let i(g) be the first derivative of w(g). Determine a, given that i(a) = 0.
-9, 1
Let y be (-20 + (-10 - -27))/(4 - (-76)/(-16)). What is z in 2/5*z**3 - 4/5*z**2 - y - 26/5*z = 0?
-2, -1, 5
Suppose -5*u = -23 + 28. Let r(v) = v**3 - 2*v**2 - 1. Let t(o) = -4*o**3 + 8*o**2 - 6*o + 6. Let q(a) = u*t(a) - 6*r(a). Factor q(l).
-2*l*(l - 3)*(l + 1)
Factor 4*w**2 - 133/2 - 125/2*w.
(w + 1)*(8*w - 133)/2
Let t(f) = f**4 - f**3 - f**2 - f + 1. Let n = -183 + 201. Let g(b) = -21*b**4 + 30*b**3 + 3*b**2 + 24*b - 18. Let i(l) = n*t(l) + g(l). Factor i(a).
-3*a*(a - 2)*(a - 1)**2
Factor -11181*a**3 + 3726*a**3 + 3729*a**3 + 3727*a**3 + 464*a - 99*a**2 + 564.
(a - 94)*(a - 6)*(a + 1)
Let n be ((-140)/30)/((4/14)/((-42)/98)). Determine m so that m**2 + n*m + 8 - 1/4*m**3 = 0.
-2, 8
Let m(t) be the second derivative of t**4/3 - t**3/3 - 9*t**2 + 109*t. Let q be m(-2). Factor -2/7*u**4 - 10/7*u**