 the first derivative of q**3/4 - 2*q**2 + 5*q/4 - 179. Factor f(k).
(k - 5)*(3*k - 1)/4
Let a(w) = w**2 + 3. Let l(y) = -3*y**2 - 3182*y + 2531269. Let s(t) = 4*a(t) + l(t). Factor s(m).
(m - 1591)**2
Suppose -r - 2*k = 2*r - 177, -5*k - 270 = -5*r. Let f be (-4)/30*r/(-38). Factor -4/5*p + 0 - f*p**2.
-p*(p + 4)/5
Let f(v) be the first derivative of -v**7/70 - v**6/20 - v**5/20 + 9*v**2/2 + 4*v + 21. Let x(l) be the second derivative of f(l). Solve x(o) = 0 for o.
-1, 0
Let b be ((-21)/(-7)*1)/454. Let z = 893/2270 + b. Let 0*t**2 - z*t**4 + 0 + 0*t - 2/5*t**3 = 0. Calculate t.
-1, 0
Let u(p) be the first derivative of -p**3 - 87*p**2 - 495*p - 2085. Suppose u(j) = 0. What is j?
-55, -3
Let w = -46 - -30. Let a be (-13)/(-5) - w/40. Factor -5*x**4 - 5*x + 65*x**a + 10*x + 35*x**4 + 12*x**2 + 28*x**2.
5*x*(x + 1)**2*(6*x + 1)
Let n = -46981 + 96305/2. Let g = 1184 - n. Suppose -g*q**2 + 10*q - 2 = 0. Calculate q.
2/5
Let u(n) = 8*n**3 + 103*n**2 + 27*n. Let i(x) = -x**3 - 13*x**2 - 4*x. Let f(w) = -51*i(w) - 6*u(w). Let f(j) = 0. What is j?
-14, -1, 0
Factor 0*z + 0 + 0*z**2 - 51*z**3 - 152/3*z**4 + 1/3*z**5.
z**3*(z - 153)*(z + 1)/3
Let g(n) be the second derivative of -59/48*n**4 - 5*n + 1/2*n**2 - 2/21*n**7 - 127/80*n**5 - 2/3*n**6 + 12 + 1/3*n**3. Determine p, given that g(p) = 0.
-2, -1, -1/4, 1/4
Let x be 6 + 193*5/(-150) - (-6)/10. Let c(v) be the second derivative of 1/15*v**6 - x*v**4 - 1/10*v**5 + 0 + 0*v**2 + 1/3*v**3 - 29*v. Factor c(d).
2*d*(d - 1)**2*(d + 1)
Factor 4056/5 - 2/5*r**3 - 28/5*r**2 + 286/5*r.
-2*(r - 12)*(r + 13)**2/5
Factor -31*i**3 + 12090*i**2 + 12108*i**2 - 16*i**3 + 11*i - 24230*i**2 - 4*i**4.
-i*(i + 1)*(i + 11)*(4*i - 1)
Factor 0 - 1/2*j**3 - 27/2*j**2 - 25*j.
-j*(j + 2)*(j + 25)/2
Let r = -208 - -210. Find v, given that 2*v**4 - 99*v**r + v**4 + 93*v**2 + 3 = 0.
-1, 1
Let i(a) be the first derivative of a**7/28 + 47*a**6/180 + a**5/10 - 2*a**3/3 - 24*a + 89. Let g(p) be the third derivative of i(p). Find m such that g(m) = 0.
-3, -2/15, 0
Let p = -654877/9 + 72765. Factor -2/9*b**2 + 10/9 + p*b.
-2*(b - 5)*(b + 1)/9
Let -101*v + v**4 - 32*v - 52 - 14*v**3 + 189*v + 9*v**2 = 0. Calculate v.
-2, 1, 2, 13
Suppose 29781 = -36*h - 1539. Let k be (-12)/5*h/5481. Solve 8/21*n**4 - k*n**2 + 0 - 10/21*n + 4/7*n**3 - 2/21*n**5 = 0 for n.
-1, 0, 1, 5
Let u be -10*((-126)/(-10) + -13). Let g(z) be the third derivative of 0*z**3 - 1/570*z**5 + 15*z**2 + 0*z + 0 + 1/1140*z**6 + 0*z**u. Factor g(d).
2*d**2*(d - 1)/19
Let p = -69 - -156. Solve 75 + 9*s - p - 3*s - 2*s**2 + 8*s = 0.
1, 6
Let t(d) be the second derivative of -d**6/105 + 3*d**5/14 - 9*d**4/7 - 516*d - 1. Factor t(i).
-2*i**2*(i - 9)*(i - 6)/7
Let r(x) be the third derivative of x**7/5040 - x**5/240 - x**4/24 - 21*x**3/2 - 11*x**2 + 2*x. Let j(q) be the second derivative of r(q). Factor j(v).
(v - 1)*(v + 1)/2
Let -40*s**3 + 5*s**3 - 61*s**3 - 118*s**4 - 121*s**4 + 236*s**4 = 0. What is s?
-32, 0
Solve -3*o**3 - 494*o + 15*o**2 - 499*o + 1480*o - 499*o = 0 for o.
0, 1, 4
Let n(b) be the first derivative of 5/8*b**4 + 25/2*b**3 + 270*b - 62 + 90*b**2. Suppose n(q) = 0. What is q?
-6, -3
Let c = 145 + -565/4. Let x(j) = 3*j - 15. Let s be x(5). Solve -c*a + 3/4*a**2 + s = 0.
0, 5
Let u(g) = 17*g**2 - 11*g + 9. Let z(v) = 3*v**2 - 2*v + 2. Let y = -179 + 146. Let o(w) = y*z(w) + 6*u(w). Suppose o(i) = 0. Calculate i.
-2, 2
Let g(s) = -9399*s + 112790. Let a be g(12). Factor -1/5*z**a - 13/5 + 14/5*z.
-(z - 13)*(z - 1)/5
Find s such that -89*s**3 - 20*s**2 + s**4 - 88*s**3 + 178*s**3 + 1 - 1 = 0.
-5, 0, 4
Let g be (-2)/(-289)*17 + (-32)/(-17). Let m(s) be the second derivative of 0 - 1/2*s**4 + 3/20*s**5 - 1/2*s**3 + 3*s**g - 11*s. Factor m(t).
3*(t - 2)*(t - 1)*(t + 1)
Factor -22/5*t**2 + 73/10*t - 18/5 + 7/10*t**3.
(t - 4)*(t - 1)*(7*t - 9)/10
Let c(n) be the third derivative of n**6/16 - 26*n**5/15 + 143*n**4/12 + 20*n**3/3 - 2*n**2 - 1038*n - 2. Find m such that c(m) = 0.
-2/15, 4, 10
Let l(z) = -15*z**2 + 12*z + 6. Let m be l(-3). Let w = -475/3 - m. Factor 80/3*x - w - 35/3*x**2.
-5*(x - 2)*(7*x - 2)/3
Let h = -46528 + 46530. Let -273*s + 165/2*s**h - 147/2 - 6*s**3 = 0. What is s?
-1/4, 7
Factor -2474*b**2 - 4 + 5546*b**2 + 680*b + 440*b - 108*b.
4*(3*b + 1)*(256*b - 1)
Let d = 6991/1755 - 1328/351. Factor 2 + 11/5*t + d*t**2.
(t + 1)*(t + 10)/5
Let j = 585 + -580. Suppose -j*f = 2*k - 6, -f - 6 = -5*k + 3*k. Find z, given that f + 0*z**2 - 4/9*z**3 + 2/9*z**5 + 0*z - 2/9*z**4 = 0.
-1, 0, 2
Let r(u) be the third derivative of u**7/525 + 17*u**6/200 + 2*u**5/25 - 5*u**4/24 - 10*u**2 + 8*u. Let r(m) = 0. Calculate m.
-25, -1, 0, 1/2
Let q(g) be the second derivative of g**6/18 + 7*g**5/6 - 20*g**4/3 + 125*g**3/9 - 85*g**2/6 - 3409*g. Suppose q(r) = 0. What is r?
-17, 1
Let r = -145/198 - -89/99. Let y(n) be the second derivative of 4/9*n**4 + 0 + 1/45*n**6 + 7*n + 0*n**2 + 4/9*n**3 + r*n**5. Suppose y(x) = 0. Calculate x.
-2, -1, 0
Solve 8 - 19*n**5 + 5040*n**4 - 24*n**3 - 2455*n**4 - 112*n**2 - 2481*n**4 - 17*n**5 + 60*n = 0 for n.
-1, -1/9, 1, 2
Let l(a) = -120*a + 120. Let s be l(1). Let d(v) be the third derivative of 0*v**3 - 1/30*v**6 + s*v + 0*v**5 + 0 - 2*v**2 + 0*v**4. Factor d(p).
-4*p**3
Let r(v) = 26*v**3 - 488*v**2 - 966*v - 6. Let f(a) = -73*a**3 + 1464*a**2 + 2897*a + 17. Let g(y) = 6*f(y) + 17*r(y). Factor g(b).
4*b*(b + 2)*(b + 120)
Let v = -80071 - -1040925/13. Determine q so that 0*q**2 - 10/13*q**4 + 0*q**3 + 0 + v*q**5 + 0*q = 0.
0, 5
Let t be (0 - 3 - 0) + 23 + 2. Let f = t - 20. Suppose z**f - 7*z + 55 - 19 - 5*z = 0. Calculate z.
6
Let z be (-2)/18 - (-84)/27. Factor -216*x**2 - 73/8*x**4 - 3/8*x**5 + 0 - 75*x**z - 64*x.
-x*(x + 8)**3*(3*x + 1)/8
Let v = -3437 + 6907/2. Factor v*y - 63/2 - 1/2*y**3 - 1/2*y**2.
-(y - 3)**2*(y + 7)/2
Let h = -2360 - -3559. Let q be h/(-759) + (-4)/3 - -3. Suppose -q*b**3 + 6/23*b**2 + 8/23*b + 0 = 0. What is b?
-1, 0, 4
Let r(q) be the first derivative of -106/7*q**2 - 1/7*q**4 + 104/7*q + 12 + 16/3*q**3. Factor r(t).
-4*(t - 26)*(t - 1)**2/7
Let a be 1/(2/4 + (-60)/112). Let m = -24 - a. Let -34 + 10 + 3*n**4 + 11*n - 2*n**2 - m*n**2 + 9*n**3 - 47*n = 0. What is n?
-2, -1, 2
Let r = 59 - 56. Let w(y) = -y + 5. Let d be w(r). Let 42 + 5*m - 4*m**3 - 57*m + 32*m**d - 18 = 0. Calculate m.
1, 6
Factor 1/5*c**2 + 6/5*c + 8/5.
(c + 2)*(c + 4)/5
Factor 22/5*c**2 + 7/5*c**3 + 4/5*c - 24/5.
(c + 2)**2*(7*c - 6)/5
Let q(d) = -10*d**4 - 8*d**3 - 23*d**2 + 14*d + 42. Let a(p) = 26*p**4 + 22*p**3 + 68*p**2 - 40*p - 128. Let f(z) = -3*a(z) - 8*q(z). Find b such that f(b) = 0.
-2, 2, 3
Factor 2*o**2 - 34*o**2 + 0*o**2 + 716*o - 6768 + 36*o**2.
4*(o - 9)*(o + 188)
Let h = -24198 - -24201. What is q in -q**2 - 2/3*q + 1/6*q**4 + 5/6 + 2/3*q**h = 0?
-5, -1, 1
Let z(x) be the first derivative of -x**4/2 - 326*x**3/3 - 476*x**2 + 1280*x + 9833. Determine k so that z(k) = 0.
-160, -4, 1
Let a(h) be the first derivative of h**4/32 + h**3/4 - h**2 - 876. Solve a(p) = 0 for p.
-8, 0, 2
Let p(t) be the first derivative of 16*t**6/3 - 144*t**5/5 - 431*t**4/2 - 104*t**3 + 163*t**2 - 48*t + 1383. Let p(m) = 0. Calculate m.
-3, -1, 1/4, 8
Factor 9*b**2 + 29*b**2 + 37*b + 3*b - 140 + 7*b**2 + 10*b**2.
5*(b + 2)*(11*b - 14)
Factor 35/4*z - 1/4*z**2 - 153/2.
-(z - 18)*(z - 17)/4
Let r(o) be the second derivative of -3/2*o**4 - 2 - 12*o**2 - 20/3*o**3 - 58*o - 1/10*o**5. Solve r(g) = 0.
-6, -2, -1
Let i(c) = -6*c**3 + 736*c**2 + 2*c - 796. Let z(w) = 13*w**3 - 1444*w**2 - 3*w + 1594. Let d(p) = 5*i(p) + 2*z(p). Factor d(q).
-4*(q - 198)*(q - 1)*(q + 1)
Let s(p) = 2*p**2 - 236*p - 6158. Let o be s(-22). Solve 10/7*n - 2/7*n**4 - 4/7*n**o + 6/7 - 12/7*n**3 + 2/7*n**5 = 0 for n.
-1, 1, 3
Let k(u) = 2*u**2 - 40*u + 164. Let y be k(8). Let g be 10*((-49)/y)/7. Factor 2*l**3 - 9/2*l**2 + g*l + 0.
l*(l - 1)*(4*l - 5)/2
Let f(l) = -42*l + 590. Let b be f(14). Let z(c) be the second derivative of 1/84*c**4 + 5/42*c**3 + 8*c + 2/7*c**b + 0. Factor z(q).
(q + 1)*(q + 4)/7
Let v(b) be the first derivative of b**3/6 - 5*b**2/4 - 18*b + 609. Solve v(t) = 0.
-4, 9
Let t(y) = -2*y**3 + 32*y**2 - 73*y + 40. Let j(r) = 79 - 218*r + 52 - 7*r**3 + 35 + 97*r**2 - 46. Let a(p) = -3*j(p) + 8*t(p). Determine o so that a(o) = 0.
1, 2, 4
Let h(z) be the sec