- 12*p**3 - 3*p**2 - 2*p**4 + 8*p + 4*p**2 - f*p**2 + 24.
-2*(p - 1)*(p + 2)**2*(p + 3)
Suppose -9*t + 8 = -28. Suppose 13*i - 51*i + 162 - 80*i - 24*i**3 + 108*i**2 + 2*i**t + 4*i - 102*i = 0. Calculate i.
3
Let h be 12*(15 + 5615/(-375)). Let l(z) be the second derivative of 5*z - 29/30*z**4 - 1/25*z**6 + 0 - 4/5*z**2 + h*z**5 + 4/3*z**3. Solve l(a) = 0 for a.
1/3, 1, 2
Find i such that -29/4 - 7/2*i**2 - 239/8*i = 0.
-58/7, -1/4
Let y(o) = 33*o**2 - 205*o - 543. Let s(h) = -14*h**2 + 98*h + 271. Let m(j) = -7*s(j) - 3*y(j). Factor m(n).
-(n + 4)*(n + 67)
Let n(o) be the third derivative of -o**5/180 + 3*o**4/8 + 119*o**3/9 + 283*o**2 + 2*o. Suppose n(b) = 0. Calculate b.
-7, 34
Let b(a) be the first derivative of -3*a**4/2 + 7*a**3 - 3*a**2 - 9*a - 5192. Factor b(y).
-3*(y - 3)*(y - 1)*(2*y + 1)
Let f = 3856/105 + -14269/420. Solve -f*a**2 + 3/2*a**3 + 3/2*a + 0 - 1/4*a**4 = 0 for a.
0, 1, 2, 3
Let j = -70 - -56. Let f be 70/30*(-4)/j. Factor -2/3*l**2 + 1/6*l**3 + f*l + 0.
l*(l - 2)**2/6
Suppose -2*z = 5*p - 11, -2*p + 0 = 4*z + 2. Suppose 8*g = 12*g - 2*y - 6, 2*g - 9 = p*y. Factor 0*i**2 + 2/5*i**3 - 2/5*i**5 + 0 + g*i**4 + 0*i.
-2*i**3*(i - 1)*(i + 1)/5
Let 6*c**3 - 121/2*c**2 - 25/2 + 155*c = 0. Calculate c.
1/12, 5
Let s be (-24)/(1 - -5)*4/(-48). Let v(h) be the third derivative of 0*h + 5/8*h**4 + 5/6*h**3 + 0 - s*h**5 - 7*h**2. Find y such that v(y) = 0.
-1/4, 1
Suppose 8473*w = 8438*w. Let i(m) be the third derivative of 1/200*m**6 - 3*m**2 + 0 + w*m**3 - 1/50*m**5 + 0*m - 3/40*m**4. Factor i(q).
3*q*(q - 3)*(q + 1)/5
Let a(i) be the first derivative of i**8/560 - i**6/120 + 44*i**3/3 + 67. Let b(m) be the third derivative of a(m). Suppose b(o) = 0. What is o?
-1, 0, 1
Let b(t) be the third derivative of t**6/1080 + 49*t**5/90 - 295*t**4/216 + 1718*t**2 - 5. Factor b(u).
u*(u - 1)*(u + 295)/9
Let w = -111/860 - -91/172. What is x in -1/5*x**3 - 1/5*x**2 + w*x + 0 = 0?
-2, 0, 1
Factor 5/3*n**2 - 15 + 3*n - 1/3*n**3.
-(n - 5)*(n - 3)*(n + 3)/3
Let o(q) = -2 - q**2 - 3 + 4*q + 7. Let g be o(4). Factor 21/4*h**g - 15/4*h - 9/4*h**3 + 3/4.
-3*(h - 1)**2*(3*h - 1)/4
Let m(d) = d**2 + 6*d - 53. Let x be m(-11). Let 3 - 82*o**2 + 4 + 18*o**x - 18 + 3 + 28*o**3 + 44*o = 0. What is o?
2/7, 1
Factor -77/2*f**2 + 13689/2 + 1/6*f**3 + 4329/2*f.
(f - 117)**2*(f + 3)/6
Let u(a) be the second derivative of 5*a**4/12 - 25*a**3 - 155*a**2/2 + 387*a. Find o, given that u(o) = 0.
-1, 31
Suppose 0*o - 2*o = -2*l - 2, 3*l = 5*o + 1. Let q be (-51)/(-6) - l/(-2). Find t, given that 0*t**2 - q*t - 3*t**2 - 2*t = 0.
-3, 0
Let y = -139 + 245. Let u = y + -92. Determine c so that 0*c + u*c**3 - 19*c - 13*c - 577*c**2 + 2*c**4 + 593*c**2 = 0.
-4, 0, 1
Determine p, given that 2/15*p**5 + 904/15*p**2 - 2290*p - 20*p**4 + 3748/5*p**3 + 1500 = 0.
-2, 1, 75
Solve 48 - 9883*g**3 + 47*g**2 + 9859*g**3 + 43*g**2 - 116*g + 2*g**4 = 0 for g.
1, 4, 6
Let g(q) = 42*q + 88. Let t be g(-2). Suppose -117*c = -115*c - t. Factor 5/7 + 6/7*o + 1/7*o**c.
(o + 1)*(o + 5)/7
Factor -4/11 + 2/11*u**2 + 2/11*u.
2*(u - 1)*(u + 2)/11
Factor 105*w**2 + 5/4*w**3 + 1615/4*w + 300.
5*(w + 1)*(w + 3)*(w + 80)/4
Let n(a) be the first derivative of -a**5/180 - 7*a**2/2 + a - 122. Let v(o) be the second derivative of n(o). Factor v(x).
-x**2/3
Let r = 5951/7 + -850. Let q(u) be the second derivative of 1/5*u**5 + 0*u**4 + 0*u**3 - r*u**7 - 39*u + 0 + 0*u**2 - 1/3*u**6. Factor q(y).
-2*y**3*(y + 2)*(3*y - 1)
Let b(d) = 9*d + 6. Let l(k) = -4*k - 3. Let q(h) = -3*b(h) - 7*l(h). Let m be q(6). What is z in 3*z - 3*z + 0*z + m*z**2 - 3*z**3 = 0?
0, 3
Let v(s) be the third derivative of s**6/72 + 17*s**5/180 - 5*s**4/18 - 34*s**3/9 - 205*s**2. Factor v(y).
(y - 2)*(y + 2)*(5*y + 17)/3
Suppose -2*x = -4*y - 8, 3*y + 5 = x - 0*y. Factor -2*h**2 + 17*h**2 + 12*h**3 + 5*h - h**5 - 54*h**4 + 56*h**4 - h**x.
-h*(h - 5)*(h + 1)**3
Let b = 168593/3 + -56191. Factor -b + 2/3*t**3 - 26/3*t - 4/3*t**2.
2*(t - 5)*(t + 1)*(t + 2)/3
Let d = -16023 - -16026. Let 18*h + 9/2*h**4 + 3/2*h**d - 33/2*h**2 - 6 - 3/2*h**5 = 0. Calculate h.
-2, 1, 2
Let h = 212072 - 212070. Find a such that 25/4*a - 3 - 1/2*a**h = 0.
1/2, 12
Let j be ((-170)/(-4))/17 - (-2)/4. Let 4*b**j + 12*b**3 + 2*b**3 + 27*b**5 + 48*b**4 + 39*b**4 = 0. Calculate b.
-3, -2/9, 0
Suppose 2685*m - 7524 = 3216. Find n, given that -46/3*n**2 + 0 + 14/3*n**m - 2*n**5 + 26/3*n**3 + 4*n = 0.
-2, 0, 1/3, 1, 3
Find m such that 766/7*m**3 - 78/7*m**4 - 690/7*m**2 + 0 + 0*m + 2/7*m**5 = 0.
0, 1, 15, 23
Let t be (-1)/(-4)*(-15)/((-90)/93). Let f = t + -2. Find n such that 3/4 + 3/8*n**3 + f*n + 3/2*n**2 = 0.
-2, -1
Let r = -156175 + 156177. Factor 2/7*b**3 - 24/7 + 12/7*b**r + 10/7*b.
2*(b - 1)*(b + 3)*(b + 4)/7
Suppose -334 = 8*n - 1806. Solve -79 + 4*r**2 + 0*r**2 + r**2 + 110*r + n = 0 for r.
-21, -1
Let w(f) = 65*f**4 + 168*f**3 - 30*f**2 + 12*f - 6. Let h(a) = -71*a**4 - 168*a**3 + 29*a**2 - 14*a + 7. Let d(t) = 6*h(t) + 7*w(t). Factor d(y).
y**2*(y + 6)*(29*y - 6)
Let x(s) = 10*s - 39. Let m(v) = 5*v - 20. Let u(g) = -5*m(g) + 3*x(g). Let o be u(4). Let 28*t**2 - 13 + 15*t + 6*t - 30*t**o - 7*t + 1 = 0. What is t?
-2/3, 3/5, 1
Let r(n) be the third derivative of -n**6/96 - 7*n**5/24 - 55*n**4/96 + 65*n**3/12 + 101*n**2 + 1. Factor r(x).
-5*(x - 1)*(x + 2)*(x + 13)/4
Let l = -1140/497 - -963975/994. Factor -1/2*u**3 - 87/2*u**2 - 1849/2 - l*u.
-(u + 1)*(u + 43)**2/2
Solve 128 + 58*y**3 + 185*y**5 + 24*y**4 - 144*y - 440*y**5 + 257*y**5 - 68*y**2 = 0 for y.
-8, -4, -2, 1
Let f(h) = 2*h**3 - 98*h**2 + 498*h + 110. Let o be f(6). Find j, given that 6 - 2/5*j**o + 4/5*j = 0.
-3, 5
Let r(w) be the first derivative of -5/6*w**2 + 59 - 4/3*w - 1/9*w**3. Find a such that r(a) = 0.
-4, -1
Let g be ((-4)/30)/(31/(-186)*8)*15. Factor 3/2*c**3 - 3/2 - 3/2*c + g*c**2.
3*(c - 1)*(c + 1)**2/2
Let d(z) be the first derivative of z**5/25 + 27*z**4/20 - 6*z**3 + 2*z**2/5 + 24*z - 7866. Factor d(v).
(v - 2)**2*(v + 1)*(v + 30)/5
Let c(a) be the third derivative of 0 - 1/30*a**6 - 4/3*a**3 + 0*a + 2/15*a**5 + 116*a**2 + 1/6*a**4. Factor c(o).
-4*(o - 2)*(o - 1)*(o + 1)
Let q be (-24)/12*445*2/4. Let i = q - -448. Factor 0 + 0*d + 0*d**2 - 1/5*d**i.
-d**3/5
Let g(s) be the second derivative of -s**6/10 - 3*s**5/20 + 31*s**4/2 + 114*s**3 + 324*s**2 - s - 114. Factor g(v).
-3*(v - 9)*(v + 2)**2*(v + 6)
Let y(c) be the third derivative of -1/270*c**5 + 0*c + 1/540*c**6 - 1/54*c**4 + 0*c**3 + 0 + 4*c**2. Let y(d) = 0. What is d?
-1, 0, 2
Let y(z) = 12*z**2 + 16*z - 30. Let p(d) = d**2 + d - 3. Let q(a) = 12*a**2 - 48*a + 2. Let t be q(4). Let r(m) = t*y(m) - 20*p(m). Solve r(s) = 0.
-3, 0
What is j in 372/11 + 14/11*j**3 - 456/11*j**2 + 670/11*j = 0?
-3/7, 2, 31
Let y(h) be the third derivative of 2/45*h**5 - 1/315*h**7 + h**2 + 1/45*h**6 + 36 - 1/504*h**8 + 0*h**4 + 0*h + 0*h**3. Find j, given that y(j) = 0.
-2, -1, 0, 2
Let g(i) be the third derivative of -i**7/210 + 11*i**6/90 - 4*i**5/5 - 6*i**4 + 10*i**3/3 - 10*i**2. Let j(u) be the first derivative of g(u). Factor j(w).
-4*(w - 6)**2*(w + 1)
Let y(c) be the second derivative of -69*c - 2/3*c**3 + 2/5*c**5 + 4/15*c**6 + 0 - 2/21*c**7 - 4/3*c**4 + 4*c**2. Solve y(u) = 0 for u.
-1, 1, 2
Suppose m - 4*x = -1 + 4, 0 = -x. Suppose -3*t - m*n = 0, -2*t - 4*n = 3*t - 4. Solve 6*d**5 + 4*d**4 - 2*d**t + d**4 + 10*d**3 + 2*d**2 + 11*d**4 = 0.
-1, -1/3, 0
Let k be -1 - 14 - (-420)/308*11. Suppose 9/2*t + 3/2*t**2 + k = 0. Calculate t.
-3, 0
Let m(q) = -q**5 + 10*q**4 + 4*q**3 - 10*q**2 - 3*q + 6. Let r(z) = 2*z**4 + 2*z**2 - z + 2. Let f(v) = -2*m(v) + 6*r(v). Factor f(w).
2*w**2*(w - 4)*(w - 2)*(w + 2)
Suppose 0 = 10*i - 7*i - 336. Suppose 0*r = 4*r + 4*b - 88, -2*r - 4*b + 48 = 0. Factor -200*f**3 + 4*f - r*f + 4*f**3 - i*f**2.
-4*f*(7*f + 2)**2
Let l(n) = -6*n**2 - 19*n + 1. Suppose m + 1 = 4. Let j(v) = -3*v**2 - 9*v. Let i(x) = m*l(x) - 7*j(x). Factor i(p).
3*(p + 1)**2
Suppose -4*n + 63 = 5*f, -6*f + 9*f + 3*n = 39. Let -16*a + 30 - 5*a**2 + 50*a - f*a - 18*a = 0. Calculate a.
-2, 3
Let n = 1299371/35 - 185623/5. Find y such that 2*y**2 - n*y**3 + 18/7 - 30/7*y = 0.
1, 3
Let u(q) be the second derivative of 3*q**5/80 - 143*q**4/16 - 171*q**3 - 2*q - 1223. Factor u(s).
3*s*(s - 152)*(s + 9)/4
Let i = 298999 + -298999. Factor 