t y be -24 + 4053/168 - 70/(-16). Let a(g) be the first derivative of -3/2*g**2 + 3/2*g**6 + 0*g - 24/5*g**5 + 0*g**3 + y*g**4 + 2. Factor a(z).
3*z*(z - 1)**3*(3*z + 1)
Let w(u) be the first derivative of -1/8*u**4 - 143748*u - 3267*u**2 + 139 - 33*u**3. Find o such that w(o) = 0.
-66
Let 12*y**3 + 9*y**4 - 24*y + 106 - 7*y**3 + 4*y**5 + 7*y**2 - 122 + 18*y**3 - 3*y**5 = 0. Calculate y.
-4, -1, 1
Let a be (-4*(-2)/44)/4 + 2879/5758. What is f in -a*f - 36/11 + 6/11*f**2 = 0?
-2, 3
What is x in 55*x**5 - 680*x**3 + 2080*x**2 + 562*x - 570*x - 320 - 17*x**4 - 1352*x - 83*x**4 = 0?
-4, -2/11, 2
Let t(x) be the first derivative of x**5/35 - x**4/28 - x**3/42 + 54*x - 93. Let r(l) be the first derivative of t(l). Suppose r(d) = 0. What is d?
-1/4, 0, 1
Suppose 3*n + 0*n = -3, -4*n + 17 = l. Let m = l - 19. Factor 9 + 33*a - 8*a**2 - 14 - 12*a**m - 13*a.
-5*(2*a - 1)**2
Solve -2/3*x**3 + 4/3*x + 5/9*x**2 + 0 + 1/9*x**4 = 0.
-1, 0, 3, 4
Let h be (-3)/2*(-3)/(81/36). Suppose 55*y - 60*y + 28 = m, -h*m - y = -11. Let 2/5*f**4 + 8/5*f - 24/5*f**2 + 2/5*f**m + 32/5 = 0. What is f?
-4, -1, 2
Let i = -857113/10 - -171437/2. Find d such that -i*d - 38/5 + 2/5*d**2 = 0.
-1, 19
Let n(f) = 4*f**2 + 11*f + 3. Let u(g) be the second derivative of -20*g**3 - 16*g**2 - 11/3*g**4 + 0 - 15*g. Let s(l) = -32*n(l) - 3*u(l). Factor s(c).
4*c*(c + 2)
Let n(u) be the first derivative of -9*u**6 + 486*u**5/5 - 315*u**4 + 700*u**3/3 + 625*u**2 - 1250*u - 1388. Find f, given that n(f) = 0.
-1, 5/3, 5
Let c(z) = z**3 - 28*z**2 - 60*z + 5. Let s be c(30). Let j(v) be the third derivative of 0*v**3 - 1/480*v**s + 1/64*v**4 - 16*v**2 + 0*v + 0. Factor j(w).
-w*(w - 3)/8
Let r(q) be the first derivative of -1/10*q**4 + 0*q - 28/15*q**3 + 3*q**2 + 117. Factor r(i).
-2*i*(i - 1)*(i + 15)/5
Let s be ((-162)/45)/(33/(-110)). Suppose -3*k = s, -5*i - 4*k - 10 = -2*i. Factor -i + 2/5*r**2 + 8/5*r.
2*(r - 1)*(r + 5)/5
Suppose 5*h - 3 = 14*t - 16*t, -2*t + 5*h + 13 = 0. Let p(o) be the second derivative of -1/126*o**t + 0 + 3*o - 5/21*o**2 + 2/21*o**3. What is j in p(j) = 0?
1, 5
Factor 0 + 2/3*v**3 + 2/3*v**2 - 4/3*v.
2*v*(v - 1)*(v + 2)/3
Let f be 16880/88000 + (-4)/22. Let k(n) be the third derivative of -f*n**5 + 2/15*n**3 - 10*n**2 + 0*n + 1/600*n**6 + 0 + 0*n**4. Factor k(d).
(d - 2)**2*(d + 1)/5
Determine m, given that 42/5*m**2 - 2/5*m**4 + 2/5*m**3 - 18*m + 0 = 0.
-5, 0, 3
Let l be ((-1)/(14/4))/((-40)/70). Let v = -120 + 120. Factor l*h**5 - h**4 - 1/2*h + v*h**3 + h**2 + 0.
h*(h - 1)**3*(h + 1)/2
Suppose 117*o = 170*o. Find s, given that o + 3*s - 3/2*s**2 - 3*s**3 + 3/2*s**4 = 0.
-1, 0, 1, 2
Let w be 2/((-4)/3)*(-97196)/141. Determine x, given that 52*x**4 - 128 + 98*x**5 - 10*x**4 + 1171*x - w*x**2 + 370*x**2 - 403*x - 1616*x**3 = 0.
-4, -1, 2/7, 4
Suppose -5538*u = -5527*u - 22. Let s(k) be the third derivative of 1/300*k**5 + 1/60*k**4 + 5*k - 1/100*k**6 + 0*k**3 - k**u + 0. Let s(v) = 0. What is v?
-1/2, 0, 2/3
Suppose -10*l + 56 = -17*l. Let z(t) = 29*t**2 - 292*t - 97. Let x(m) = 9*m**2 - 97*m - 32. Let v(k) = l*x(k) + 3*z(k). Factor v(n).
5*(n - 7)*(3*n + 1)
Determine k so that -48*k**3 - 131917*k**2 + 21*k**4 + 131581*k**2 + 3*k**5 + 0*k**5 = 0.
-7, -4, 0, 4
Let m(x) be the first derivative of x**3/4 + 123*x**2 - 996*x - 6429. Let m(j) = 0. What is j?
-332, 4
Let l(a) = a**2 - 10*a - 125. Let v be l(30). Let c = 478 - v. Determine j, given that -1/3*j**c - 2/3*j + 0 - j**2 = 0.
-2, -1, 0
Let x = -12970 - -12975. Find b, given that 2*b**4 + 0 + 3*b**3 - 4*b + 1/3*b**x - 4/3*b**2 = 0.
-3, -2, 0, 1
Let a(k) = -4*k**2 + 13*k + 9. Let d be (-103 - -20) + (0 - 3). Let j = 88 + d. Let m(v) = -v**2 + 3*v + 2. Let g(x) = j*a(x) - 9*m(x). Factor g(h).
h*(h - 1)
Let n = 14 + 381. Suppose 5 = 5*c, -5*r = 2*c + 3*c - n. Suppose r + 0*u**2 - 2*u**2 + 12*u - 88 = 0. What is u?
1, 5
Let p(w) = -106*w**2 - 32980*w - 7384. Let t(x) = -70*x**2 - 21987*x - 4922. Let o(a) = -17*p(a) + 26*t(a). Determine j so that o(j) = 0.
-611, -2/9
Suppose -25*j + 748 = 19*j. Let z be ((-9877)/(-364))/j - 6/(-39). Suppose 5/4*u**2 + 3/4 + z*u + 1/4*u**3 = 0. What is u?
-3, -1
Let i(c) = -7*c**2 - 6*c + 40. Let l(b) = -17*b**2 - 2 + 3*b**2 + 12 - b + 12*b**2. Let y(v) = -6*i(v) + 22*l(v). Solve y(x) = 0 for x.
2, 5
Let j(o) be the third derivative of -o**7/210 + 19*o**6/120 - 5*o**5/3 + 11*o**4/2 - 1870*o**2. Suppose j(s) = 0. Calculate s.
0, 2, 6, 11
Let -245*v**3 - 1083*v + 11620*v**2 + 7783*v + 843 + 117 = 0. Calculate v.
-2/7, 48
Factor -2/9*a**2 + 244/9 + 242/9*a.
-2*(a - 122)*(a + 1)/9
Let q(b) be the second derivative of 13/6*b**4 - b**5 + 1/15*b**6 + 6 + 36*b**2 + 3*b + 20*b**3. Find k such that q(k) = 0.
-1, 6
Let b be 80/(-200)*22395/(-6). Let f = b + -1493. What is q in f + 0*q + 3/5*q**2 - 3/5*q**3 = 0?
0, 1
Let x be (1/(-20))/((-690)/13800) - 1. Solve 16/5*s - 12/5*s**2 + 12/5*s**4 - 14/5*s**3 - 2/5*s**5 + x = 0.
-1, 0, 1, 2, 4
Let w(i) be the second derivative of -i**5/60 - i**4/18 + 13*i**3/18 - 5*i**2/3 - i. Suppose w(d) = 0. Calculate d.
-5, 1, 2
Let t(d) be the third derivative of d**5/105 - 5*d**4/21 + 2*d**3 - 1094*d**2. Factor t(h).
4*(h - 7)*(h - 3)/7
Let j(x) be the first derivative of x**8/1680 + x**7/420 - x**6/120 + 12*x**3 + x + 197. Let m(r) be the third derivative of j(r). Determine v so that m(v) = 0.
-3, 0, 1
Suppose 0 = q - 20 + 19, -5*q + 5 = 4*x. Let n(g) be the third derivative of x + 18*g**2 - 1/60*g**5 + 1/12*g**4 + 0*g + 1/2*g**3. Factor n(z).
-(z - 3)*(z + 1)
Let x(z) = -z**2 + 47*z - 1097. Let u(l) = 22*l - 548. Let v(y) = -5*u(y) + 2*x(y). Suppose v(r) = 0. What is r?
-21, 13
Let f be ((-75)/(-4))/(-9*(-3)/9). Let o be (-1)/(-5)*(-6 - -4 - -2). What is x in -5/4*x**3 + o - 5*x - f*x**2 = 0?
-4, -1, 0
Let z(s) be the first derivative of -2*s**3/27 + 52*s**2/3 + 632*s/9 + 47. Factor z(n).
-2*(n - 158)*(n + 2)/9
Let q(f) be the second derivative of -3/8*f**2 - 1/16*f**4 - 5/12*f**3 + 0 - 50*f. Factor q(m).
-(m + 3)*(3*m + 1)/4
Let j(n) be the second derivative of n**7/2520 + n**6/180 + n**5/72 + 6*n**3 - 2*n + 3. Let m(v) be the second derivative of j(v). What is s in m(s) = 0?
-5, -1, 0
Let w be (28/16)/((-28210)/(-9920)). Factor -w*y**2 + 8/13 + 2/13*y**3 - 2/13*y.
2*(y - 4)*(y - 1)*(y + 1)/13
Factor 1/4*a**4 - a**3 - 25/4*a**2 + 7*a + 0.
a*(a - 7)*(a - 1)*(a + 4)/4
Let m(p) = 1197 - 2402 + 1204. Let b(x) = x**5 + 0*x**5 + x**3 - 5*x**4 - 3 + 3*x**4. Let h(d) = -b(d) + 3*m(d). What is q in h(q) = 0?
0, 1
Let t be ((-3)/4)/(12 + 594/(-48)). Suppose 558*f - t = 557*f. Find l such that l - 6/5 - 1/5*l**f = 0.
2, 3
Let p(o) = 2*o**2 + 44*o - 18. Let l(c) = 3*c - 11. Let y be l(-4). Let x be p(y). Factor -4*k - 27*k**2 + x*k**2 + k - 6 + 2.
(k - 4)*(k + 1)
Let v(p) = 7*p - 135. Let b be v(25). Solve -u**4 + 24 - 58*u**2 + 1094*u**3 - b*u - 1078*u**3 + 11*u**4 = 0 for u.
-3, -1, 2/5, 2
Let d be 5*1*(6/15)/(-1). Let t be -3 - (-5)/(-2)*d. Let -7*i**2 + 4*i**4 - 2*i - t*i**2 + 4*i**3 + i**2 + 3 + 1 - 2*i**5 = 0. Calculate i.
-1, 1, 2
Let a(h) be the second derivative of h**5/20 - h**4/12 + h**3 - 13*h**2/2 - 256*h. Let p be a(2). Factor -3*r - 12/5*r**2 - 6/5 - 3/5*r**p.
-3*(r + 1)**2*(r + 2)/5
Suppose 1/4*k**2 - 45/4*k - 125/2 = 0. Calculate k.
-5, 50
Let l = -13 + 17. Suppose 30*m**2 - 6 - 14*m - 5*m**l - 18*m**3 + 7*m**4 + 6 = 0. Calculate m.
0, 1, 7
Let g be 0/(-1*(9/3 - 4)). Let p(x) be the third derivative of 11*x**2 + 1/150*x**5 - 1/60*x**4 + 0*x + g + 0*x**3. Factor p(d).
2*d*(d - 1)/5
Let l be (12/39)/((-880)/(-8580)). Determine p so that -3/2*p**2 - 3*p - 1/4*p**l - 2 = 0.
-2
Factor -1/2*m**4 + 105*m + 107/2*m**2 + 0 - 52*m**3.
-m*(m - 2)*(m + 1)*(m + 105)/2
Let l(r) be the second derivative of r**6/10 + 69*r**5/10 + 89*r**4/4 + 22*r**3 - 196*r - 2. Factor l(q).
3*q*(q + 1)**2*(q + 44)
Let z(f) be the second derivative of -464/39*f**3 + 13/10*f**5 + 36/13*f**2 - 72*f + 113/6*f**4 + 0. Factor z(a).
2*(a + 9)*(13*a - 2)**2/13
Let i(p) be the third derivative of p**7/525 + 27*p**6/100 - 83*p**5/50 + 251*p**4/60 - 28*p**3/5 + 7506*p**2. Determine r, given that i(r) = 0.
-84, 1
Let w(y) be the first derivative of -3*y**7/700 - y**6/36 - y**5/25 + y**4/15 + 116*y**3/3 - 76. Let i(p) be the third derivative of w(p). Factor i(q).
-2*(q + 1)*(q + 2)*(9*q - 2)/5
Let